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Summer 1991

Chemical Engineering Education

Volume XXV Number 3 Summer 1991

EDUCATOR
118 Andreas Acrivos, of the City College, City University of
New York,
Sheldon Weinbaum, L. Gary Leal

DEPARTMENT
122 University of Massachusetts

CURRICULUM
126 Inventing Multiloop Control Systems in a Jiffy with
Interactive Graphics,
Alan S. Foss, Peter J. Goodeve
164 An Introduction to Equilibrium Thermodynamics: A
Rational Approach to Its Teaching.
Part 2. Internal Energy, Entropy, and Temperature,
Donald F. Williams, David Glasser

RANDOM THOUGHTS
132 It Goes Without Saying, Richard M. Felder

CLASSROOM
134 A Novel Freshman Class to Introduce ChE Concepts and
Opportunities,
William M. Miller, Mark A. Petrich
140 Errors: A Rich Source of Problems and Examples,
Wallace B. Whiting
150 Chemical Reaction Engineering Applications in Non-
Traditional Technologies: A Textbook Supplement,
Phillip E. Savage, Steven Blaine
158 Development and Use of Open-Ended Problems,
Paul R. Amyotte

LABORATORY
145 Determining the Kinetic Parameters Characteristic of
Microalgal Growth, Ma Eugenie Martinez, Vincente
Bravo, Sebastiin Sdnchez, Emillo Molina

CLASS AND HOME PROBLEMS
154 A Simple Heat of Crystallization Experiment,
Noel de Nevers

131, 142, 156, 163 Book Reviews
163, 153 Books Received

CHEMICAL ENGINEERING EDUCATION (ISSN 0009-2479) is published quarterly by the
Chemical Engineering Division, American Society for Engineering Education and is edited at the
University of Florida. Correspondence regarding editorial matter, circulation, and changes of
address should be sent to CEE, Chemical Engineering Department, University of Florida, Gainesville,
FL 32611. Advertising material may be sent directly to E.O. Pointer Printing Co., PO Box 877,
DeLeon Springs, FL 32130. Copyright 1991 by the Chemical Engineering Division, American
Societyfor Engineering Education. The statements and opinions expressed in this periodical are
those of the writers and not necessarily those of the ChE Division, ASEE, which body assumes no
responsibility for them. Defective copies replaced if notified within 120 days of publication. Write
for information on subscription costs and for back copy costs and availability. POSTMASTER:
Send address changes to CEE, Chem. Engineering Dept., University of Florida, Gainesville, FL
32611.

educator

ANDREAS ACRIVOS

of The City College, City University of New York

SHELDON WEINBAUM, L. GARY LEAL1
City College of CUNY
New York, NY 10031

When Benjamin Levich passed away, New York
State's only Albert Einstein Chair in Applied
Science and Technology became vacant. All of the
State institutions compete vigorously for this presti-
geous chair, so there was little hope for keeping it at
City College unless a candidate of truly unusual
reputation and achievements could be located. That
person was found behind an ever-present black bow
tie: Andreas (Andy) Acrivos, a mentor of mentors.
In addition to holding the Albert Einstein Chair
in Applied Science and Technology at City College,
Andy is editor of The Physics of Fluids, a past chair
of the U.S. National Committee on Theoretical and
Applied Mechanics, director of the Levich Institute
at City College, and a member of the NAE and of the
NAS. Beyond these more visible activities, he has
also played a major leadership role in establishing
fluid mechanics within the AIChE, has helped
broaden the purview of the Fluid Dynamics Division
of the APS, and has ably represented the field in
the larger scientific community. As a result of
his wide-ranging research interests he holds joint
appointments in three departments at City
College-chemical engineering, mechanical engineer-
ing, and physics.
Two of us have undertaken to write this article
since we know Andy from different perspectives-
one as a former student from the early days when he
first came to Stanford University, now a colleague,
and the other as a recent collaborator and colleague
who was instrumental in spiriting him away from
Stanford. We shall each try to impart some of our
personal perceptions.
THE VIEW BEHIND THE SCENES
Many have questioned how Andy could leave the
comfortable and affluent surroundings of a presti-
geous private university such as Stanford to start
SUniversity of California, Santa Barbara, CA 93106

Andy and Jennie with his former advisor,
Neal Amundson

his academic life anew at a school known for eco-
nomically-deprived, hard-working immigrants and
minorities-a school with few frills and where every-
one is a commuter. In fact, one supporting letter for
the Einstein Chair stated, "If you succeed in wooing
Andy to City College, 'mazel tov,'- we have been
trying for ten years without success."
The answer is that we realized that Andy was a
hard-working immigrant himself (born in Greece in
1928; BS, Syracuse University, 1950; PhD, Univer-
sity of Minnesota, 1954; mentor, Neal Amundson)
and that he would probably love the melting-pot ex-
citement, culture, and restaurants that make up
New York; that he would not be intimidated by its
subways and the backways of Harlem. Even more
important, we felt that he would be intrigued by the
challenge of developing an Institute for Physico-
Chemical Hydrodynamics at an institution where
past students include eight Nobel Laureates and
which is often referred to by its alumni as the "Har-
vard of the Proletariat." When one prominent alum-
nus returned recently to give a seminar, he opened
his talk with the remark, "I remember fondly when I
would take the subway up to Harlem from Brooklyn
and then walk up Convent Avenue, but I guess that
is part of the past." Acrivos quickly retorted, "I do
Copyright ChE Division, ASEE 1991
Chemical Engineering Education

TABLE 1
Acrivos' PhD Students Now In Teaching

PhD in i Nam Curmrnt .irflib nur Rank
1959 D. Wilde Stanford University, Professor, Me-
chanical Engineering (retired)
1960 E. Gose University of Illinois. Chicago Circle
Campus. Professor
1961 J.D. Goddard University of California, San Diego
Professor. Chemical Engineering
1963 F.H. Shair California State University, Long
Beach, Dean of Natural Sciences
1964 I.C. Berg University of Washington. Professor,
Chemical Engineering
1967 R.E. Davis Scripps Institute, U.C. San Diego.
Professor, Oceanography
1969 L.G. Leal Univ. ofCalifornia. Santa Barbara.
Professor, Chemical Engineering
1970 C.R. Robertson Stanford University, Professor,
Chemical Engineering
1972 D. Barthes-Biesel Universitl of Compiegne (France).
Professor
1973 W.B. Russel Princeton Liniversity. Professor,
Chemical Enineering
1973 A. Nir Technion. Israel, Professor, Chemical
Engineering
1973 C A. Kossack University ofTrondheim (Norway),
Professor. Petroleum Engineering
1979 F. Gadala-Maria University of SouthCarolina,
Associate Prof., Chemical Engineering
1982 R.H.Davis University of Colorado. Associate
Professor, Chemical Engineering
1982 A. Sangani Syracuse University. Associate
Professor. Chemical Engineering
1985 D.T. Leighton University ol'Notre Dame. Assistant
Professor, Chemical Engineering
1987 E.S.C. Shaqfeh Stanford University, Assistant
Professor, Chemical Engineering
1988 A. Borhan Penns ylvania State University,
Assistant Prof.. Chemical Engineenng

TABLE 2
Acrivos' Students: Presidential Young Investigators
J.F. Bradyv
R.H. Davis
D.T. Leighton
E.S.G. Shaqfeh
G.G. Fuller (Leal's former students
A.P. Cast IRussel's former student
S. Kim IRussel's former student
P Frattini iFuller's formerstudent)
S. Karel IRobertson's former student
H.A. Stone ILeal's former student
D.L. Koch iBroad's former students
N.I. Wagner (Russel's former student
J.J.L. Higdon (former post-doc

that every day, and sometimes at 10 o'clock at night!"
A major concern in recruiting Acrivos was Jen-
nie, who (after thirty-five years of marriage) Andy
still affectionately refers to as his bride Jennie, also
an immigrant (from Cuba), is a prominent physical
chemist with a distinguished career of her own. She
is a regular visitor to the Cavendish Laboratory at
Cambridge University (where she has collaborated
for many years with Sir Nevil Mott), in addition
to being a former Fellow of Trinity College in
Cambridge and a recent recipient of an NSF Visiting
Women's Professorship. She is a professor at Cali-
fornia State University, San Jose, but often divides
her time between that campus and Berkeley since
her campus does not have doctoral students.

Although Andy and Jennie both have demanding
careers, have often had to travel separately, and
have had visiting academic appointments in sepa-
rate places, living between two homes on opposite
coasts would be quite different, and there was some
initial trepidation over the possibility of living apart.
However, the Acrivos' philosophy is to try to main-
tain travel between the best of two worlds and when
working, work hard,... when playing, play hard,...
and in between talk on the phone every night.

It is not so surprising that Andy would be willing
to interrupt a successful career and accept the chal-
lenge and risk of building a new institute at a new
location. Early in his professional life, Andy aban-
doned the established grounds of chemical engineer-
ing at Berkeley and accepted an invitation (from
Dave Mason, then chair) to join a program at Stan-
ford that was just getting off the ground and at-
tempting to establish itself as a teaching and re-
search force in the field. Together he, Michael Bou-
dart (also recently arrived from Berkeley), and his
new colleagues quickly catalyzed Stanford's rapid
rise to one of the top departments in the country.

ANDY-THE TEACHER

While Andy has been a mentor to more than forty
PhD students, even more extraordinary is the fact
that nearly half of them now hold academic appoint-
ments of their own (see Table 1). Many of his stu-
dents, influenced by his high expectations and stan-
dards, are now recognized for their own achieve-
ments. Three of them (A.S. Grove, L.G. Leal, and
R.E. Davis) are members of the NAE or NAS, and
twelve of his former students, or their students, and
one post-doc have been recipients of Presidential
Young Investigator Awards (see Table 2).

Summer 1991

Andy's broad outlook has also rubbed off on many
of his students, and several have developed reputa-
tions quite outside the subject matter of their disser-
tations, e.g., A.S. Grove (semiconductors), R.E. Davis
(oceanography), W.B. Russel colloidss), J.B. Klemp
(atmospheric science), and C.R. Robertson (bioengi-
neering).
Andy's impact as a mentor to his research stu-
dents has already been mentioned. However, his
influence on academic life at Stanford was far more
pervasive than any list of forty PhD students can
indicate. A student's first experience as a new PhD
at Stanford (independent of research and career goals
and the like) was to appear at 8 A.M. on the first day
of class (and three times a week thereafter) to par-
ticipate in Andy's graduate transport course. The
subject matter was mostly asymptotic analysis of
transport problems, largely based on Andy's own
original research papers, but the "gift" carried away
by all students (and enduring long after their as-
ymptotic skills may have become rusty) was the
ability to think clearly, logically, and innovatively.
Of course, this gift was likely to become evident later
rather than sooner in a student's career, so the ma-

TABLE 3
Acrivos' Most Frequently Ciled Papers

1. "On the Steady State Fractionationof Nlulticomponent and
Complex Mixtures in an [deal Cascade: Part 1, Analytic So-
lution of the Equations for General Mixtures.
A. Acrivos, N.R. Amundson, Chemn Eng. Sci., 4, 29 (1955)
2. "Heat and Mass Transfer From Single Spheres in Stokes
Flows,"
A. Acrivos, T.D. Taylor; Phys. Fluids, 5, 387 (1962)
3. "An Experimenlal Investigation ofthe Steady Separated
F lo Past a Circular Cvliner.
A.S. Grove, F. H. Shair, E.E. Petersen, A. Acrivos; J.
Fluid lech.. 19,60 (1964-)
4. "Stead) Flows in RectangularCavlties,"
F. Pan, A. Acrivos: J Fluid AlMch, 28. 643 (1967)
5. "SolitaryInternal \Va es in Dee.p Water,"
R.E. Dax is, A Acrivos; Fluid AMech., 29,593 (1967)
6. "Stokes Flow Past a Particle of Arbitrary Shape: A Numeri-
cal Method of Solution,"
G.K. Youngren, A. Acrivos; J. Fluid Mech., 69,377 (1975)
7. "Deformation and Burst of a Liquid Droplet Freely Sus-
pended in a Linear Shear Field,"
D. Barthes-Biesel, A Acrivos;J. Fluid Mech., 61, 1 (1973)
8. "Enhanced Sedimentation in Settling Tanks with Inclined
Walls,"
E. Herbolzheimer, A. Acrivos;J. Fluid Mech., 92,435
(1979)
9. "Shear-Induced Structure in a Concentrated Suspension of
Solid Spheres,
F. Gadala-Maria, A. Acrivos; of Rheology, 24, 789 (1980)
10. "The Shear-Induced Migration of Particles in Concentrated
Suspensions,"
D. Leighton, A. Acrivos; ]. Fluid Mech., 181, 415 (1987)

Recognition for his scientific achievements
came very early. His first academic appointment
at Berkeley was only eight years long...but
by the time he arrived at Stanford...he
had published his fortieth paper...

jor challenge of the moment was to get to Andy's
class before 8 A.M.-it was impossible to slip unno-
ticed into class at 8:01 A.M.!
Andy has always given one-hundred percent of
himself to his academic endeavors, and he demanded
no less of anyone expecting to receive a PhD from
Stanford. His friendly interest and penetrating in-
quiries extended to all students and all facets of
their research. Most chemical engineering depart-
ments find that seminar attendance is a problem,
but during Andy's years at Stanford this was not the
case. Prior to introductions, he would stand up in
front of the room and make a rapid visual survey of
attendees. Non-attendance by anyone, graduate stu-
dent or faculty member alike, would be noted and
commented upon at their next meeting.
All departments exhibit their own personality,
and in the early days it took only a casual glance to
see Andy's imprint on the Stanford department. His
legacies of quality, absolute integrity, and a lifelong
ability to get somewhere before 8 A.M. are shared by
all those who were fortunate enough to be students
under Andy's influence.

ANDY-THE RESEARCHER
Andy has been the author or coauthor of over 160
full-length journal articles during his thirty-seven
years in academia. He has been one of the most
prolific contributors to the Journal ofFluid Mechan-
ics (45 papers to date), and many of his papers are
viewed as cardinal contributions that initiated new
ideas or approaches to solving problems which have
been widely adopted by later investigators.
Recognition for his scientific achievements came
very early. His first academic appointment at
Berkeley was only eight years long (1954-62) but by
the time he arrived at Stanford in 1962 he had
already published his fortieth paper and was shortly
to receive the A.P. Colburn Award of the AIChE. A
selection of ten of Andy's most frequently cited pa-
pers in given in Table 3.
Andy is widely recognized for his major contribu-
tions to the modern theory of fluid, heat, and mass
transport processes. In his earliest work (begun as a
PhD student with Neal Amundson) he became well-
Chemical Engineering Education

known for his elegant use of advanced mathematical
techniques to analyze the dynamics of separation
processes. Later, beginning about 1960, Andy and
his students became involved with the development
and application of asymptotic analysis to a wide
variety of problems in fluid mechanics, especially
those in heat and mass transfer. This work revolu-
tionized existing understanding of scaling laws and
correlations between dependent and independent
dimensionless parameters in transport systems.
Then came work on internal wave propagation,
the response of heated fluids to Marangoni and
buoyancy driven instabilities, and a long (still con-
tinuing) quest to understand the asymptotic nature
of flows in the limit of high Reynolds numbers. In
more recent years, Andy has done very important
work on suspension mechanics, enhanced gravita-
tional sedimentation, transport processes in suspen-
sions, and low Reynolds number hydrodynamics,
including an extensive series of studies on drop
deformation and breakup (which involves the devel-
opment of new numerical techniques for treating the
non-linear coupling between the droplet shape and
the surrounding flow field). A new effort is the phase
separation of red and while blood cells at microvas-
cular bifurcations and particle entrainment at small
side pores.
The hallmarks of Andy's collected body of re-
search are its breadth, the quality of virtually every
paper to which he has been a contributor, and the
impact that his work has had on other researchers.
Andy had blazed many new trails in breaking artifi-
cial barriers which had previously limited the scope
and range of problems and techniques within fluid
mechanics. The resulting legacy from Andy, and
others like him, can be clearly seen today in the
cross-disciplinary identities of the authors of research
papers in the leading fluid mechanics journals.

ANDY-THE FAMILY MAN AND FRIEND
The examples set by Andy and Jennie, individu-
ally and as partners, were lofty and worthy stan-
dards for emulation, but in certain areas the goals
were impossible to attain. One area was Andy's
mastery of games. In 1947 he placed second in the
U.S. Intercollegiate Chess Championship, losing to
U.S. Grand Master Robert Byrne (currently the New
York Times chess editor). A virtual unknown in chess
circles at the time, Andy's picture was chosen for the
cover of Chess Review and pictures of that champi-
onship game with Byrne still adorn the wall above
his desk. Less obvious was his prowess at bridge, a

game which he claimed not to play but which the
noon-time addicts often persuaded him to join, much
to their chagrin when he would casually pull off a
grand slam.
Andy has always been interested in current prob-
lems of the day, whether they fit into a pre-estab-
lished mold of what he already knows or what his
colleagues deem appropriate for chemical engineers.
This gives his students a chance to play a part on the
"world stage" of fluid mechanics, including the op-
portunity to test their abilities in making a contribu-
tion, even among such exalted company, and thus to

Andy's 60th birthday party with hisformer advisor and
some of his former students.

develop the self-confidence required for a successful
research career.
Many of his former students continue to visit
him at the Institute, where there is a feeling of
family even though there is still no nonsense when it
comes to science. No one is spared from his probing
inquiries or his sometimes disbelieving questions at
a seminar. As a collaborator, there is an unwritten
understanding that nothing will be published until
it is "poifect," even if the galleys have arrived.
It is no accident that Andy has had so many
academic offspring and collaborators since he holds
a continuing interest in his students and their ac-
tivities long after their departure. That interest and
concern is mutual. Recently, many of his former stu-
dents, dispersed around the globe, traveled great
distances to be present at his student-organized 60th
birthday celebration.
As a research advisor, Andy commanded (but
never demanded) respect. He was addressed as
"Professor Acrivos" right up to the day a student
earned his PhD, but was magically "Andy" forever
after that day. 0

Summer 1991

View of the south end of the campus across a campus pond.

)

UNIVERSITY OF MASSACHUSETTS

Chemical engineering at the University of Massa-
chusetts is a vigorous program with a distinc-
tive vision. Traditional strengths are built on within
reaction engineering and separations. At the same
time, we address contemporary opportunities in
areas of polymeric and electronic materials. Mean-
while, we are blending new approaches to macro-
scale design and molecular-scale chemistry with the
power of transport phenomena, creating a new per-
spective on chemical engineering
The University is situated in a picturesque sec-
tion of New England along the Connecticut River
valley. Ninety miles to the east is Boston and the
coast, the Berkshires lie to the west, and New York
City is about a four-hour drive to the south. Al-
though Amherst is a small town with a population of
about 25,000 residents, it has been home to a sur-
prisingly large number of prominent citizens, in-
cluding poets Emily Dickinson and Robert Frost,
lexicographer Noah Webster, and sculptor Daniel
Chester French.
In this scenically and intellectually rich environ-
ment, our department has grown in a relatively brief
time. Between 1951 and 1966, it evolved from a
small undergraduate department to a modest-sized
program offering undergraduate and graduate de-
grees to the MS level. The first PhD degree was
awarded in 1968. Since then, the program has ma-
Copyright ChE Dwision, ASEE 1991

tured into an established teaching and research de-
partment granting about thirty BS, five MS, and
thirteen PhD degrees each year.
The chemical engineering department was be-
gun within the fledgling School of Engineering in
1951 by Ernie Lindsey, formerly of Yale. It was a
small program during its first ten years, with five
faculty, twenty seniors each year, and no graduate
program.
In 1962, John Eldridge accepted the task of forg-
ing a graduate program in chemical engineering
during a time of incredible growth and change in
Amherst. In the ten years between 1960 and 1970,
UMass grew from 8,000 to over 20,000 students. It
was a vital time when everyone was eagerly building
programs, and John's persistence, optimism, and
charm worked wonders for the department. In eight
years he hired eleven new faculty, saw a miniscule
graduate program grow to fifty-five students, and
found new research funds and space.
In 1976, after fourteen years of building a pro-
gram, Eldridge let the reins fall to Leigh Short.
These were difficult economic times for New Eng-
land, however, and Leigh left the university in 1978,
leaving Jim Douglas to serve as interim head for a
year while the search for a new head got under way.
Jim used the opportunity to begin planning activi-
ties that brought new focus and new directions to

Chemical Engineering Education

artment

rIm dep

L

the program. As a result he was appointed head of
the department and remained until 1982 when Bob
Laurence took over. The ten years during which
Douglas and Laurence had responsibility was an-
other period of dramatic growth. It was a period
when research activity grew significantly and new
faculty were taken on board. When Bob decided to
step down, Mike Doherty became head.
Twenty-three years have passed since the first
PhD was awarded. Since then, 132 PhDs have com-
pleted their work in chemical engineering and an
additional 37 PhDs from the Polymer Science and
Engineering Department have been advised and
supported by chemical engineering faculty.
In 1966 the chemical engineering and chemistry
departments played a key role in the creation of a
new program-Polymer Science and Engineering
(PSE), a program of international prominence. The
two departments have close ties, and over the years
there have been many chemical engineering stu-
dents advised by PSE faculty and vice versa.

PHILOSOPHY OF THE DEPARTMENT
The large turnover of faculty during the years
from 1977 to 1986 gave us an opportunity to restruc-

__

Department heads in
(left); Jim Douglas ij
Laurence (below)

ture the department, and after numerous discus-
sions we decided to try some different approaches.
Although the general departmental model at that
time was for each faculty member to be an expert in
a single area, we decided to build groups of three to
five faculty, each with a different viewpoint, who
would work in the same general area. We hoped that
the "creative tensions" encountered in each group
would lead to novel approaches. In addition, our goal
was to get members of the specific areas to engage in
dialogue with members of other groups and in this
way to define significant research problems at the
interfaces between traditional problem areas.
All of us love to learn and love to teach. Hence,
we made a commitment to integrate our research
programs as much as possible with both our under-
graduate and graduate curricula. That is, we would
transfer research results to our undergraduate and
graduate courses as quickly as possible. We would
periodically revise the undergraduate and graduate
courses, and when we had developed enough new
material we would write new textbooks based on our
ideas. The first two books to be written out of this
period were Jim Douglas' book, Conceptual Design of
Chemical Processes, and Julio Ottino's book, The
Kinematics of Mixing: Stretching, Chaos and Trans-
port. Readers familiar with these books
will probably agree that they represent
S rather significant departures from tra-
ditional thinking. Other books are also
currently under way.
We also decided to try to achieve a
better balance between fundamental sci-
ence and process engineering. Thus, we
hoped to develop different approaches
for solving widely recognized practical
problems of importance, such as process
S design, polymer engineering, solids
processing, and
action: John Eldridge andfishy friend mixing problems.
n full highland dress (above); and Bob
who is also the varsity rugby coach. Ths effort would
be balanced by
programs focused
on fundamentals
S .l such as kinetics
and catalysis,
thermodynamics,
fluid mechanics,
etc. Most of the
design research
at that time was
focused on the
computational

Summer 1991

As a statement of commitment to our teaching and
scholarship, the faculty agreed to rotate the
teaching of our undergraduate courses
every three or four years.

problems associated with flowsheeting and optimi-
zation. We decided to focus instead on process syn-
thesis and conceptual design. We expected that a
new approach to conceptual design would provide
better material to teach undergraduates than the
design courses that were taught to most of us.
Traditionally we had strong interaction with the
Polymer Science and Engineering Department, and
several faculty had joint appointments in both de-
partments. We had a strong support base in polymer
chemistry and one of the large and rapidly growing
areas of material science. We could use this support
base to develop a stronger research program in poly-
mer processing operations and the design of flow-
sheets for complete polymer plants. In conjunction
with the Polymer Science and Engineering Depart-
ment we have developed several joint courses at
both the undergraduate and graduate levels. In ad-
dition, we have incorporated polymer components in
many of the traditional chemical engineering courses,
including the undergraduate laboratory which has
an extruder, a blow molder, and a methyl meth-
acrylate polymerization experiment.
When we considered the scales of chemical tech-
nology, which cover the spectrum of scales from mo-
lecular to continuum to unit operations and finally
complete plants, it was clear that we had several
faculty with strong backgrounds in transport phe-
nomena and unit operations. Therefore, we decided
to bring in faculty who would strengthen our chem-
istry expertise in the areas of catalysis, design of
unconventional reactors (ceramic membranes and
magnetically stabilized fluid beds), statistical thermo-
dynamics and adsorption, molecular kinetics and
applications in emerging areas of technology, and
quantum mechanics and applications to materials.
For many years there have been growing com-
plaints that chemical engineering students do not
know enough chemistry. Even a cursory examina-
tion of the curriculum at that time indicated that the
focus was limited to physics and mathematics and
that we had essentially purged chemistry from the
engineering courses. One of our goals became to look
for ways to include some chemistry, as well as a
molecular perspective, in many of the undergradu-
ate courses.
Our research results have led to a complete re-

structuring of the graduate and undergraduate de-
sign courses, as well as our separations course (much
of this course is now focused on the separation of
multicomponent nonideal mixtures). Currently, Jim
Douglas is moving much of the synthesis material
down into the introductory course. The new course is
a major revision of the old industrial chemistry
courses. Instead of memorizing flowsheets, students
are given a set of reactions that produces a product
and are taught how to invent a flowsheet. The inven-
tion of a flowsheet provides a context for studying
phase diagrams, vapor-liquid equilibria, and other
introductory material normally covered in the first
chemical engineering course. Then the students de-
velop the material and energy balances for the flow-
sheets, as well as the raw material costs and the
utilities costs. This approach has the advantage of
solving open-ended problems from the outset, and it
provides a context for the remainder of the curricu-
lum. At the same time, Phil Westmoreland is creat-
ing a senior/graduate-level course on the "Chemistry
of Chemical Engineering." His focus is teaching the
use of modern techniques to estimate and correlate
thermochemistry, kinetics, and physical properties
based on molecular structures. Curt Conner has also
developed a senior/graduate-level elective course,
"Advanced Engineering Solids," which integrates
structure, properties, and manufacturing processes
for a variety of "high-technology" solids.
As a statement of commitment to our teaching
and scholarship, the faculty agreed to rotate the
teaching of our undergraduate courses every three
or four years. This policy has been in existence for
about a decade, and most of our faculty are now
capable of teaching many of the courses in the cur-
riculum, including the undergraduate lab! One of
the great advantages of this policy is that it substan-
tially widens the expertise of the faculty.
There are five major thrusts in the department:
process design and control, polymer engineering,
kinetics and catalysis, transport processes, and ap-
plied theoretical chemistry. Each thrust has several
faculty and graduate student participants and many
faculty have their feet in more than one camp. A
brief discussion of these thrusts follows.

Design and Control
There is a major research effort in the areas of process
design and control involving Mike Doherty, Jim Douglas,
Mike Malone, Ka Ng, and Erik Ydstie. The programs have
close ties with industry, including an Industry/University
Center which was established in 1985. Regular meetings
on campus provide students with an opportunity to meet
industrial sponsors and give updates on recent research
Chemical Engineering Education

results. The Center receives no direct government sup-
port, but contributions from the sponsors supplement and
complement substantial government and industrial re-
search funding of the individual faculty in the general
area of chemical process design and control.
Research results also provide important feedback for
the evolution of the graduate and undergraduate curricu-
lum. New materials are often taught first in short courses
to practicing engineers; more than thirty short courses in
conceptual design and six in distillation systems have
been taught in the last ten years. Some of the material is
then incorporated in course offerings at the university,
throughout the undergraduate program, and in the gradu-
ate process design and control courses.
Polymer Engineering
The department has a long tradition of research and
teaching in polymer engineering that began in the 1960s
with Bob Lenz, Bob Laurence, and Stan Middleman, who
between them covered much territory from polymer syn-
thesis, kinetics, and characterization to polymer diffusion,
reactor engineering, rheology, and polymer processing. The
effort was expanded significantly around 1980 with the
addition of Julio Ottino, Mike Malone, and Henning Win-
ter. They all came with backgrounds in fluid mechanics
(albeit with very different perspectives), and each devel-
oped his own unique niche in the polymer business.
Today we find a wide spectrum of interests in this
field. Molecular-scale phenomena such as molecular orien-
tation are studied in order to understand the behavior of
liquid-crystal polymers and the properties of blends. A
variety of experiments has been designed to probe these
systems, including fluorescence and light-scattering tech-
niques. Polymer processing is studied to find the influence
of the elasticity of the material on the processability and
on the molecular orientation in the flow.
Several projects explore the relationship between trans-
port and morphology in polymer blends, mixed polymer
systems, and copolymers. Research in this area involves
theory, experiments, and novel computer image analysis.
In recent years a novel effort has been initiated to
explore the design and optimization of batch and continu-
ous processes for polymer production. A systems approach
shows interactions of process components, economic trade-
offs, and optimal flowsheet design. For teaching purposes,
this approach has the attraction of identifying design prob-
lems where non-trivial transport effects (velocity gradi-
ents, diffusion, etc.) play dominant roles in the design cal-
culations. For such processes, our old and friendly as-
sumptions like "well mixed" and "plug flow" rarely give
satisfactory results, especially in the finishing operations
of polymer processing.
Reaction Systems
Another large research effort is directed toward a wide
variety of problems involving chemical reactions. Seven
faculty direct approximately twenty graduate students in
problems spanning heterogeneous metal and metal oxide
catalysis, chemical vapor deposition, reaction and separa-

Summer 1991

tion by reactive distillation or with catalytic inorganic
membranes, and multiphase catalysis.
There is a strong element of chemistry in these proj-
ects. Phil Westmoreland and his students measure de-
tailed compositions of steam-cracking products and of free
radicals and stable species within flames; then they inter-
pret the reaction chemistry with reactor models involving

There are five major thrusts in the department:
process design and control, polymer engineering,
kinetics and catalysis, transport processes, and
applied theoretical chemistry...many faculty
have their feet in more than one camp.

200 to 1000 elementary reactions. The observation of phe-
nomena such as steady-state multiplicity and oscillations
and measurement of more conventional kinetic trends
provide the basis for Mike Harold's procedure of kinetic
model development and discrimination for a wide class of
noble-metal-catalyzed oxidation reactions. Together with
Curt Conner, Harold uses Fourier-transform infrared spec-
troscopy to monitor surface species and catalyst structure
during reaction on metal oxide catalysts. Val Haensel
studies molecular rearrangement, fragmentation, and scav-
enging in metal-catalyzed hydrocarbon reactions.
Interactions between reaction and transport processes
are of paramount importance for chemical reactor analy-
sis and design. The common approach used in several of
these projects is the focus at the local level. Conner and
Laurence observe and model reaction and transport dur-
ing olefin polymerization in a fragmenting catalyst pellet.
Harold and Ng are concerned with multiphase transport-
reaction interactions and their impact on performance of
multiphase reactors. Progress towards the development of
a realistic trickle-bed reactor model exploits Ng's focus on
local flow features and Harold's focus on single-pore and
pellet multiphase reaction and diffusion phenomena.
In addition to the polymerization and multiphase re-
actor projects, several new types of reactors are being
developed for use in emerging technologies. Doherty stud-
ies simultaneous reaction and distillation of components
in highly nonideal liquid mixtures. Design and synthesis
schemes are being developed to achieve reaction and sepa-
ration in a single unit. Coupled reaction and separation is
also a motivation for Harold's development of catalytic
ceramic membranes. A new type of catalytic membrane
reactor has been developed which segregates the gas and
liquid streams and thus reduces mass transport limita-
tions for the wide class of volatile-reactant-limited mul-
tiphase reactions. Westmoreland's understanding of plasma
chemistry provides the basis for improved plasma-enhanced
CVD reactors.
Transport Processes
Several research projects focus on problems of fluid
dynamics, rheology, porous material characterization and
mass transport. An underlying theme in these projects is
Continued on page 157.

H curriculum
MR Cur_______

INVENTING MULTILOOP CONTROL

SYSTEMS IN A JIFFY

WITH INTERACTIVE GRAPHICS

ALAN S. Foss, PETER J. GOODEVE
University of California
Berkeley, CA 94720

nventing multiloop control systems isn't easy-
especially multiloop systems for chemical processes.
That's the usual task facing us as chemical engi-
neers; attending to the regulation and coordination
of many variables is what makes the task difficult.
For example, consider being presented with a
challenge to synthesize a control system (and to
demonstrate that it works!) for the little process
shown in Figure 1. The distillation column in this
process is to produce a top product with impurity not
exceeding one percent, and it must do so during pro-
duction rate changes requested by the sales force
and during unexpected appearances of a reaction-
rate inhibitor in the reactant feed to the CSTR. But
that's not all: during such process upsets and pro-
duction-rate changes, the reactor must be guarded
against overflowing and the distillation column must
not be allowed to flood or weep. There are eight
valves and twelve measurements.
What to do?

Exploring new approaches to educating students in
process control systems has been a major activity of
Alan Foss in recent years. These new approaches
are coming to flower now, thirty years into his teaching
career at Berkeley. Prior to his Berkeley years he
practiced engineering with the DuPont Company. He
studied chemical engineering at Worcester Polytech-
nic Institute and the University of Delaware.

Peter Goodeve is a software development engineer
and consultant at UC Berkeley and with other organi-
zations. He received a BSc degree in psychology from -
University College London and an MS in human fac-
tors engineering from UC Berkeley. His particular
computer programming expertise includes real-time
control and the development of efficient user inter-
faces.

FIGURE 1. Diagram of a reaction and separation process
used as a three-week project in control system synthesis
and implementation. (Computer display redrawn to meet pub-
lication quality standards.)

Our undergraduate students need to encounter
this sort of challenge. It serves as a superb exerciser
of their inventive talents-and talents they have. It
is not heresy (is it?) to assert that inventive talents
ought to be exercised somewhere in the curriculum?
Our observation has been that students are just
"itching" for this sort of opportunity after learning
something about control-system concepts.
Two of our students, for example, teamed up at
the tail-end of our process control course and created
the system shown in Figure 2. They reckoned that
they would reduce the demands on the column con-
trol system by holding a reactor conversion reason-
ably constant through adjustments in the residence
time. The column overhead control system employs
an interesting structure that produces a D/V-ratio
as the output of the top product concentration con-
troller. This system also guarded against column

Copyright ChE Division, ASEE 1991

Chemical Engineering Education

flooding or weeping by incorporation of an override
system to hold column differential pressure within
high and low limits. An override feature also keeps
the reactor from overflowing, they say.
In their report, the students said that they also
tried a couple of feedforward links, but did not incor-
porate them into the final system because the links
did not contribute much to the system's perform-
ance. Their report showed scores of system tran-
sients displaying the performance of the controlled
process in the face of production rate changes and
the appearance of the reaction inhibitor.
We have presented this piece of student work
simply to display the capability that is available to
students with this program. We dare not attempt
any deeper explanation of the workings of this team's
control system.
All of the above did not just spring into the stu-
dents' heads as they first sketched out their thoughts
about the system. It took several trials over a period
of two weeks. Trying and testing must therefore be
efficient and speedy.
Time is even tighter in a 3-hour laboratory. There,
students have to develop control systems in tens-of-
minutes, not days. We have attempted to enhance
both efficiency and speed by developing a computer
program that permits a student to develop a dia-
gram of a control system configuration on the screen
of an IBM AT or a PS/2 personal computer. We call

FIGURE 2. Students' control system: Configuration to regu-
late product quality and reactor conversion while guard-
ing against reactor overflow and insuring that column
operation is held within flooding and weeping limits. (Com-
puter display redrawn to meet publication quality standards.)
Summer 1991

In their report, the students said
that they also tried a couple of feedforward
links, but did not incorporate them into the final
system because the links did not contribute
much to the system's performance.

this new program UC SIGNAL. It affords a rapid
means of configuring the signal paths in multiloop
control systems. The control system structure out-
put by the program can be introduced into our real-
time computer control program UC ONLINE and
executed either on simulated processes or on labora-
tory apparatus. The features of UC SIGNAL and its
contribution to process control instruction is the
subject of this paper.

ENHANCING THE PROCESS OF INVENTION
There are two steps in the invention process:
system configuration and testing. An exercise in
configuration only is not satisfactory because the
student will not know whether his system is work-
able or how well it will perform. It is essential that
there be a means to test system workability and that
it be immediately available. The immediate feed-
back of facts about workability and performance is
an essential ingredient in making the invention proc-
ess speedy.

THE CONFIGURATION STEP
We prepare a diagram of the process under con-
sideration, such as the one in Figure 1, and display
it on the computer screen. The diagram corresponds
to a process simulation we have prepared or an
apparatus in our laboratory. Students thus work
directly with a pictorial representation of the proc-
ess. The drawing of control loops is done automati-
cally on the diagram in response to the student's
declarations of the links he wants to make between
measured and manipulated variables and the con-
trol elements he wants to incorporate in those links.
The act of drawing the control-system structure on a
diagram of the physical process (as distinguished
from a conceptual abstraction) focuses the student's
attention on the functionability of the control loops
and the contribution they can make to the workabil-
ity of the process. The visual association of the con-
trol system with the process equipment is an impor-
tant and subtle element in the invention process.
Just how the student arrives at the control-
system structure that he sketches is as varied as the

individuals in the class. Most subject the uncon-
trolled simulation to step inputs through use of our
program UC ONLINE, then observe the behavior of
the several variables and form a cause-effect mental
model. Many of them attempt (after prompting)
"manual" control before settling on their first con-
figuration. Others carry the analysis deeper by fash-
ioning empirical quantitative representations of the
responses, which are then used in a linear-system
analysis and design package (e.g., the program "CC"
by Systems Technology, Inc.) to learn something
about the underlying dynamic characteristics of the
process or parts of it. The relative gain array, if it
can be obtained readily, may be of some assistance
when thinking about proposed configurations. Our
students' decision to use a D/V-ratio in the distilla-
tion overhead system was derived from such an RGA
analysis. (We have a module associated with our dis-
tillation simulation that makes the RGA analysis for
the column effortless.) One can, of course, direct stu-
dents to still other analytical tools if the students
have been prepared for them and if computing capa-
bility is available.

THE TESTING STEP

For control systems as complex as the one illus-
trated in Figure 2, the testing step is essential (at
least for the student, and also for the instructor who
has to be convinced of the workability of some of the
labyrinthine systems). Without a demonstration of
the workability of a control system and an investiga-
tion of its performance, the invention is incomplete.
This step is also essential for even the simplest
control system, because inexperienced designers may
not be able to think through their designs with per-
fect clarity. And the testing capability has to be
immediately available and easily executed; other-
wise reticence to use it will surely build with time as
the designer gets further and further into his system
development.
We feel that it is important that the system used
to implement the control system be interactive, ei-
ther in real time (with laboratory apparatus) or in
scaled time (with process simulations). A system
with such capability allows the student to observe
the evolution of process variables, to debug and com-
mission loops one by one, and to make changes in
process disturbances, setpoints, tuning parameters,
controller status, etc., in real time.
Students in a first course in process control should
not be expected to develop a first-principles model

for a process that is as involved as the one shown in
Figure 1. Most could not do it, and even if they could
the exercise would not be an appropriate use of their
time. A course in process control should be focused
primarily on the systems problems that need to be
solved in carrying out process operations. Therefore,
we prepare the process model for the students. The
models are then immediately available for testing a
control system. They can be (and usually are) non-
linear, they can be "noisy," and they can display
variations in static and dynamic character simply
through changes in throughput rate. Models can be
written in Fortran or C, or even fashioned by using
some of the dynamic elements of our multiloop con-
trol program. Several undergraduate students have
assisted us in developing these models.
The testing phase is accomplished with our inter-
active multiloop control program UC ONLINE."' We
are presently using a considerably enhanced version
of that program.

LITTLE CHALLENGES AND THEIR SEQUENCING

Of course, students cannot jump into a project
such as the one illustrated in Figure 1 without some
preparation. We accomplish this with a sequence of
laboratory projects and homework assignments of
increasing sophistication over the course of the se-
mester. All of our laboratory apparatus can be oper-
ated with any of several objectives in mind and any
of a number of control system configurations.
We start very early in the semester (third week)
by requiring that students use UC ONLINE to ac-
cess measurements of laboratory process variables,

Laboratory Apparatus

Catalytic Chemical Distillation Overhead System Fired Heater
Reactor

Water/Steam Heat Exchanger Two Tanks
FIGURE 3. Simplified diagrams of laboratory apparatus
used for student exercises on multiloop control systems.
Chemical Engineering Education

convert them to engineering units, and display them
in real time on the computer screen. They also con-
nect output signals to valves and make changes in
the flows with keyboard commands for the purpose
of observing the process response to those flows. No
computer programming is involved in any of this.
Simplified diagrams of the apparatus in our labora-
tory used for such exercises are shown in Figure 3.
The students are subsequently introduced to UC
SIGNAL, which they then use for the rest of the
semester to develop control-system diagrams for the
laboratory equipment and process simulations. Dia-
grams of some of our simulated processes are shown
in Figure 4.
The sophistication of the control-system configu-
rations in both activities evolves over the semester,
starting with single feedback loops and moving on to
cascades, feedforward, feedforward-feedback, 2 or 3
loops, gain scheduling, auctioneering, overrides, and
variable structure systems. The experience is just
right to whet their appetites for projects such as the
one in Figure 1.

CAPABILITIES OF UC SIGNAL

UC SIGNAL was designed to aid students in
stating their ideas for a process control system as
quickly as possible. Our intention was to make its
workings as close as possible to what one would
sketch on paper and as free as possible of the endless

Process Simulations

Blender
Production Rate/Inventory

Distillation Reaction and Separation

Autothermal Reactor

Four Filters Distillation Preheat Process
FIGURE 4. Simplified diagrams of simulated processes
used for student exercises on multiloop control systems.

Summer 1991

paraphernalia and multi-volume user's manuals of
the ultimate industrial system. It also had to be
coordinated with UC ONLINE in both its "real-world"
and its simulation modes. That we have done. The
student sees UC SIGNAL working as follows:
1. The Process Diagram
This diagram (constructed by the instructor as
described shortly) is displayed on the screen when
the user loads it from a file. This is accomplished by
making a selection from a pop-up menu; the pro-
gram then prompts for the name of the file. All
measurement transducers and valves are included
in these diagrams. The menu selection is accom-
plished with a mouse-driven screen cursor, and the
name of the file is entered through keyboard input.
When activity is directed to a process simulation,
the names of all measured and manipulated vari-
ables are set identical to those used in the simula-
tion module (a responsibility of the instructor); the
program prohibits the student from changing them.
Nominal values of process variables may also be
read in. When working with "real-world" laboratory
apparatus, the naming of the variables and the des-
ignation of an I/O channel number is at the discre-
tion of the student and may be changed at any time.
The instructor has the option of supplying or not
supplying the parameters needed to convert
transducer signals to engineering units (e.g., milli-
volts to degrees Celsius). So that they know how to
do this, our students have to work these out early in
the semester; we supply the parameters in the later
part of the semester.

2. Making Links
One item in a pop-up menu is named LINK, and
its selection with the mouse (or alternatively, with
the keystroke L) enables the user to link any sensor
with any actuator simply by first pointing to the
sensor (the signal source) and then the actuator (the
signal destination). A line representing the signal is
immediately drawn on the screen without the user
having to specify its route. The line is drawn to avoid
all objects on the screen, with the exception that
crossing of other signal paths and process streams is
permitted. Using the same protocol, links can be
made from an output of a control element (described
shortly) to the input of another, or from any point on
a signal to an input of an element or actuator. If the
automatic signal routing is found inconvenient, the
signal path can be rerouted. The signal can also be
deleted and restored. Such "sketching" sets the skele-
ton of the loops. They have to be "fleshed out," how-
ever, with control elements before the structure can

be considered complete.
3. Inserting Control Elements
Any of a slate of control elements comprising a
PID controller, a summer, a multiplier, a divider,
high- and low-selection operators, a square root, and
a lead-lag element can be selected from a pop-up
menu and inserted at any point in any signal path.
Linking among them can be accomplished in the
manner just described. Elements can be exchanged
with others if, for example, a multiplier was in-
tended instead of a summer. They can be removed
by elision and the signal restored automatically
as it was before the element was inserted. And
elements can be moved to any unoccupied location,
with their signal links relocated automatically. It is
also possible to place elements in "thin air" before
links to them are made. Examples of the results of
these operations are evident in the configuration
shown in Figure 2.
The linking and inserting modes of the program
are the workhorses of the system-configuration op-
eration. The procedures used in these two modes are
about as close as one can come to mimicking the pen
strokes of an engineer as he sketches a system dia-
gram on paper. And they are fast-just what we
have been striving for. The procedures might even
be considered as an advance over the pen-and-paper
method because the signal paths are routed auto-
matically. Most importantly, however, the visual
relationship of control system to process is made
clear-a relationship that can aid the designer in his
system deliberations.
4. Setting Parameters and Interrogating
Element Connectivity
A certain amount of "bookkeeping" has to be at-
tended to before the control system can be consid-
ered operational. Parameters have to be set to con-
vert measurement signals to engineering units, high
and low limits need setting in both controller and
system variables, and controller tuning parameters
and initial valves of controller outputs have to be
set. These tasks can be dispatched easily by entering
numerical values in a pop-up parameter panel for
every controller and system variable. To bring up
the panel, the user simply picks the control element
with the cursor. To help speed this data-input task,
all high and low limits have been set to default
values. The panels for the control elements have a
field for accepting a name from the user. Usually,
only controllers need to be specially named to aid the
user in identifying the function of the controller.
Any control elements not named by the user are

given arbitrary names by the program upon request
or upon output of the configuration to a file.
The assignment of function to the three input
signals of each controller should be checked by the
user before completing the system synthesis. Pop-up
information panels (which are brought to the screen
by pointing to a controller input signal), state whether
that signal is assigned as a measured variable in the
control algorithm or assigned as a setpoint or a guard
variable. Provision is available for interchanging
functions if need be.
5. Saving the Configuration
Complete information about the system (the gra-
phical depiction, control element parameters, and
linkages among the elements) can be saved to a file.
That file can then be read back into UC SIGNAL
again for the purpose of continuing work or to make
modifications in the control system. A full-screen
display of the system is recreated and a printed copy
of the screen may be made at any time. The most im-
portant use of the file, however, is its use in commu-
nicating the control-system structure and content to
UC ONLINE, the multiloop control program that
executes the algorithms of the control elements placed
in the system. All this can be done in a matter of
seconds.
6. Features of the Instructor Mode
The program incorporates facilities to aid the
instructor in constructing diagrams of the labora-
tory apparatus or simulated process. Such facilities
are available only to the instructor. Process dia-
grams can be constructed rapidly through assembly
of a set of prepared symbols and objects, using the
same graphics operations employed in the student
mode of operation. Actuators and sensors can be
placed, named, and "fixed" into position so that they
are unmodifiable by the student. These "diagram"
files that the instructor creates are those that are
presented to the student; the diagrams appear on
the screen when the files are called up by UC SIG-
NAL. Figure 1 is such a diagram.

CLOSING COMMENTS
The thrust of our endeavors in developing UC
SIGNAL and UC ONLINE is to open up opportuni-
ties for students to exercise their creative abilities in
control-system synthesis. Without a facile and un-
fettered means of stating a proposed structure and
without a means for demonstrating the workability
of that structure, there would be little hope of achiev-
ing that goal. We now have those capabilities, and

Chemical Engineering Education

through a carefully-crafted sequence of examples
and encounters with various types of control-system
substructures, one can expect to build in the stu-
dents an expertise in control-system synthesis barely
imagined just a few years ago. When we add to that
the enthusiasm displayed by students in meeting
such challenges, we are confident that we are get-
ting better at this enterprise of engineering educa-
tion.

REFERENCES
1. Foss, A.S., "UC ONLINE: Berkeley's Multiloop Computer
Control Program," Chem. Eng. Ed., 21, 122 (1987) 0

book review

CHEMICAL REACTOR ANALYSIS AND
DESIGN, Second Edition
by G.F. Froment and K.B. Bischoff
John Wiley & Sons, Inc., 1 Wiley Drive,
Somerset, NJ 08875-1271; 664 pages, $59.95 (1990)

Reviewed by
Edmund G. Seebauer
University of Illinois, Urbana

Overall, I found this book to be quite suitable for
a graduate-level course in reactor analysis, but too
advanced for undergraduates. I disagree with the
authors' statement in the Preface to the First Edi-
tion that the book may be used in a less-extensive
treatment as a text for undergraduates. The chap-
ters are not set up to clearly distinguish elementary
from advanced material and there are relatively few
simple, straightforward examples of elementary
concepts that many undergraduates need in order to
grasp the material. The style of writing is quite
formal and compact. The overall level of mathemat-
ics is also too advanced for most undergraduates. In
principle, such students have seen the matrix alge-
bra, vector notation, and differential equations which
are presented in this book. However, I believe that
most undergraduates have little facility with these
concepts, so that the mathematics becomes an im-
pediment rather than a tool for understanding. The
problems at the end of each chapter contain too few
drill problems for simple concepts that undergradu-
ates need in their homework assignments.
However, the above statements should not be
taken as criticisms; the style and content of the text
and problems are quite suitable for graduate stu-
dents. The treatment of important concepts is up-to-

date and very well documented with literature refer-
ences. Numerous summary paragraphs are included.
While it might have been better to set these para-
graphs off from the main body of the text, they are
still quite useful. The table of symbols at the begin-
ning of the book is also helpful. The detailed Table of
Contents and the Author Index are execellent fea-
tures, although the Subject Index is only average.
The treatment of chemical kinetics in Chapter 1
overreached itself in Example 1.4.4 and Section 1.6.
The book does not pretend to be a text in physical
chemistry (and rightly so). Hence, I found the treat-
ment of transition state theory and the Lindemann
mechanism to be so cursory as to be confusing. I
would have mentioned these concepts in passing
with only two or three sentences.
On the whole, however, it is a fine book. O

AN INTRODUCTION TO RHEOLOGY
by H.A. Barnes, J.F. Hutton, and K. Walters
Elsevier Science Publishers B.V., Amsterdam, The Neth-
erlands; $100 hardbound, $65.75 paperback (1989)

Reviewed by
Charles Manke
Wayne State University

In the preface to An Introduction to Rheology, the
authors acknowledge that rheology is a "difficult
subject" and that those seeking an introduction are
often discouraged by the mathematical complexity
of standard textbooks. This new book aims to pro-
vide an understandable introduction to rheology for
newcomers to the field, particularly those without
strong backgrounds in mathematics. The mathemati-
cal content of the book is minimized by a strategic
organization of the subject material that defers con-
sideration of continuum mechanics and constitutive
equations (where mathematical complexity is un-
avoidable) until the final chapter. However, certain
mathematical treatments (such as the tensor repre-
sentation of stresses) are regarded as essential, and
they are used throughout the book. Overall, this
approach is effective, and the authors succeed in
presenting a well-balanced, understandable overview
of rheology without oversimplification or lack of rigor.
The early chapters of the book focus on rheologi-
cal phenomena, with individual chapters devoted to
non-Newtonian viscosity, linear viscoelasticity, nor-
mal stresses, and extensional flow. Here the reader
is introduced to the nature and origins of theological
Continued on page 172.

Summer 1991

Random Thoughts...

IT GOES WITHOUT SAYING

RICHARD M. FIELDER
North Carolina State University
Raleigh, NC 27695-7905

I never liked lectures as a student. Regardless of
the subject or the lecturer I could never keep my
attention from wandering, and even when I thought
I was learning something I usually discovered later
that I really hadn't gotten it. I like lectures even less
as a teacher; I consider myself a pretty good lec-
turer, but the inevitable sea of glazed eyes in class
and the subsequent questions in my office about
things I taught explicitly have convinced me that
I'm not accomplishing that much when I stand up
and talk at students for fifty minutes.
The fact is that what routinely goes on in most
college classes is not teaching and learning, but ste-
nography: professor transcribes notes from notebook
to chalkboard, students transcribe from chalkboard
back to notebook. Even if the notes are supplemented
with all sorts of insightful commentary, research
shows that students in lectures generally retain a
reasonable percentage only of what they hear in the
first ten minutes and relatively little of anything
that happens thereafter. They really only learn by
thinking and doing, not watching and listening. And
so I've been spending a growing amount of my time
lately seeking ways to shift the focus from me to
them during class.
For example, here is an in-class exercise I used in
our second-semester sophomore course on chemical
process analysis, just after we derived the transient
open-system energy balance equation. (The exercise
could equally well be used in the junior transport
course.) I had the class divide themselves into groups
of three at their seats and presented a series of
problems. After I posed a problem I would give the
groups some time to work on it (rarely enough to get
a complete solution, often only enough to get started),
then stop them and either present my solution or
call on one or two of the groups to present as much
as they had gotten. Here's how it went-my ques-
tions and comments to the class are in italics.
SI'm going to ask you several questions about a teakettle
filled with water. In answering them, you'll need the
heat capacity of liquid water (J/g-.C) and the heat of

vaporization (J/g). Take a moment and come up with
round-number estimates of these quantities. (They did,
and we then agreed to use 4 J/g-.C and 2000 J/g in our
calculations.)
OK. Now, suppose we put the kettle on the stove and
crank the burner up to maximum heat. Get me a rough
estimate of the rate of heat input (kW) to the water in
the kettle. Work in your groups-three people talking,
one writing. Go.
Initially there was bafflement, as this was anything
but a well-defined problem. Some groups figured out that
they would have to come up with estimates of how much
water a typical teakettle holds and how long it takes to
bring a full one to a boil, and others just scratched their
heads. I let them go at it for a few minutes, then gave
hints about the required information and let them re-
sume. Then I stopped them and we reached consensus
that a typical kettle holds about three liters or 3000 g of
water, and it takes about five minutes to heat the water
from room temperature (assume 250C) to 1000C, which
translates to a heat input of about 3 kW. (Group estimates
in class ranged from 1.5 to 7 kW, a respectable range.)
So that means I've got to pay the electric company for 3
kW, right? (Wrong! Only a fraction of the heat output
from the burner goes into the water-I'm using
considerably more than 3 kW.)
Where does the additional heat go? (Into the kettle itself,
the stove, and the room air.)
All right-let's agree that our system initially consists of
3 kg of water at 25C and we are adding heat to it at a
constant rate of 3 kW. My plan is to leave the kettle on
the burner until there's no more water left in it. The
next question is, if the system is the water in the kettle,
which system variables change with time? (T and M, the
temperature and mass of the water.)
Take about 30 seconds and sketch plots of T vs. t and M
vs. t.

0 tb 0 tb tf
t(s) t(s)

The class and I agreed that we couldn't be sure with-
out more analysis that the ramps would be straight lines
but that the curves would certainly look something like
those two. I then asked them if they were quite sure that
the M vs. T plot would be horizontal up to tb, and after a
short time it occurred to several of them that pre-boiling
evaporation would lead to a slight decrease in M. We
Chemical Engineering Education

Copyright ChE Division, ASEE 1991

agreed to neglect this effect in our analysis, and then
reached consensus that the mass-time variation would be
described by the transient mass balance
dM
dt = -ri out
-t
and the temperature-time variation by the transient en-
ergy balance equation we had just derived in the last class
dU= Q mout HIout
dt
(input, kinetic and potential energy, and shaft work terms
having been dropped). In these equations riout (g / s) is
the rate of evaporation, U(J) is the total internal energy
of the water in the kettle, and Hfout (J / g) is the speci-
fic enthalpy of the vapor.
In the next series of exercises, the groups concluded or
were led to conclude that the periods before and after
boiling commences must be analyzed separately, and that
for the first phase of the process, (1) rhout = 0, (2) M is
constant, and (3) provided that the heat capacity C, is
constant, U = MCV(T Te). The last result harked back to
material in the stoichiometry course that they had not
seen for months, and we spent a little time reviewing it.
Now use all that to simplify the energy balance.
I expected them to jump immediately to
dUMC dTQ
dt vdt
Instead, I got blank stares, which puzzled me but should
not have. This transition from dU/dt to dT/dt is a trivial
application of the chain rule for differentiation, which I've
used so much I no longer think about it. They had never
seen it outside of last year's calculus class, however, where
it was taught abstractly and didn't mean anything to
them. Once I figured out what was going on (after some
unproductive knee-jerk chastising on the order of "Haven't
any of you seen this stuffbefore?"), I backtracked and gave
them a two-minute calculus refresher that might have
been the most valuable thing they got in the hour. Then
they went back, derived the equation, substituted for MC
and Q, integrated to solve for T(t), and confirmed that it
takes 300 seconds for the water to reach the boiling point.
We then looked at the period t > 300 s. I wrote the
energy balance equation again
dU d (M'i dJ -mItHout +Q
dU = d(M = M = -mout Hout +Q
dt dt \'- dt
SRight?
All of them bought it, but being used to my tricks they
weren't too surprised when I announced "Wrong!" I gave
them a moment to figure out the error, and it finally
occurred to several of them that M is also a variable and
the long-forgotten product rule for differentiation was re-
quired. I then wrote the correct formula:
dU d (M = M d + U dM= -_out Hout + Q
dt dt' I- dt dt
This equation baffled them completely-they had not
previously encountered one with two derivatives in it. I
asked if anyone could figure out how to get rid of one of
them; no one could, so I pointed to the material balance
equation still up on the board and substituted -mout for
Summer 1991

dM/dt to arrive at
M L= -Rhout (Hout ) + Q
dt
It only remained to lead them to the conclusions that
(1) U, the specific internal energy of liquid water at 1000C,
is constant, so that the derivative drops out, and (2) pro-
vided that = ) =

for liquid water at 100C (which I convinced them is the
case by pulling values of UJand H from the steam table),
the final result for the energy balance is the intuitive one
that r
Q = out HH20(v,100oo C HH20 (,0loocj= mout AHv

Thus, we could finally calculate the rate of evaporation as
mout = Q / AHv = [3000 J / s]/[2000 J / g] = 1.5 g / s
and the time for all the water to evaporate as
(3000 g)/(1.5 g/s) = 2000 s = 33.3 minutes. All of the values
on the plots of T vs. t and M vs. t could now be filled in,
which I did. I ended with a short review of everything we
had done.
This exercise covered several important concepts
in a variety of topics, including transient material
and energy balances, thermophysics, thermodynam-
ics, applied calculus and differential equations, and
order-of-magnitude estimation, and showed how to
put the concepts together to analyze a familiar sys-
tem. It took me a little over an hour to get through
it-all of one class period and about a third of the
next one.
Could I have covered the same material in less
time by simply lecturing? Sure, but I don't think the
students would have gotten much out of it. Many
(perhaps most) would have tuned out early in the
lecture; others would have dutifully copied down
whatever I wrote on the board but few would have
understood enough of it to be able to use it on a
slightly different problem. As it was, though, most of
them stayed actively involved throughout the pres-
entation (it's hard to hide in a group of three); they
worried about the problems I wanted them to worry
about, and after trying and sometimes failing to
solve them, listened intently to hear what they should
have done. When I later gave homework problems
that required the use of similar analyses they did
extremely well on them, and they also did much
better on related test questions than I believe a
normally taught class would have done. In short,
they learned the material.
It isn't necessary to do something like this every
class period-in fact, I'm not sure it would be desir-
able or even possible to do that. However, as a break
from the usual straight lecture format, it's worked
well for me every time I've tried it. Check it out for
yourself. 0

Classroom

A NOVEL FRESHMAN CLASS

TO INTRODUCE

CHE CONCEPTS AND OPPORTUNITIES

WILLIAM M. MILLER, MARK A. PETRICH
Northwestern University
Evanston, IL 60208-3120

One goal of this elective class is to attract stu-
dents into our program by introducing them to
the roles that chemical engineers play in a variety of
industries. Our objective is a balanced presentation
of the glamour and the challenges involved. We also
hope to retain the interest of students who have
already selected chemical engineering by allowing
them to take a class in their major at the end of the
freshman, rather than the sophomore, year.
Another goal of perhaps even greater importance
is to provide a perspective for subsequent special-
ized classes. Students will have a better apprecia-
tion for courses such as kinetics and thermodynam-
ics if they see "how it all fits together" at the begin-
ning of their program instead of during the senior
design course.
Outlines from the first two class offerings are
shown in Table 1. The class is taught in 8-hour
modules, with each module emphasizing a particu-
lar industry. Selected processes for each industry
are discussed in detail (for approximately two hours),
and the discussion includes product applications and
demand, raw materials, and key process steps. Tech-
nical and ethical concepts are presented in the con-
text of each process. We were unable to find a text
that takes this approach, so we make extensive use
of handouts (see list of references). Plant visits,
videos, and guest speakers are used to provide a
more complete picture of each industry. Homework
is assigned, and students are quizzed on the mate-
rial in each module. Projects with oral and written
reports allow students to independently investigate
topical problems. About six hours of class time is
allotted for the oral presentations (ten to fifteen
minutes per student).
Copyright ChE Division, ASEE 1991

William M. Miller is an assistant professor of chemi- _
cal engineering at Northwestern University. He re-
ceived his BS from Lehigh University (1973) and his
MS from MIT (1975). After eight years in industry he
obtained his PhD in chemical engineering from the- -
University of California, Berkeley (1987). His research
on mammalian cell regulation in well-characterized
bioreactors has applications in biotechnology and
medicine.

Mark A. Petrich is an assistant professor of chemi-
cal engineering at Northwestern University. He re-
ceived his BS from Washington University (1982)
and his PhD from the University of California,
Berkeley, in 1987. His research interests are in
plasma processing of electronic materials, NMR of
solids, and resource recovery from solid wastes.

The class has been very successful despite the
tight schedule of required classes faced by our fresh-
men engineering students. The first- and second-
year enrollments of 20 and 24 students, respectively,
represented about half of the freshmen who declared
a chemical engineering major. A dramatic increase
in department enrollment over the last two years
cannot be solely attributed to student response to
our class, but that response has been overwhelm-
ingly favorable.
The students especially enjoyed the plant visits
and the term projects-those parts of the class that
are most different from the standard freshman-year
curriculum. An interesting qualitative observation
is that interest in the co-op program seems greater
among students who have taken this class. We are
continuing to offer the class on an annual basis, and
are working to build on our early success.

PROCESS MODULES AND LECTURES
Selected process examples, described in the fol-
lowing paragraphs, illustrate our approach. We made
a conscious effort to incorporate topics from fresh-

Chemical Engineering Education

man chemistry classes and the news media in order
to increase class participation.
As shown in Table 1, we began each class offer-
ing with a module on water and food processing.
This allowed us to introduce processing concepts by
using products familiar to the students. Water puri-
fication is straightforward and easy to comprehend.
The video Always Pure, Never Runs Dry (American
Water Works Association) illustrates the treatment
steps and emphasizes the need for strict quality
control. We discussed the need for water desalina-
tion that results from local imbalances of fresh-
water supply and demand in many parts of the world.
The high cost of desalinated water (in spite of the
free raw material) easily leads to a discussion of
processing costs. Desalination provides a good con-
ceptual example of how separation processes exploit

TABLE 1
Class Outline

Spring 1989
Introduction
Water and Food Processing
Water desalination coffee processing corn processing
(plant visit) cooking and extrusion processes
Health Care and Biotechnology
industrial enzymes fuel alcohol biomedical applica-
Lions penicillin and other pharmaceuticals (plant visit)
Chemical Process Industries and Petroleum
discussion of the life history ofa process plant from in-
ception to commercial production; topics included
process development and design, plant design, construc-
tion. start-up, and manufacturing (refinery visit).
Electronics and Advanced Materials
production of metallurgical-grade silicon microelec-
tronics fabrication engineering polymers advanced
materials for transportation and recreation
Student Project Presentations

Spring 1990
Introduction
Water and Food Processing
water purification (plant visit) and desalination dairy
and oil-based consumer products (plant visit) a corn oil
processing
Monomers and Polymers
petroleum processing and monomer production poly-
mers for "pop" bottles (HDPE and PET) recycling of
plastics polymers for water treatment (plant visit)
Electronics and Inorganic Chemicals
air separation and uses for oxygen and nitrogen safety
considerations in NH, and HNO, production elec-
tronic materials (sand to silicon to circuits) develop-
ing replacements for chlorofluorocarbons
Biotechnology
enzymes and sugar processing antibiotic production
(plant visit) product recovery and purification prin-
ciples and applications of modern biotechnology
Student Project Presentations

Summer 1991

differences between compounds. The most obvious
difference between salt (solid) and water (liquid)
cannot be directly exploited, as it can for separating
sand and water. Other differences between salt and
water lead to a discussion of evaporation, crystalli-
zation, and membrane processes, which provide ex-
amples for simple mass and energy balances. Safety
considerations for human consumption provide the
basis for a discussion of process control requirements
for indirect vs. direct recycling.
Coffee is a familiar product that can be used for
an in-class demonstration of extraction (for the cof-
fee break). It is also a good example of a product that
is sold based on qualitative end-user acceptance,
rather than absolute specifications or performance
in quantitative applications tests.
Separation processes required for the operations
illustrated in Figure 1 include screening, density-
dependent air classification, magnetic removal of
iron, liquid extraction, and drying. The concept of
open-ended design was illustrated by the many ways
in which the process steps can be arranged. The
rationale for selecting the process scheme shown in
Figure 1 was also discussed. Roasting provides an
introduction to poorly-characterized chemical reac-
tions, as well as illustrating the need for tight proc-
ess control to maintain product quality. It also pro-
vides an introduction to forced convective heat trans-
fer and recycling for energy conservation. Finally,
product safety and environmental concerns associ-
ated with methylene chloride were discussed.
Corn oil is another common product that can be
used to illustrate many concepts. Although it is a
premium product, corn oil is present in dried corn at
low levels (about 5%) and is primarily a byproduct of
starch production. The publication Corn Oil, distrib-
uted by the Corn Refiner's Association, provides a
clear discussion of the processing steps involved and
their effects on various aspects of product quality.
The production of crude corn oil was used to illus-
trate grinding, centrifugal separation, oil expression,
and solvent extraction. The latter process was used
to introduce distribution coefficients and solvent se-
lection criteria such as flammability, toxicity, and
volatility. Corn oil refining removes components that

curing sorting remove
and debris blending light decaffeination
hulling removal impurities

pac:agng extractionremove
n & drying o l grinding heavy roasting
impurities

Figure 1. Steps in coffee processing.

adversely affect taste and/or appearance. Refining
steps include degumming (centrifugation of precipi-
tated phospholipids), removal of fatty acids as so-
dium salts, removal of color bodies by adsorption,
winterization (crystallization of waxes), and removal
of odor components using vacuum distillation with
steam stripping. The degumming and winterization
steps are of special interest because the undesirable
properties of phospholipids (gumming in hot water)
and waxes (crystallization in the refrigerator) are
exploited to remove them from the crude oil. Due to
the similarity in many of the operations, corn oil
refining provides a good lead-in to crude oil process-
ing (see below).

The "Monomers and Polymers" module had as its
theme the production and disposal of plastic bever-
age containers. We began with a discussion of crude
oil processing and the production of precursors such
as ethylene and p-xylene. After con-
sidering the reactions used to pro-
duce ethylene glycol and tereph-
thalic acid, we used high-density
polyethylene and polyethylene tere-
phthalate as examples of addition TrLE
and condensation polymers, respec- Oil
tively. The importance of molecular
weight and crystallinity was dis- Out of the Air I
cussed in the context of bottle fabri-
cation. Polymer recycling was used Out of the Air II
to introduce the concepts of resource
recovery and waste minimization. G
Genelic Enginee]
We compared the fuel value of the The Naruie of C
bottles to the energy expended in
their production and discussed prob- Wdys with Coal
lems involved in bottle collection and
segregation by composition. Polyethylene

The penicillin process was used Te C
The Chemical En
to illustrate key steps in product/ and Biotechnol
process development:
Opportunities in
1) discover (natural) or create danced Nlateria
product
2) select organism (catalyst) Opportunities in
ronmenlal Prote
3) optimize process conditions to
maximize productivity
4) modify organism (catalyst) to The New Engine
increase productivity
5) develop separation/purification Always Pure Ne
process Runs Dry
6) iterate on steps 3, 4, and5 to The Rise of a Wo
maximize overall process Drug
efficiency
Portions of a NOVA film ("Rise 'Films c n be rente
of a Wonder Drug") were used to il- from Moder Talk

lustrate the many disciplines required to develop a
commercial process. Key contributions from chemi-
cal engineers in media sterilization, efficient supply
of sterile air, optimization of fermentation parame-
ters, and penicillin recovery and purification were
highlighted. As part of the last item, we discussed
the major contribution of product recovery to the
total product cost, as well as how the multi-step
purification scheme affects the overall penicillin yield.
We discussed the production of electronic-grade

Figure 2. Block diagram of silicon purification.

TABLE 2
Video Tapes (VHS) Used in the Class'

DESCRIPTION PRODUCER (YEAR) TIME

oil and chemical industry

air separations, appli-
cations of N and ,O
manufacture of ammonia,
nitric acid
ring: genetic engineering.
change especially for plants

gineer
og',
Ad-
Is
Envi-
clion

ers

river

under

combustion efficiency ,
alternate fuels, coke
polymerization, applica-
tions of polymers
roles of ChE's in pro-
cessing and purification
roles of ChE's in a
variety of industries
waste-water treatment,
hazardous waste issues,
biodegradation
opportunities in engi-
neering. some ChE
drinking-water treatment

history of penicillin
development

Current Affairs
Multimedia (1990)

18 min

Films for Humanities 20 min
and Sciences (1987)

Films for Humanities
and Sciences (1987)
Monsanto

Films for Humanities
and Sciences (1987)
Films for Humanities
and Sciences (1987)
AIChE (1988)

AJChE (1988)

AIChE (1989)

National Science
Foundation
American Water
Works Association
NOtVA

20 min

16 min

20 min

20 min

10 min

15 min

25 min

27 min

17 min

58 min

d oi brnowed from unireriry film lIbranes. Manm free videos are available
ing Picture Service (5000 Park Street North, St. Petersburg, FL 33709-9989.)

Chemical Engineering Education

silicon from sand in both class offerings. This proc-
ess serves as an introduction to the microelectronics
industry and the problems associated with prepar-
ing ultrapure materials. Solids purification is an
unfamiliar concept to the students, so the purifica-
tion strategy was carefully outlined. The process
(see Figure 2) first converts solid SiO2 to liquid,
metallurgical-grade Si. Liquid silicon is solidified
and reacted with hydrogen and SiC14 to form
Si-containing gaseous molecules (SiHxCl4-x). SiH4
is removed and the remaining SiHxCl4x is converted
to SiH4 and SiC14 in a series of disproportionation
reactor/separators. SiC14 is recycled, and the com-
bined SiH4 stream is thermally cracked to deposit
electronic-grade silicon on a seed crystal. Impurities
are removed in a purge from the fluidized-bed reac-
tor, as well as during replacement of ion exchange
resin in the disproportionation reactors. Methods
of gas/solid contacting were discussed, and fluid-
ization was introduced. Recycle of unused
reactants was emphasized. This process provides
examples of heterogeneous chemical reactor technol-
ogy, as well as many examples of phase-change
operations such as melting, distillation, and chemi-
cal vapor deposition.

GUEST SPEAKERS AND VIDEOS
Three lecturers were used during the first class
offering. Each of them lectured on areas that they
were familiar with, and their expertise was supple-
mented by an industrial speaker on biomedical ap-
plications. Multiple viewpoints are useful for provid-
ing perspective, but it is important to coordinate the

TABLE 3
Plant Visits
Evanston Waler Treatment Plant, E\ mansion, TL
Pumping, water treatment (chlorination and flocculation),
filtration, and quality control
American Maize Corporation, Hammond. IN
Corn iwet mailing for starch recovery. waste treatment, and
staOch packaging operations
Krafl General Foods, Glenview, IL
Pilot plant Dair products, salad dressings. emulsions.
and mixing operations
Abbott Laboratories, North Chicago and Abbott Park. IL
1989. Abbon videoo and general tour ojj frmentation. jor-
mulation, tahleting and killing areas iI ith guides from
public relations. 1990. Tour ol fermentation plant and
fermentation and recover' pilot plants with practicing
engineers
Mobil Oil Corporation, nJliet. IL
Refiner' bus tour and control room visit
Nalco Chemical Company, Chicago. IL
Synthesis and formulation of nater treatment chemi als.
Pilot plant and production folilities

material and the level at which it is presented.
In the second offering there was one primary
lecturer, with guest lectures on two topics. Added
perspective, as well as illustration of laboratory ex-
periments and plant equipment, was provided by
videotapes. Many videotapes are not geared towards
technical audiences, so it is important to screen them
before use. We have compiled a list of useful videos
in Table 2. AIChE career guidance tapes (e.g., "Bio-
technology" and "Advanced Materials") are very good
because they focus on what individual chemical en-
gineers do in various industries. The "Chemistry in
Action" series (distributed by Films for the Humani-
ties and Sciences) focuses on specific process indus-
tries. Two of these videos ("Out of the Air: 1 and 2")
were used as the basis for lectures on air separation,
uses of oxygen and nitrogen, sulfuric acid produc-
tion, and production of ammonia and nitric acid. The
latter topic provided the focus for a discussion of
process safety considerations.

PLANT VISITS
Plant visits provide a sense of the scale of opera-
tions involved, illustrate production processes dis-
cussed in class, and give students a chance to inter-
act with practicing engineers. We visited a variety of
facilities and working environments (see Table 3)
because different students have different interests,
and because we wanted to give a balanced perspec-
tive. In selecting trips, it is important to remember
that freshmen have had limited exposure to the
chemical industry. For example, students are im-
pressed by the size and complexity of a petroleum
refinery, but have a hard time following what
is going on in all of the closed process units. Exami-
nation of flow rates and temperatures on a simu-
lator in the control room helps to bring the process
down to size. Samples that illustrate the conversion
of raw materials (through a variety of inter-
mediates) to final products are especially helpful for
process visualization.
Student benefits from a plant visit can be im-
proved by prior preparation. We recommend dis-
cussing the tour with the prospective host to be sure
that it will meet class needs. In this regard, it is
important to note that freshmen are even more in-
terested in what they would do if they worked at a
particular plant than they are in the various process
steps involved. The learning experience from a tour
can be increased by discussing the process in class
prior to the trip, and by discussing in a quiet location
what will be observed in noisy areas during the

Summer 1991

plant tour. It is also useful to prepare students for
the noises and smells that will be encountered. The
noises and smells of a chemical plant disenchant
some of our students, but others react very posi-
tively to the production environment.
Our most successful visit was one to the Kraft
General Foods Pilot Plant. All of the products (ice
cream, mayonnaise, and oil-free salad dressings) were
familiar to the students. The changes taking place in
each process unit were readily apparent from the
differences between raw material and product
samples, and the process steps were easy to follow
due to the small unit size. Recent engineering gradu-
ates discussed their duties and accomplishments at
selected process units during the tour, as well as at a
subsequent question-and-answer session. Student
enthusiasm during the bus ride back to campus
resulted in questions (which were addressed in a
follow-up lecture) about the differences between batch
and continuous processes and about mayonnaise
manufacture.

STUDENT PROJECTS

Group projects are an important component of
the course. The primary project objective is to have
students analyze a particular topic in depth, includ-
ing technical, societal, and market considerations.
Selection of topical projects increases student inter-
est, and shows them how chemical engineers can
contribute to the solution of current problems. Stu-
dents are not prepared for detailed process design.
However, they can discuss limitations in current
technology, as well as the trade-offs between con-
flicting goals. They can also obtain an appreciation
for the large number of possible solutions to complex
problems. Additional project objectives are to intro-
duce students to the technical library, provide expe-
rience working in groups, and improve oral and writ-
ten communication skills. Group papers were pre-
pared, and all students participated in oral presen-
tations of the group's findings. Feedback was pro-
vided by student and faculty questions and by fac-
ulty critiques. Small prizes were awarded for the
best oral reports, as selected by student balloting.
Project topics for the first year, along with some
of the concerns addressed, are shown in Table 4. The
students had a little trouble getting started on these
open-ended projects, but periodic progress meetings
with faculty helped to provide direction. All of the
students put a lot of effort into the projects, and
many independently found reference material at
other libraries or government agencies. The mate-

rial presented in the written reports exceeded our
expectations. There was some confusion about spe-
cific process steps, but the students showed a good
appreciation for the interaction of technological and
societal concerns. Student projects also provide a
good way to obtain background material for subse-
quent class offerings, For example, lectures in 1990
on polymers for pop bottles and chlorofluorocarbon
replacements were based in part on 1989 student-
project reports and references.
The project theme for the second year was alter-
natives to petroleum for production of energy and
chemical feedstocks. A homework assignment on
petroleum consumption and imports got students
into the library early in the quarter. Each group was
also required to hand in a list of references soon
after project assignments were made. Periodic meet-
ings between each group and the instructor helped
to keep the students from getting lost. To increase
interest in the oral reports, each of the three groups
working on a topic was asked to focus on a particular
aspect of the problem, as indicated in Table 4. As for
the first year, a wide range of organizational, speak-
ing, and writing abilities was demonstrated by the
class, suggesting that additional practice in commu-
nication skills is required.

TABLE 4
Term Project Topics

Spring 1989
Life Support and Environmental Control in Space
requirements of a life-support system
alternative methods for meeting the needs
selection of environmental control system configuration
Polymeric Packaging (Polymers and Pop Bottles)
requirements for food packaging. especially pop bottles
relative ad antages of different packaging materials
PET properties and manufacturing process
recycling and biodegradation
Phasing out Chlorofluorocarbons (CFCs)
Effects of CFCs on ozone degradation
present uses for CFCs; key properties for each use
reduction of CFC emissions
technology required for CFC replacement

Spring 1990
Coal as a Supplement for Petroleum
use ol coal tor electrical energy generation
production ofliquid Fuels from coal
production of chemical feedstock., from coal
Biomass as a Supplement for Petroleum
combustion of naste and trees to general electricity
production of liquid fuels and chemicals from grain
production of liquid fuels and chemicals from waste
Nuclear Power as a Supplement for Petroleum
expanded use of light-water reactors
nuclear waste disposal practices
fusion and fast breeder reactors

Chemical Engineering Education

GRADING

We rejected P/N grading because of concerns that
it would reduce student incentives to complete class
assignments. Grades were based on four 30-minute
quizzes (30%), weekly homework assignments (30%),
and the oral (10%) and written (30%) project reports.
Homework and quizzes included quantitative and
discussion questions. Quiz formulation and grading
is challenging because the students have a wide
range of mathematics and chemistry backgrounds.
An example quiz is shown in Table 5.

ACKNOWLEDGEMENTS

We would like to thank Bernie Wendrow for his
help in teaching the class in the spring of 1989. We
would also like to thank all of the companies listed
in Table 3 that made our plant visits so successful.

REFERENCE MATERIALS

Chemical Process Industries
"Synthetic Ammonia," in Shreve's Chemical Process Industries,
R.N. Shreve and G. T. Austin, McGraw-Hill, New York (1984)

TABLE 5
Quiz: Electronics and Inorganic Chemicals
(Closed Book and Notes)

1. (35) Safety is a major concern in the chemical industry and
for chemical engineers: List three general types of hazards
encountered in chemical processing. For each type of
hazard:
1) give two specific examples of the hazard taken from
processes discussed in class, and
2) briefly describe (in general terms or with a specific
example) one way in which that type of hazard can be
mitigated.
2. (35) Purity is essential in electronic materials.
a) Consider the many steps involved in taking metallurgical
silicon to fabricated electronic components. Briefly
discuss three steps in the process that can lead to con-
tamination or product degradation, and for each note the
type of contamination or degradation involved.
b) Briefly discuss the relative purity requirements of
electronic components as compared to food products.
Recall that refined corn oil contains 98.8% triglycerides.
3. (30) The largest use for CFCs is in refrigeration and air condi-
tioning systems. The physical properties are listed below for
several replacement candidates.
a) Discuss which candidate is the most promising replace-
ment and why.
b) List (with no discussion) three other properties of the
compounds that would have to be considered in selecting
a replacement for CFCs.

Compound
Boiling point at 1 atmosphere (OC)
Boiling point at 10 atmospheres (OC)
Heat of vaporization (kcal/mol)

A B C D E
-30 -30 -30 20 20
20 40 40 60 60
12 6 12 12 6

Speight, J.G., "Petroleum Processing" and "Petroleum Products,"
in McGraw-Hill Encyclopedia of Science and Technology,
McGraw-Hill, New York (1987)
Energy and the Environment
Makhijani, Arjun, A. Bickel, and Annie Makhijani, "Beyond the
Montreal Protocol: Still Working on the Ozone Hole," Technol-
ogy Review, p. 53, May/June (1990)
MacKerron, C.B., "Chemical Firms Search for Ozone-Saving
Compounds," Chem. Eng., p. 22, January 18 (1988)
Stolarski, R.S., "The Antarctic Ozone Hole," Scientific American,
258, 30, January (1988)
Taylor, J.J., "Improved and Safer Nuclear Power," Science, 244,
318(1989)

Health Care and Biotechnology
Gebhart, F., "GEN's 10 Prime Areas for Biotech Commercializa-
tion," Genetic Engineering News, p. 7, January (1990)
Hopwood, D.A., "The Genetic Programming of Industrial Microor-
ganisms," Scientific American, 245, 90, September (1981)
Langlykke, A.F.,"The Engineer and the Biologist," in The History
of Penicillin Production, A.L. Elder, Ed., Chem. Eng. Prog.
Symp. Series No. 100, Ch. 11, p 91 (1970)
Rosen, C.-G., "Biotechnology: It's Time to Scale Up and Commer-
cialize," CHEMTECH, p. 612, October (1987)
Wick, C.B., "Biodegradation Will Play Key Role In Hazardous
Waste Treatment in '90s," Genetic Engineering News, p. 5,
May (1990)

Materials
Pogge, H.B., "Material Aspects of Semiconductors," CHEMTECH,
p. 497, August (1985)
Hart, A.M., B.C. Peters, J.H. Plonka, W.H. Werst, Jr., and J.M.
Macki, "Advanced Ceramic Opportunities: A Review," Chem.
Eng. Progress, p. 32, April (1989)
Larrabee, G.B., "ChE Challenge: Microelectronics," Chemical En-
gineering, p. 51, June (1985)
Dolde, M.E., "Sporting Plastics," CHEMTECH, p. 523, September
(1988)
Thayer, A.M., "Solid Waste Concerns Spur Plastic Recycling Ef-
forts," Chem. and Eng. News, p. 7, January (1989)
Thayer, A.M., "Degradable Plastics Generate Controversy in Solid
Waste Issues," Chem. and Eng. News, p. 7, June (1990)
Voss, D., "Plastics Recycling: New Bottles for Old," Chem Eng.
Progress, p. 67, October (1989)

Water and Food Processing
Cammarn, S.R., T.J. Lange, and G.D. Beckett, "Continuous Flu-
idized-Bed Roasting," Chem. Eng. Progress, p. 40, June (1990)
Giacone, J., and S.J. Sommerfeld, "The Food Industry in the Year
2000," Chem. Eng. Progress, p. 19, May (1988)
"Nutritive Sweeteners from Corn," "Corn Starch," and "Corn Oil,"
booklets available from Corn Refiners Association, 1001 Con-
necticut Ave. NW, Washington, DC 20036

Other Topics and General Sources
Americal Chemical Society pamphlets including "Pesticides,"
"Biotechnology," "Acid Rain," "Ground Water," "Hazardous
Waste," and "Chemical Risk: A Primer." Contact ACS, Dept. of
Gov. Relations and Science Policy, 1155 Sixteenth St. NW,
Washington, DC 20036
AIChE pamphlets "The Expanding Domain of Chemical Engi-
neering" and "Careers in Chemical Engineering," from AIChE,
345 E. 47th St., New York, NY 10017
Travis, C.C., S.A. Richter, E.A.C. Crouch, R. Wilson, and E.D.
Klemma, "Risk and Regulation," CHEMTECH, p. 478 (1987)
Kirk-Othmer Encyclopedia of Chemical Technology, Wiley, New
York(1984) J

Summer 1991

classroom

ERRORS

A Rich Source of Problems and Examples'

WALLACE B. WHITING
West Virginia University
Morgantown, WV26506-6101

Engineering instructors are constantly on the look-
out for new and better problems and examples
to use in homework assignments, lectures, or exami-
nations. Yet a rich source of these problems is gener-
ally overlooked: the numerous errors in textbooks or
published articles, and even our own assignments
and examination questions. Problems developed from
errors simulate real-world situations in which engi-
neers must catch and correct their own and other
people's errors. They can also show students that
real engineering problems are open-ended-not
well-posed mathematical situations that can be solved
simply by plugging new numbers into an old
equation.

WHY USE PEOPLE'S MISTAKES?
Engineers make mistakes. In fact, Petroski'1l
presents a convincing case that errors are the driv-
ing force for engineering advances. Do engineering
students typically confront this idea in school? Would
they be more interested in their courses and would
they more fully comprehend their future profession
if they did?
Many of us try to prepare homework assignments
and examinations that are straightforward: straight-
forward to write, straightforward to do, straightfor-
ward to grade. In fact, one criterion often espoused
for a well-written test question is that the instructor
can anticipate all possible student responses. The

Honest errors appearing
in textbooks, articles, and
instructor-generated assignments
can serve as meaningful vehicles of instruction.

' This material was presented at the 1987 ASEE Annual Confer-
ence. Reference 2 is a more complete version of the paper.

Wallace B. Whiting, P.E., is Associate Professor of
chemical engineering at West Virginia University, where
he has taught for the past decade. He is active in
ASEE and AIChE, and his research and teaching
interests range from thermodynamics to process safety
and process design. He welcomes dialogue on this
and all of his articles. New homework assignments
often grow out of such discussions.

strong bias toward generating questions with as few
conceivable responses as possible can result in a
simple mistake (typographical or otherwise) render-
ing a question "unanswerable." If we uncover such
an error (usually during the grading process), we
apologize to the students (or try to cover up) and
discount the grade for that question. After all, it was
not the students' fault that the instructor posed an
impossible question. We wouldn't want them to think
that engineering problems are sometimes ill-posed,
that they can be frustrating, or that they may not
have an answer. Or would we?
Textbooks and technical articles are full of er-
rors. Some stem from the author's misconceptions
and some are the result of inadequate proofreading.
What happens to students faced with a homework
assignment that (unknown to the course instructor)
has a typographical error making the problem inde-
terminant? After much time and frustration the stu-
dents finally give up, figuring that they will learn
the solution in class. When the class meets, the in-
structor explains that the problem should have in-
cluded an additional piece of information or a differ-
ent equation, and if it had, it could be done in such-
and-such a way. In a blaze of chalk dust, the solution
to a different problem is presented, and the students
dutifully write down this new question and answer.
The same scenario may occur again and again, until
the students are convinced that engineering prob-
lems can only be solved when they are presented in
an error-free and well-posed form.

Copyright ChE Division, ASEE 1991

Chemical Engineering Education

Good engineering textbooks take years to write but most still contain numerous errors,
many of which may be typographical (and presumably will be corrected in subsequent printings)....
Most instructors find that the difficulty is not in finding textbook errors,
but in deciding what to do about them.

One cannot really avoid using errors as a source
of problems and examples. The choice is only how
they will be used and to what end.

SOURCES OF ERRORS

Below are some examples of errors that I have
used. The list is not meant to be exhaustive, it sim-
ply suggests where to look. More details are given
elsewhere.[21
Textbooks
Good engineering textbooks take years to write
but most still contain numerous errors, many of
which may be typographical (and presumably will be
corrected in subsequent printings). To show what
kind of problems occur, I will describe some errors in
first-rate engineering texts that I have used. (In the
interest of the authors, I will not cite the references.)
There are, of course, many other examples of errors.
Most instructors find that the difficulty is not in
finding textbook errors, but in deciding what to do
about them.

Missing Information In one homework prob-
lem that I have used, the conversion of a reactor is
omitted from the problem at the back of a chapter.
Without this specification, the problem is indetermi-
nant-there are more unknowns than the number of
independent linear equations that can be derived to
solve for them. The instructor may assign this prob-
lem, skimming the problem statement and the solu-
tion in the Solutions Manual to be sure that the
problem is of an appropriate difficulty. However, the
Solutions Manual uses an 80% single-pass conver-
sion in the solution, even though this information is
not in the problem statement (and cannot be in-
ferred from the information that is given). When
they attempt this homework problem, students give
up after reaching varying levels of frustration. The
instructor often doesn't notice the printing error until
a student asks a question about it during class as
the instructor is going over the problem.

Corrected Printing Errors Very popular texts
often go through numerous printings and it is not
uncommon for some errors to be eliminated but oth-
ers to be added. An interesting situation can arise
Summer 1991

when the instructor and the students have different
printings of the same edition of the text. I have
found three different versions of a problem in a text
on numerical methods. In one version a printing er-
ror leads to a non-physical numerical answer; subse-
quently, an erroneous correction leads to yet a new
problem. An incorrect assumption is made in the
problem statement, but a footnote attempts to guide
students to a correct solution. An additional mis-
print results in violation of the conservation of mass.
Thus, the misfortune of the authors and the pub-
lisher of this fine textbook increases the richness of
the problem several-fold, exposing the students to
these concepts:
Printers make mistakes
Equations may have to be reformulated if certain
assumptions are not valid
Footnotes are important
Complex or imaginary numbers may be an indication of
errors in problem formulation or computer
programming
Material balances should always be checked
When I used the above problem in class, we ended
up solving four different problems-the three flawed
printed versions and the other "correct" version
(which appears in none of the printings that I saw).
The ensuing discussion of nonlinear equations, fluid
mechanics, and problem-solving techniques lasted
the entire class period and was one of the most
worthwhile sessions of the semester.

Deliberate Errors Some textbook homework
problems incorporate intentional errors. These prob-
lems range from reproductions of newspaper articles
describing impossible processes to mis-specification
of design variables. Students initially see such prob-
lems as "trick questions," but many problems incor-
porating deliberate errors provide ideal vehicles for
teaching content and problem-solving skills.
For example, the "Ice Skating Problem," which
appears in numerous thermodynamics texts, pro-
poses that the pressure under the skate blade is
great enough to lower the melting temperature of
the ice to the ambient temperature. In this case, the
thin layer of water that forms would lubricate the
blade continuously, and this phenomenon would

explain the very low friction that is experienced in
ice skating. One expects students to recognize that
they can use the Clapeyron equation to determine
the pressure required to melt the ice and that they
need to make engineering approximations and as-
sumptions about ambient conditions, skater weight,
and contact between the skate blade and the ice
surface. Overall this is a very good problem, but the
answer given in some thermodynamics texts (and
solution manuals) is wrong. When the problem is
looked at in detail, the melting-point depression is
but one of several factors contributing to the low fric-
tion that makes ice skating such an exhilarating ex-
perience. The students learn that often many differ-
ent factors contribute to phenomena and that the
first one they think of may not be one of the more
significant ones. Perhaps equally important, students
gain confidence in their own abilities when they
think of additional factors, especially if the textbook
ignores them.

Difficult Written Passages Often, technical
writing is dense-difficult both to write and to com-
prehend. One particularly demanding type of writ-
ing is the process description. Even in a first course
in chemical engineering, students are confronted with
process flowsheets consisting of over a dozen units, a
score of streams, and a recycle or two. Our students
must be able to develop a flowsheet from a verbal de-
scription of a process. This is a skill that the stu-
dents will need in their profession, and it is a com-
mon and effective teaching technique.
Many texts and articles include process descrip-
tions. The problem is that the descriptions are often
difficult to read and to comprehend. The numerous
interconnections in the process and the often unfa-
miliar process units often confuse students. They
immediately realize that the description is difficult,
and some even suggest that they could write a bet-
ter, clearer process description.
Although a convoluted written passage may not
properly be called an "error," it demonstrates that
even well-respected authors have limitations. Stu-
dents can learn a great deal about engineering (as
well as about technical writing) by being asked to
decipher dense prose.

Other Books
Engineering students read many books in their
field other than their textbooks (or so we hope), and
the errors in these references can also be a source of
examples and problems. One example is a printing

error in the solution procedure for cubic equations in
the Chemical Engineers' Handbook.'3' I have not used
this particular example in class yet since I feel the
students may become too frustrated when trying to
use the method presented. Instead, I alert the stu-
dents to the error and ask them to correct the equa-
tions in their copy of the handbook. By bringing the
error to their attention and describing the frustra-
tion they might have experienced had they tried to
use the erroneous equations, I hope that they will
learn the importance of verifying printed informa-
tion rather than simply assuming that it is correct.
Articles
Trade Journals Many periodicals of this type
are printed in a hurry and without peer review. As a
result, it does not take long to find articles contain-
ing errors. I am especially fond of an article printed
in Consulting Engineer entitled "Breakthrough! Elec-
tricity Without Fuel."'41 Reactions of engineers to
this article are diverse. Some laugh when they read
the title, realizing that it must be about a perpetual-
motion machine, while others are puzzled by a simple
sketch in the article showing how endless supplies of
electricity can be obtained from the judicious and se-
lective use of gravity.
As a first assignment in my graduate thermody-
namics course, I give the students copies of this
article and ask them to prepare short reports evalu-
ating the process and proposing any improvements
they would like to make. Many students with high
grade-point averages suggest exotic process modifi-
cations backed up by "impressive" calculations. We
spend an entire class period on this article alone,
and the students learn much about the laws of
thermodynamics and their consequences. They also
become more confident in their own ability to think
critically. (Note to the reader: If you get a copy of
this article, please be sure to read the boxed items
on the second page.)
Research Journals Anyone who has ever writ-
ten an article, reviewed one, or read one, can see
that research journals are a bounteous source of
errors.
Other Newspapers and popular magazines of-
ten contain articles describing devices that could not
possibly operate as described or data that are incon-
sistent. In the appropriate course, these can be fine
sources of class problems.
Computer Programs
Most of the effort in writing computer programs

Chemical Engineering Education

is spent finding and correcting errors. Students
quickly realize this during the first assignment. What
they may not realize, however, is that most of their
learning occurs during this debugging process. Some
instructors have suggested that students should be
required to debug each other's programs, but I have
not tried this assignment, yet.
Our Own Assignments!
Instructors, mere mortals that we be, produce an
abundance of flawed homework assignments and ex-
amination questions. While I do not suggest that we
should be less diligent in trying to develop well-
thought-out assignments, I do propose that some of
our better problems may be those that have small,
honest errors that make the problems more realistic
and open-ended. There is, however, great danger in
trying to introduce a trick error. Honest errors are
more realistic, and they are certainly less upsetting
to students.

HOW TO USE ERRORS
Some of the ways that errors can be used have
been mentioned in the foregoing paragraphs. The
following is a brief summary of these approaches
along with some additional techniques. I have found
some of these methods useful; others I have only
thought about using. Although I cannot claim that
any of them are guaranteed to work, I believe that
they can be effective, and I encourage experimenta-
tion with them.
Assignments With the numerous printing and
other errors in even the best textbooks, all of us have
assigned (or soon will assign) a problem containing
an error. Rather than an embarrassment, this is an
opportunity. Instead of trying to minimize the error,
the instructor can use it to explore the subject mat-
ter and help the students learn to ask appropriate
questions. How far can one go in solving the stated
problem? What minimum additional data are needed?
What reasonable assumptions can be made about
the missing parameters? Would it be expensive (or
even feasible) to measure the missing values in a
real situation? How might the solution to the prob-
lem differ for various assumptions about the missing
data? How can errors be identified in the future?
The list goes on and on.
Classroom Examples Using errors can be chal-
lenging (and even intimidating) for both instructors
and students. A good way to introduce this approach
is to use an example in a lecture. In this controlled
situation, students will be less frustrated than they
Summer 1991

would when working on a problem at home. Some
frustration is helpful, however. As in most circum-
stances, but especially when discussing errors, stu-
dents must ask questions during the lecture or they
will neither internalize concepts nor develop a strat-
egy for dealing with errors. The instructor must be
prepared for unexpected questions and be constantly
aware of the students' need for structure and for
meaningful notes from which to study after the class
session is over. The questions that the instructor
might ask, and the directions that the discussion
may take, are similar to those described above under
"Assignments." The difference is that the instructor
has more control in a lecture format and that the
students will encounter less frustration than they
would if tackling the problem alone.

Examination Questions Is it appropriate to
use errors in examination questions? The answer is
yes-maybe. An examination is not the ideal place
to introduce students to errors in problem formula-
tion, but it is a good place to use such problems once
they have been introduced in one of the other ways
described above. Only during an examination can
the instructor be fairly certain that students will
read what they have been asked to read and think
about it.

Projects It is probably impossible to develop a
meaningful project assignment of any scope that
does not contain some errors. And, in fact, this may
be the most appropriate place for students to learn
how to deal with errors. During a project students
have time to think, explore, and try alternative solu-
tion methods. They need to be exposed to the reali-
ties and frustrations caused by engineering errors.
The instructor must avoid formulating unrealistic or
"trick" errors, however, lest the students view them
as existing only in the pseudo-world of academia.
Plenty of errors are inherent in most projects. The
point is to deal with them as honest errors indicative
of the real world of engineering.

DOES THE USE OF ERRORS WORK?
I have no statistically valid or quantitative data
to show that using errors improves the quality of
instruction. I do, however, have anecdotal evidence
that it stimulates students and gives them a new
and more realistic viewpoint of their profession. As
to the effectiveness of this technique, I can only sug-
gest that it is worth a try. I have found it successful.
In any case, errors certainly are a rich and excit-
ing source of problems and examples that can stimu-

late lively classroom discussion. They can also pro-
vide a model of an engineer (the instructor) solving
an ill-defined engineering problem in real time.

CONCLUSIONS
Honest errors appearing in textbooks, articles,
and instructor-generated assignments can serve as
meaningful vehicles of instruction. They demonstrate
that engineering problems are often ill-posed, re-
quiring frequent checks and creative problem-solv-
ing techniques. They thus help to prepare students
for dealing with the many errors that they will
inevitably encounter during their careers.

ACKNOWLEDGEMENT
I would like to thank all those authors whose
errors I have used. The high quality of the texts that
I use make these errors all the more meaningful and
useful. I hope others will feel free to use errors that
they find in my published work as classroom ex-
amples.

REFERENCES
1. Petroski, H., To Engineer Is Human, St. Martin's Press,
New York (1985)
2. Whiting, W.B., "Textbook Errors: A Rich Source of Prob-
lems and Examples," 1987 ASEE Annual Conference Pro-
ceedings, Reno, June 1987, p 1631.
3. Perry, R.H., and C.H. Chilton, Editors, Chemical Engi-
neers'Handbook, 5th ed., McGraw-Hill, New York (1973)
4. Dickens, R., "Breakthrough! Electricity Without Fuel," Con-
sulting Engineer, p. 76, Sept. (1981) O

book review

AN INTRODUCTION TO NUMERICAL
METHODS FOR CHEMICAL ENGINEERS

by J. B. Riggs
Texas Tech University Press, Box 4139, Lubbock,
TX 79409-4139; $45 (cloth) (1988)

Reviewed by
Santosh K. Gupta
Indian Institute of Technology; Kanpur, India

The need for teaching a course in numerical tech-
niques to undergraduate chemical engineers is being
recognized more and more these days, and several
schools have started offering such courses. As a re-
sult, a large number of textbooks have appeared in
the area. However, only a few of them are addressed
primarily to chemical engineering students. The book

by Riggs is thus very timely, and it is an excellent
text. A floppy disc containing several programs is
also included. It can be used to solve problems in the
text as well as being used later.
Chapter 1 of the book gives an introduction to
matrix operations and round-off and trunction er-
rors. Chapter 2 treats algebraic equations, and the
method of LU decomposition for solving linear equa-
tions is of particular importance. Regula falsi and
Newton's method are used for non-linear equations.
The treatment in Chapter 3 of the various finite dif-
ference approximations of the first and second de-
rivatives is good. This is followed by cubic spline
interpolation, as well as quadratures.
Chapter 4 presents techniques for solving initial
value problems (ODE's and PDE's) using both im-
plicit and explicit methods. Several software pack-
ages have been referred to for solving stiff ODE's.
The presentation of finite difference methods as
applied to PDE's in space and time is excellent.
In Chapter 5 the finite difference approximations
are suitably used to obtain the recursion (SOR) rela-
tions for the governing differential equation and for
the boundary points, and these are combined to ef-
fect a numerical solution for a boundary--value prob-
lem. Also, good examples are given on direct meth-
ods using the Thomas algorithm and shooting meth-
ods. The use of a finite element library routine (FEC)
is shown through an example.
Chapter 7 deals with regression analysis of ex-
perimental data. Very useful and common examples
on chemical kinetics are presented and the use of
optimization is shown for non-linear regression.
Chapter 8 discusses how the homotopy method
can be used to find the roots of nonlinear algebraic
equations. This chapter also discusses some more-
advanced examples.
The most fascinating feature of the book is that
several illustrations and problems from various fields
of chemical engineering (mass transfer, kinetics,
thermodynamics, etc.) are discussed. In some cases,
the limitations of the techniques are clearly explained
and the methods to overcome the difficulties are
presented. For example, systems of nonlinear equa-
tions arising out of material balances on a CFSTR
are solved by Newton's method (Chapter 2), but in
the case of extreme non-linearity they are converted
to coupled ODE's constituting an IVP, and these, in
turn, are solved using a powerful algorithm (LSODE)
Continued on page 153.

Chemical Engineering Education

EDITORIAL NOTE:

The following detachable pages describe
some industrial employment opportunities for
graduating chemical engineers. Please post the
information in a conspicuous place for the
benefit of your students, or distribute the pages
to students who may be interested.
These companies have expressed a definite
interest in hiring chemical engineers in the
areas described, and we strongly encourage
students seeking employment to respond as
indicated.

Ray W. Fahien
Editor
Chemical Engineering Education

0 -00 -0

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DOW CHEMICAL USA
University Relations
Box 1713-CH
Midland, MI 48674

GENERAL INFORMATION
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ucts, pharmaceuticals, specialty products and services, and agricultural prod-
ucts. Dow USA has over 2600 chemical engineers working in all functions and
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CITIZENSHIP REQUIREMENTS: Only U.S. citizens, aliens who have a legal right to work and remain
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ENTRY LEVEL OPPORTUNITIES FOR CHEMICAL ENGINEERS

BS/MS1

Functional Area Degree Level Major Hiring Locations

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BS,MS Michigan, Texas, Louisiana, Ohio, California

BS,MS Michigan, Texas, Louisiana, Ohio, California

BS,MS Michigan, Texas, Louisiana, Ohio, California

BS,MS Michigan, Texas, Louisiana, Ohio, California

BS,MS Offices in over thirty major cities

PhD
Fields of Special Interest Tech Center Locations

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Polymer Processing Michigan, Texas, California, Ohio

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Catalysis Michigan, Texas

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College Relations Department, M-260E
P.O. Box 1926
Spartanburg, SC 29304

GENERAL INFORMATION
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home, and industrial markets, as well as specialty chemicals for a wide variety
of applications. The company was founded in 1865 and has nearly 50 plants and
13,000 associates in the US. Milliken is a world leader in quality manufacturing
and was the 1989 winner of the Malcolm Baldridge National Quality Award.
Careers at Milliken involve challenge, innovation, advanced technology,
promotion from within based on individual performance, and extensive education
and training opportunities. Entry level opportunities are available in South
Carolina and Georgia.

CITIZENSHIP REQUIREMENTS: U.S. citizenship or Permanent Resident Visa

REGIONS WHERE BS/MS CAMPUS RECRUITING IS CONDUCTED: Southeastern United States

HOW TO APPLY IF UNABLE TO SCHEDULE CAMPUS INTERVIEW: Send cover letter with functional area
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ENTRY LEVEL OPPORTUNITIES FOR CHEMICAL ENGINEERS

BS/MS I

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operations and in Specialty Chemicals production.
Responsibilities include manufacturing compliance with
customer product quality specifications and process
efficiency/improvement project assignments.

Manufacturing Management: Responsible for the production resources ofpeople and
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AND PLASTICS COMPANY INC.

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~GENERAL INFORMATION
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CITIZENSHIP REQUIREMENTS: U.S. citizens and individuals legally authorized for full-time employment without
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ENTRY LEVEL OPPORTUNITIES FOR CHEMICAL ENGINEERS

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BSMS FunctionalArea Degree Level Major Hiring Locations
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ns, LA; Houston and Victoria, TX;
WV

,WV; Tarrytown, NY

e

Fields of Special Interest
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Tech Center Locations
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ADDITIONAL INFORMATION
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^1111101111^ -r1

laboratory )

DETERMINING THE

KINETIC PARAMETERS CHARACTERISTIC

OF MICROALGAL GROWTH

MARTINEZ SANCHO, MAE.,
BRAVO RODRIGUEZ, V.,
SANCHEZ VILLASCLARAS, S.,
MOLINA GRIMA, E.
Universidad de Granada
Jaen, Spain

Due to the importance of biotechnology in today's
world, the subject "biochemical engineering" has
now been introduced into almost all syllabi for chemi-
cal engineering studies. It is therefore a worthwhile
endeavor to increase the number of practical ses-
sions pertinent to this discipline in chemical engi-
neering laboratories.
Of particular interest in the study of the kinetics
of microorganism growth is the situation where a
nutrient, administered to the culture medium at a
constant rate, limits growth. This may occur when
restrictions are imposed by nutrient gases or by the
light energy source in the case of photosynthetic
cultures. In the former case, the transfer rate of the
nutrient must be taken into consideration and in the
latter the reduction of light intensity in the culture
must be considered.
The basic aim of this practical session is to en-

able students to study experimentally the kinetics of
growth in the unicellular algae Chlorella pyrenoidosa
cultures under light-restricted conditions.

BASES

When unicellular algae grow under low light in-
tensities, a linear relationship is observed between
the specific growth rate, p, and the light intensity, I.
At high values of light intensity the specific rate,
however, becomes constant. The most usual kinetic
models for reproducing this variability are
Hyberbolic Model by Tamiya et al.'11

= aI (1)
gm + al
Exponential Model
S=1 m[1 -exp(-I/I)] (2)

The high extinction coefficients of microalgae in
suspension determine a considerable reduction in
light intensity according to the depth of the growth
chamber. Moreover, if the cultures are developed

Ma Eugenia Martinez is professor of biochemical en-
gineering at Granada University, where she has been
since 1975. Her principal areas of research are the
cultivation of microalgae, ethanolic fermentation, and
mass transfer.

Vicente Bravo is professor of chemical engineering
at the University of Granada, where he has been
since 1974. His research interests are in the areas
of ethanolic fermentation, enzyme technology, and
flue-gas desulfurization.

Copyright C
Summer 1991

Sebastidn Sanchez is professor of chemical engi-
neering at the University of Granada. He has been a
member of the chemical engineering department in
the Faculty of Experimental Sciences in Jaen since
1982. His research interests are in the areas of culti-
vation of microalgae, ethanolic fermentation, and gas
absorption with chemical reaction.

Emilio Molina is professor of chemical engineering at
the University of Granada. He has been a member of
the chemical engineering department in the Faculty of
Experimental Sciences (Almeria) since 1973. His re-
search interests include mass transfer, the refining of
edible oils, and the cultivation of microalgae.
'hE Division, ASEE 1991

Byfollowing the variation in the biomass concentration with time
in an autotrophic culture of Chlorella pyrenoidosa with no limitations imposed
by nutrients or CO,, we ask that students obtain a growth curve for the algae, identify the
exponential and linear growth phases, and calculate the parameters which characterize both phases.

discontinuously using artificial light, even though
the incident light intensity is constant, then the
intensity within the suspension varies according to
position and time.
Since the specific growth rate is an average value
for the whole culture, the spatial variation of the
light intensity determines that the relationship be-
tween the average growth rate and the distribution
of the light may be expressed as follows12"

:f f(I)-dV
=V c (3 )
Vc
or
S= (Im) (4)
where
Im fffI d (5)
V,
depending on the adaptation rate of the cells to the
changing light intensities and the degree of mixing
within the culture medium.
EXPERIMENTS
By following the variation in the biomass concen-
tration with time in an autotrophic culture of
Chlorella pyrenoidosa with no limitations imposed
by nutrients or CO we ask that students obtain a
growth curve for the algae, identify the exponential
and linear growth phases, and calculate the parame-
ters which characterize both phases.
The overall interpretation of the results obtained
by the students, using different incident light
intensities, allows each of the two distinct kinetic
models to be distinguished and their parameters to
be obtained.
The integration of the kinetic model based on the
two extreme situations possible for the distribution
of light (Eq. 3 or 4) and its comparison with experi-
mental results, concentration-time, would allow a
quantitative difference to be established between
the two situations.

MATERIALS REQUIRED
The cultures are developed with equipment as
shown in Figure 1.131 Air is pumped in by a compres-
sor (1), through a hydrophobic cotton filter (2), a sta-
bilizing column (3) and a flow gauge, and passes into

the tank (5) where the air is humidified and mixed
with CO, from the bottle (6).
By means of a gas distributor (8), the gaseous
mixture (which is prepared in 5% CO2 [v/v]) bubbles
in the culture medium in the growth vessels. Filters
by valves (13) are inserted into the three branches of
the distributor.
The culture vessels (9), placed on magnetic stir-
rers (14), are three cylindrical containers with a
capacity of one litre, covered by a jacket for the
circulation of thermostatically-controlled water
(10,11,12). These vessels have a glass top with two
openings, one in the center for the bubbbler and the
other on one side for the loading of the culture (which

FIGURE 1. Experimental installation.

Chemical Engineering Education

TABLE 1
Microorganism: Chlorella pyrenoidosa'
Culture medium: A pH: 6.5 Temperature: 30C
Air-CO,: 0.5 v/v/min (5% CO2 v/v)
1o: 740 lux
t,h C, g-L-' t,h C, g-L-
0.00 0.0078 79.25 0.2246
7.75 0.0122 94.25 0.3103
22.25 0.0253 103.25 0.3593
31.25 0.0359 118.75 0.4606
48.25 0.0833 127.75 0.5031
55.25 0.1123 151.75' 0.6272
70.25 0.1804 166.25 0.7432
SData obtained'] with Chlorella pyrenoidosa. Chick 8H Emerson, from
the collection held at the School of Botany in Cambridge which was
provided by the Maime Ferrdn Institute of the Sciernce Research Cuun-
cil. The culture medium used is medium A, as proposed b) Rodriguez.
L6pez "'

must be previously sterilized by filtration with 0.2
gm nitrate cellulose filters), for the measurement
and control of pH, and for the collection of samples.
The equipment is sterlized in an autoclave before
carrying out the experiment.
Two Westinghouse PLANT-GRO fluorescent light
tubes (Mod. F. 40 w) (15), placed on a mobile panel
(16), provide the light. The light intensity, measured
with a luxometer, may be varied by altering the

0 50 100 150 200

FIGURE 2. Variation of biomass concentration vs. time
(semilogarithmic coordinates).

0 LIi
0 50 100 150 200
FIGURE 3.. Variation of biomass concentration vs. time
(linear coordinates).

distance between the lamps and the growth vessels,
or by introducing black metal meshes with different
apertures.

PROCEDURE AND EXPERIMENTAL CONDITIONS
1. Preculture of the cells in a mineral medium solidified
with 2% agar for four days before performing the
practical session, under continuous lighting and at room
temperature.
2. Sterilize the material.
3. Place the culture vessels in the equipment and adjust
the light intensity desired within the range 200-2000
lux.
4. Prepare the culture medium, adjust the pH to 6.5,
sterilize and add 500 cc to each of the culture vessels.
5. Adjust the temperature to 30C.
6. Resuspend the preculture cells. Measure the
concentration and calculate the volume to be inoculated
so that each experiment is performed with an initial
concentration of 0.008 gL- expressed in dry weight.
Inoculate.
7. Adjust the composition and flow rate of the gaseous
mixture added in the proportion of 0.5 v/v/min.
8. Collect samples throughout the experiments.

ANALYTICAL TECHNIQUE

The cellular concentration (g dry biomass).L-1 is
determined indirectly after suitable dilution through
the absorbance of the cell suspension measured at
600 nm. To convert absorbance to concentration, the
calibration line valid up to A60, < 0.5 is used,

C(g') = 0.49 A600

2
r = 0.999

which has been obtained by measuring the absor-
bances of the suspensions of determined concentra-
tion after centrifugation, washing, and dessication
at 1050C until a constant weight is achieved.
This correlation has previously been obtained
with the microorganism and the culture medium
specified in Table 1, and is valid for the experimen-
tal conditions to be used in the practical session.

RESULTS AND DISCUSSION
Interpretation of Individual Results

As an example, the biomass concentration at dif-
ferent culture times is shown in Table 1 in an experi-
ment performed under the conditions indicated. The
representation of the experimental data in semi-
logarithmic and linear coordinates (Figures 2 and 3)
demonstrates graphically the exponential growth
phase (the straight line in Figure 2) and the linear
growth phase (the straight line in Figure 3).

Summer 1991

By integrating the biomass balance during the
exponential growth phase, in which p is constant
and with the initial condition that at t = 0, C = C (as
no appreciable lag phase is observed, then the fol-
lowing is obtained:
en(C / Co)= max t (7)

From the slope of this line, the maximum specific
growth rate in h-1 may be calculated.
The integration of the biomass balance during
the linear growth phase, in which
S- C = constant = P (8)
leads to
C=P.t+b (9)
where b represents an integration constant. This
equation provides P in gL -h-1.
Overall Interpretation of the Results
The maximum specific growth rates during the
exponential phase and the growth rates during the
linear phase in experiments performed at seven
different incident light intensities are recorded in
Table 2. The graph representing these parameters
in linear coordinates vs. the incident light intensity
shows the experimental variation obtained (Figures
4 and 5).
The specific rate during the exponential growth
phase seems to vary linearly with Io up to approxi-
mately 1000 lux, and a saturation effect is observed
thereafter.
The adjustment of pairs of values gma-I, to the
kinetic models is carried out through the least squares
method to the linearized form of the hyperbolic model
by Tamiya,
1 1 1 (10)
lmax --m O Io
and through non-linear regression to the exponen-

TABLE 2'
Microorganism: Chlorella pyrenoidosa
Culture medium: A pH: 6.5 Temperature: 30C
Air-COZ: 0.5 v/v/min (50b CO, v/v)
I, lux _...h' P.g-L'-h'
252 0.0205 0.00241
494 0.0427 0.00348
740 0.0478 0.00577
1128 0.0727 0.0101
1194 0.0777 0.0118
1688 0.0837 0.0139
2410 0.0891 0.0184
'Data from [31.

tial model (Eq. 2).
The model which best reproduces the experimen-
tal variation may be selected by using the minimum
from the accumulative sum of the squares of the
residues as a criteria. For data collected in Table 2,
the exponential model provides the optimum adjust-
ment when the following values are used for the
parameters
um = 0.099 h- and Is = 926 lux
The linear variation P-I0 confirms the light limi-
tation in the linear growth phase. The adjustment of
these values allows the prediction of growth rate
during this phase for any value of incident light

20-

I, .1o-' u

FIGURE 4 Variation of specific growth rate vs. light
intensity.

V. /l/h

30 C

0, 10- .l
0 1 2 3
FIGURE 5. Variation of growth rate during linear phase
vs. light intensity

Chemical Engineering Education

intensity. In this case the relationship is
P = 8.45 106 ,, (11)
For integration of the most appropriate kinetic
model, in respect of the extreme situations for light
distribution, the point-by-point variation of the light
intensity in the culture vessel must be known a
priori. The difficulty in establishing this variation in
a cylindrical vessel illuminated from the front leads
to the need for an analogy with a parallelepipedic
vesselE51 in which the point-by-point (I[x]) and aver-
age (Im) light intensities may be calculated by means
of

I(x) = Io exp(-kaCx)

Im = [1-exp(-kaLC)]
Im:kaLC[1

(12)

(13)

where k is the extinction coefficient with a value
of 2.42 Lg-1cm-1, and L is the equivalent length of the
culture chamber in centimeters.
Inclusion of Eq. (12) into Eq. (2) provides the
solution to the integral of Eq. (3), and results in

SI= 1- exp(-kaLC)]

I- 4Im [- exp(-2kaLC)]
Is 4kLC

+ I [m 1-exp(-3kaLC)] +... (14)
Is 18kLC

O.Ok2 i I t.I
0 50 100 150 200
FIGURE 6. Variation of biomass concentration vs. time
(= experimental values; - Eq. ( 3), L = 4.5 cm;
Eq. (4), L = 5 cm).
Summer 1991

which provides the average specific growth rate as a
function of the concentration when cell growth adapts
to the point-by-point light intensity which the micro-
algae receive.

Furthermore, inclusion of Eq. (13) into Eq. (2)
leads to

= ,m 1- exp(-I [1- exp(-kaLC)])/(kaLCI)}
(15)
which allows the calculation of the average specific
growth rate when the cells adapt to an average value
of light intensity.
In both situations, the numerical integration of
the biomass balance
1 dC (16)
C dt
through Eqs. (14) or (15) will allow the prediction of
the variation in biomass concentration in time. This
calculation has been carried out for both situations,
modifying the value of the equivalent length until a
satisfactory reproduction of the experimental results
is obtained. Figure 6 shows this adjustment with a
value of L = 4.5 cm, for the situation described by
Eq. (3) and for the situation corresponding to Eq. (4)
with a value of L = 5 cm.
The almost negligible difference between both
values for L clearly shows the difficulty involved in
distinguishing between the two situations. In a pre-
vious study,[61 however, using a different procedure,
the value of L was found to range from 5.1 to 7.1 cm,
which would seem to indicate that cellular growth
adapts to average light intensities. This adaptation
was proved in another study by altering the stirring
rates.E[5

REFERENCES
1. Tamiya, H., E. Hase, K. Shibata, A. Mituya, T. Iwamura,
T. Nihei, and T. Sasa, "Kinetics of Growth of Chlorella,
with Special Reference to its Dependence on Quantity of
Available Light and on Temperature," in Agal Culture
from Laboratory to Pilot Plant, J.S. Burlew, Carnegie Inst.
Publ. 600, p. 204 (1953)
2. Fredrickson, A.G., and H.M. Tsuchiya, "Microbial Kinet-
ics and Dynamics," in Chemical Reactor Theory:A Review,
S. Lapidus, N.R,. Amundson, Prentice-Hall, p. 405 (1977)
3. Camacho Rubio, F., and Martinez Sancho, MaE.,An. Quim.,
79, p. 265 (1983)
4. Rodriguez L6pez, M., Nature, 203, p. 666 (1964)
5. Camacho Rubio, F., Padial Vico, A., and Martinez Sancho,
MaE., An. Quim., 78, p. 371 (1982)
6. Martinez Sancho, MaE., "Influencia de la Intensidad de
Iluminaci6n en el Crecimiento de Chlorella pyrenoidosa,"
PhD Thesis, Granada University (1980) O

classroom

CHEMICAL REACTION ENGINEERING

APPLICATIONS IN

NON-TRADITIONAL TECHNOLOGIES

A Textbook Supplement

PHILLIP E. SAVAGE, STEVEN BLAINE
University of Michigan
Ann Arbor, MI 48109-2136

Recent years have witnessed an expansion of
chemical engineering activity in areas such as
materials processing (e.g., microelectronics, super-
conductors, composites) and biotechnology. This
expansion has been accompanied by a reduction in
chemical engineering opportunities in the more tra-
ditional areas of petroleum processing and commod-
ity chemicals.
These events have led to much introspection in
the chemical engineering community. One effect on
education has been a new and widely-recognized
need to broaden the technological base of under-
graduate education. Students must be exposed to
chemical engineering applications in the frontier
areas in addition to continued exposure to applica-
tions in traditional petroleum processing and petro-
chemical applications.
One approach to providing the necessary expo-
sure is to develop elective courses dealing with spe-
cific technologies (e.g., biochemical technology, mi-
croelectronics processing, polymer processing). A sec-
Phillip Savage is an assistant professor of ChE at the
University of Michigan. He received his BS from Penn
State and his MChE and PhD degrees from the Uni-
versity of Delaware. His research interests are in re-
action pathways, kinetics, and mechanisms.

Steven Blaine received a BSChE from the University
of Florida in 1986 and a MSE in chemical engineering
from the University of Michigan in 1988. Currently, he
is a candidate for the PhD in chemical engineering at
the University of Michigan
150

ond approach is to incorporate examples dealing with
non-traditional technologies in each of the core un-
dergraduate courses. This second approach has the
advantage of more easily integrating the new tech-
nologies with fundamental principles and obviating
the need to find additional room in an already
crowded curriculum.
A barrier to weaving examples from new tech-
nologies into existing courses, however, is that most
chemical engineering textbooks, though good at pre-
senting fundamental principles, generally do not
provide examples and applications from non-
traditional technologies. Thus, the instructor is forced
to identify and develop such examples on his own. In
some cases the problem has been recognized and
steps have been taken to provide instructors with
useful materials. A good example is the book Chemi-
cal Engineering Education in a Changing Environ-
ment"1 which provides the proceedings of a confer-
ence sponsored jointly by the Engineering Founda-
tion, the National Science Foundation, and the Ameri-
can Institute of Chemical Engineers. It presents a
large number of problems that deal with non-
traditional technologies, along with their solutions.
The problems are intended for use as examples in
lectures or as homework assignments. Another ex-
ample is a set of articles on microelectronics process-
ing that recently appeared in Chemical Engineering
Education.'2-61
This paper describes a set of educational materi-
als that we have developed which deal with chemical
engineering applications in "emerging" technologies.
These materials take the form of a textbook supple-
ment. Our goal was to develop materials for use in a
chemical reaction engineering course. Thus, we se-
lected examples from microelectronics processing and
Copyright ChE Division, ASEE 1991
Chemical Engineering Education

A barrier to weaving examples from new technologies into existing courses... is that most chemical
engineering textbooks, though good at presentingfundamental principles, generally do not
provide examples and applications from non-traditional technologies. Thus, the
instructor is forced to identify and develop such examples on his own.

biochemical technology that illustrate key concepts
in kinetics and reaction engineering. Here we will
describe the organization and content of our text-
book supplement and show how it can be integrated
into an undergraduate reaction engineering course.
A copy of the supplement can be obtained by writing
to the authors.

MOTIVATION FOR DEVELOPING THE
COURSEPACK

We began developing the materials described in
this paper in the spring of 1988. At that time there
were very few such educational materials available
to the chemical engineering community even though
it was quite clear that examples from microelectron-
ics processing (for instance) could easily be used to
illustrate key reaction engineering principles. Un-
fortunately, existing textbooks provided very few ap-
plications of reaction engineering principles to prob-
lems encountered in microelectronics processing and
biotechnology.
Table 1 lists several reaction engineering texts
and the number of pages each devotes to these two
particular technologies. As can be seen, many of the
texts completely omit any reaction engineering ap-
plications in these technologies. Hill and Fogler,
however, include several pages on enzyme kinetics.
Nauman likewise covers Michaelis-Menten kinetics,
and he also includes a few pages on fermentation.
Reaction engineering applications in microelec-
tronics processing are much more scarce, however.

TABLE 1
Textbooks and Non-Traditional Technologies
Pages Devoted to
Author Biotechnology Microelectronics

Carb.rr\ (1976)' 0 0
Hill (1977)"[ 7 0
SIolland and Anthony (1979)1" 0 0
Butt (1980)"11 0 0
Smith (1981)"i" 0 0
Fogler (1986)'"' 8 3
Nadmian (1987)"' 11 3
Froment and Bischoff (1990)"14 0 0

Nauman gives a brief and largely qualitative discus-
sion of reaction engineering issues in the fabrication
of electronic devices. Fogler provides a few problems
dealing with chemical vapor deposition at the end of
his chapter on heterogeneous reactions, along with
three problems (without solutions) concerning mi-
croelectronics fabrication in an appendix.

An encouraging trend, evident in the table, is
that the most recent books have the most material
relevant to biotechnology and microelectronics proc-
essing. This trend will certainly continue as new and
revised textbooks are published. Fogler's second edi-
tion, for instance, has an expanded treatment of
these topics.

Our desire to integrate examples from non-
traditional technologies into the traditional chemi-
cal reaction engineering course and the omission of
such examples in most texts motivated our work in
developing a textbook supplement. This supplement
took the form of a spiral-bound coursepack that the
students could purchase for a nominal fee from a
local copying center.

OVERVIEW AND ORGANIZATION OF THE
COURSEPACK
The coursepack comprises two main sections. One
deals with microelectronics processing and the other
with biochemical technology. The microelectronics
processing section contains three chapters, and the
topics covered are chemical vapor deposition, plasma
etching, and the thermal oxidation of silicon. The
biochemical technology section contains two chap-
ters: one concerns fermentation and bioreactor de-
sign and the second discusses catalysis by immobi-
lized enzymes.

Each of the chapters comprises three sections:
Introduction, Applications of Chemical Reaction
Engineering, and Problems. The first section intro-
duces one particular aspect of an emerging technol-
ogy and provides background material necessary for
the subsequent sections. The second section illus-
trates, via examples, how established reaction engi-
neering principles can be applied to this particular
aspect of the technology. Detailed derivations are
often omitted, and the student is expected to refer to

Summer 1991

the textbook for basic explanations of the principles.
The final section provides several problems that al-
low the students to use what they have learned in
the earlier sections.
We have designed this textbook supplement so
that it can be easily integrated into a chemical reac-
tion engineering class. The coursepack is structured
so that the chemical reaction engineering principles
that are being employed are clearly evident within
the applications section of each chapter. Table 2
summarizes the general reaction engineering prin-
ciples emphasized in each chapter in the coursepack.
Organizing the coursepack around reaction
engineering principles facilitates the integration of
relevant examples from non-traditional technologies
into the traditional course. For example, the con-
cepts involved in the design of an isothermal CSTR
can be illustrated using a rate law for cell growth
kinetics as well as one for a generic reaction such as
A -> B + C. Additionally, the key ideas behind the
derivation of rate laws for heterogeneous catalytic
reactions (i.e., Langmuir-Hinshelwood-Hougen-Wat-
son kinetics) can also be applied to derive rate ex-
pressions for chemical vapor deposition processes.
As a final example, transport and reaction in the
inter-wafer region of a horizontal plasma etching
reactor is amendable to the same type of analysis
employed in modeling diffusion and reaction in a
catalyst particle.
To illustrate more fully the manner in which the
coursepack can be integrated into the reaction engi-
neering class, consider the chapter on chemical va-
por deposition which features four different applica-
tions of chemical kinetics and reaction engineering:
collisional activation of gas-phase reactions, hetero-
geneous reaction kinetics, diffusion and reaction, and
chemical equilibrium.

The illustration of the first principle uses the
reaction SiH4 -> SiH2 + H2, which can ocur in the gas
phase during the CVD of polycrystalline silicon from
silane. Here we employ the simple Lindemann mecha-
nism for unimolecular reactions and the pseudo-
steady-state approximation to derive a rate law for
the reaction. The rate equation clearly shows that
the reaction can be second order in silane at low
pressures and first order at high pressures. This
example can be used in the reaction engineering
course to reinforce the concepts of elementary reac-
tion steps, active centers, and the steady-state ap-
proximation.
The second application in the CVD chapter deals

with heterogeneous reaction kinetics. In this section
we use the standard Langmuir-Hinshelwood-Hougen-
Watson formalism to derive a rate law for deposition
of polycrystalline silicon from silane. This example
illustrates the application of elementary reactions
(adsorption, desorption, surface reaction) and the
concept of a rate-limiting step.
The third application in the CVD chapter in-
volves an analysis of reaction and diffusion in a
horizontal, multiple-wafer-in-tube, low-pressure CVD
reactor. The reactor contains a large number of closely
spaced wafers upon which it is desired to deposit a
thin, uniform film. The direction of flow of the gase-
ous reactants is normal to the wafer surface so diffu-
sion is the dominant mode of transport between the
wafers. Mathematically, this problem is identical to
that of reaction and diffusion in a porous, cylindrical
catalyst particle. Thus, the principles of coupled rate
processes (i.e., diffusion and surface reaction) can be
applied in this case, and the Thiele modulus and the
concept of an effectiveness factor emerge quite natu-
rally.
The final application in the CVD chapter
deals with chemical equilibrium for the reaction
SiH4 => Sits + 2H2. Here, we calculate the equilib-
rium constant for the reaction and then use it to
show that the reactor pressure and temperature and
the feed stream composition determine the direction
in which the reaction occurs. That is, some operating
conditions can lead to etching (i.e., removal of silicon
from the surface) whereas other conditions can lead
to deposition of Si. This example illustrates the im-
portance of thermodynamics in chemical reaction
engineering.
One of the pedagogical benefits of using examples
from non-traditional technologies alongside their
more traditional counterparts is that doing so helps
to emphasize the importance of the underlying physi-
cal and chemical phenomena rather than the spe-

TABLE 2
Reaction Engineering Principles in Coursepack

Principles Chapter
Silicon
Plasma Oxida- rm.rnn- Enz:,
CVD Etching tion station Catalysis

Reactor Modeling V V V V
Chemical Equilibrium V
Reaction Kinetics V V V
Diffusion and Reaction / V V

Chemical Engineering Education

cific example that is being used to illustrate the
phenomena. For instance, when students begin to
realize that the same set of principles can be used to
understand the behavior of a fixed-bed catalytic
reactor and the behavior of a low-pressure, chem-
ical vapor deposition reactor, then they are be-
ginning to focus on those fundamental principles
rather than on the specific technological applica-
tions. As a result, the students obtain a deeper ap-
preciation for the general applicability of chemical
engineering science.

SUMMARY

We have developed a textbook supplement that
facilitates the integration of examples from non-
traditional technologies into a reaction engineer-
ing course. These educational materials provide a
means for introducing students to the application of
chemical reaction engineering principles in micro-
electronics and biochemical technology. The
coursepack has been used in classes at The Univer-
sity of Michigan, and the student evaluations have
been generally favorable.

ACKNOWLEDGEMENT

The work described in this paper was supported
by a Faculty Development Grant from the Univer-
sity of Michigan Center for Research on Learning
and Teaching.

REFERENCES
1. Sandler, S.I., and B.A. Finlayson, eds, Chemical Engineer-
ing Education in a Changing Environment, Engineering
Foundation, New York, NY (1988)
2. Anderson, T.J., Chem. Eng. Ed., 24, 26 (1990)
3. Hess, D.W., Chem. Eng. Ed., 24, 34 (1990)
4. McConica, C.M., Chem. Eng. Ed., 24,38 (1990)
5. Takoudis, C.G., Chem. Eng. Ed., 24,42 (1990)
6. Orazem, M.E., Chem. Eng. Ed., 24,48, (1990)
7. Carberry, J.J., Chemical and Catalytic Reaction Engineer-
ing, McGraw-Hill Book Company, New York, NY (1976)
8. Hill, C.G., An Introduction to Chemical Engineering Ki-
netics and Reactor Design, John Wiley & Sons, Somerset,
NJ (1977)
9. Holland, C.D., and R.G. Anthony, Fundamentals of Chemi-
cal Reaction Engineering, Prentice-Hall, Englewood Cliffs,
NJ (1979)
10. Butt, J.B., Reaction Kinetics and Reactor Design, Pren-
tice-Hall, Englewood Cliffs, NJ (1980)
11. Smith, J.M., Chemical Engineering Kinetics, McGraw-Hill
Book Company, New York, NY (1981)
12. Fogler, H.S., Elements of Chemical Reaction Engineering,
Prentice Hall, Englewood Cliffs, NJ (1986)
13. Nauman, E.B., Chemical Reactor Design, John Wiley and
Sons, Somerset, NJ (1987)
14. Froment, G.F., and K.B. Bischoff, Chemical ReactorAnaly-
sis and Design, John Wiley and Sons, Somerset, NJ (1990)
0

REVIEW: Numerical Methods
Continued from page 144
until a steady state is reached. Another interesting
feature of the book is its excellent compilation of
problems.
The reviewer has serious doubts whether a stu-
dent can truly appreciate the chemical engineering
orientation of the book at the sophomore level-one
can easily get weighted down by new concepts which
can divert the attention away from the numerical
techniques themselves. It would be better to use this
text at the senior level, after a student has been
exposed to the basic courses in chemical engineer-
ing. But at that level, one could possibly introduce
the orthogonal collocation method, which is quite
popular now but which does not find a place in this
text. Also, one could then do more justice to the
stiffness of ODE's (although some introductory dis-
cussion exists on stability criteria for IVP's) and to
finite element techniques.
Overall, this book will satisfy the demands of
undergraduate chemical engineering students who
usually have difficulty in understanding the presen-
tations in more general texts. With some additional
material incorporated by an instructor, it could be
an excellent text at the senior level. Some instruc-
tors can possibly use this as a text at earlier stages
in the curriculum. O

Books received
Computational Quantum Chemistry, by Alan Hinchliffe; John
Wiley & Sons, 1 Wiley Dr., Somerset, NJ 08875-1272; 112 pages,
$34.95 (1988)
Diffusion and Convection in Porous Catalysts, Webster and Strie-
der, eds; AIChE, 345 East 47th St., New York, NY 10017; 96
pages; $20 members, $35 Others (1988)
Separation Technology, Li and Strathmann, eds; AIChE, 345
East 47th St., New York, NY 10017; 633 pages; $50 Members, $70
Others (1988)
Environmental Management Handbook: Toxic Chemical Materi-
als and Wastes, by Kokoszka and Flood; Marcel Dekker, Inc., 270
Madison Ave., New York NY 10016; 656 pages, $125 (1989)
Fatty Acids in Industry: Processes, Properties, Derivatives, Appli-
cations, edited by Johnson and Fritz; Marcel Dekker, Inc., 270
Madison Ave., New York, NY 10016; 688 pages, $150 (1989)
Droll Science, compiledby Robert L. Weber; The Humana Press
Inc., PO Box 2148, Clifton, NJ 07015; 352 pages, $22.50 (1987)
How to Write and Publish a Scientific Paper, 3rd edition, by
Robert A. Day; Oryx Press 2214 North Central at Encanto, Phoe-
nix, AZ 85004; 224 pages, $21.95 (1988)

Summer 1991

class and home problems)

The object of this column is to enhance our readers' collection of interesting and novel problems in
chemical engineering. Problems of the type that can be used to motivate the student by presenting a
particular principle in class, or in a new light, or that can be assigned as a novel home problem, are
requested, as well as those that are more traditional in nature and which elucidate difficult
concepts. Please submit them to Professors James 0. Wilkes and Mark A. Burns, Chemical Engineer-
ing Department, University of Michigan, Ann Arbor, MI 48109-2136.

A SIMPLE

HEAT OF CRYSTALLIZATION

EXPERIMENT

NOEL DE NEVER
University of Utah
Salt Lake City, UT 84112

A permanent problem in engineering education
is to find simple, portable, low-cost classroom
demonstrations of the principles we present to our
students. The more we can convince them that the
equations in their textbooks describe what actually
occurs in nature, the better engineers they are likely
to become. For that reason, educators are always
looking for opportunities to present experimental
confirmation of textbook principles. If possible, we
seek to find simple things, available to the public in
general, which illustrate engineering principles-
and then to show the students how those principles
apply to things in their daily lives.
A sportsman's handwarmer is a great comfort on
cold days. It is also a simple, portable tool that can
be used to show students that textbooks do describe
the real world. The "Heat Solution Reusable Heat
Pack"'' is available in sporting-goods stores for $3.00.
It is a 3-by-4 inch clear-plastic pouch, containing
approximately 100 gm of an approximately 50 wt%
solution of sodium acetate (NaAc) in water, plus a

Noel de Nevers has been a faculty member at the
University of Utah since 1963. His principal technical
interests are fluid mechanics, thermodynamics, and
air pollution. He has also developed a course and
edited a book of readings on Technology and Society.
_._ In addition to his technical work, he had three of his
laws published in the 1982 Murphy's Laws compila-
tion and won the coveted title of "Poet Laureate of
Jell-O" at the annual Jell-O Salad Festival in Salt Lake
City.

Copyright ChE Division, ASEE 1991

roughly 5/8-inch diameter, thin, stainless steel disc.
This device can be used in a sophomore heat and
material balances class by first assigning the follow-
ing as a homework problem or exam question:

A solution of 50% by weight water and 50% by weight
sodium acetate (NaAc), (CH3CO2Na, molecular weight 82),
is at 25 "C. This solution now crystallizes adiabatically by
the reaction
CH3CO2Na (aq) + 3 H20 (1) = CH,CO2Na 3 (H20) (c)
for which the heat effect is AH = 30.74 kJ/mol of NaAc.
Here assume that the original solution was one mole of
NaAc (82 gm) and 82 gm of water. At equilibrium at the
final temperature the composition is 56.44 gm of crystalline
CHCO2Na 3(H20), and a solution consisting of 59.59 gm
of water and 47.97 gm of dissolved NaAc.
The heat capacities are: water, C = 4.18 J/gm OC,
CHCO2Na 3(H20)(c), Cp = 2.4 J/gm 'C, and dissolved
NaAc, Cp = 2.58 J/gmoC.
What is the final temperature of the mixture of NaAc
solution and crystals after equilibrium is reached?

SOLUTION

For an adiabatic, constant-pressure batch proc-
ess with no work other than expansion against the
surroundings, we have
AH = 0 = crystallized AHcrystallization + YmCpAT

AT = -mcrystallized AHcrystallization
XmCp

56.44 gm of trihydrate
crystallized = = 0.415 mols
mol of trihydrate
Chemical Engineering Education

-0.415 mol (-30,740 1 )
AT = mol= 25.1 C
56.44 gm 2.4 + 59.59 gm 4.18 + 47.97 gm 2.58J
gm C gm C gm JC

Tfinal = 25 + 25.1=50.1 C
Thus one would expect the final temperature to
be about 25'C higher than the initial temperature,
for this initial temperature.
After the problem has been discussed in class,
the instructor measures the temperature of the un-
crystallized pouch; this is most easily accomplished
by using a small portable LCD thermocouple gauge
(Kiethley Model 870 Digital Thermometer or equiva-
lent). The instructor (or a student) lays the pouch on
a piece of any kind of insulating plastic foam with
the thermocouple between the pouch and the plastic.
The gauge quickly shows the temperature, which
should be practically room temperature.
Then the instructor initiates crystallization by
flexing the stainless steel disc inside the pouch, which
presumably causes a small oxide particle to flake off,
which in turn starts the crystallization. The entire
crystallization takes place in three to five seconds,
with a visible, white, opaque crystallization front
moving across the pouch from the initiation point.
The instructor (or the students) then measures the
temperature as described above, finding that it does
increase by very close to 25'C. The instructor then
hands the pouch around to the students so they can
feel that it is quite warm.
This is probably as much as the instructor would
want to do with the demonstration and/or the calcu-
lations in a typical sophomore heat and material
balances class. But there are even more possibilities
for instruction in this simple device.
The instructor can use the experiment for dem-
onstrating supersaturation and nucleation. The de-
vice can be regenerated and reused by placing it in
boiling water for a few minutes and then allowing it
to cool. The published melting point of the pure
trihydrate is 580C, so at room temperature it is
about 350C supercooled. It can be supercooled to
freezer temperature (-13'C) without initiating
solidification.
The homework or examination problem can be
made more complex by not specifying the final masses
of crystals, water, and dissolved NaAc, but rather by
specifying the initial state and giving the final con-
dition that the uncrystallized solution has 0.805 gm
dissolved NaAc per gm of water (which corresponds
Summer 1991

to equilibrium at 490C) in the final state. In that
case the student may solve for the values of the final
masses shown in the problem by writing three mate-
rial balances. If x represents the grams of crystalline
trihydrate, y the grams of water, and z the grams of
dissolved NaAc, then
x+y+z = 164gm
z = 0.805 y
y = (164 82) x (54 gm water ofhydration/136 gm
trihydrate)
These may be solved together to find the values
in the problem statement.
The problem can again be made more complex by
using a heat capacity equation for the crystalline
trihydrate instead of using the average values shown
above. The data in reference (2) are reasonable well
represented by
Cp = 1.44 J/gm C + (0.028 J/gm C2) T
The average C value used in the problem corre-
sponds to T = 34.3C in this formula, which is about
half-way between room temperature and the final
temperature of the crystallized system.
The final temperature of the hand warmer is
surprisingly insensitive to the initial temperature
because the solubility of sodium acetate in water
increases rapidly in the range from about 45C to
the melting point of the trihydrate at 58C.31 Using
the above equations and working backwards from
assumed final temperatures, one computes that
Assumed Final NaAc Solutibility Computed Starting
Temperature, C gm/gm Water Temperature C
48 0.78 20.4
50 0.83 27.5
52 0.90 37.7
Thus, for initial temperatures between 20.4 and
37.7C the computed final temperatures change only
from 48 to 520C. Experimentally, the independence
of final temperature on starting temperature seems
even stronger than this calculation suggests, but the
experimental temperature measurements are not
very precise. For an initial temperature of -13C
(freezer temperature) the observed AT was 46C,
and the resulting crystalline mass at 33C was quite
firm. For an initial temperature of 410C the final
temperature was 510C (AT = 100C) and the resulting
crystalline mass was quite mushy.

The calculated results are quite sensitive to the
assumed initial water content. Again, using the above
assumptions we may calculate

Assumed
Final
Temperature, C
50
50
50

Assumed Initial
NaAc wt.
Fraction in Solution
0.49
0.50
0.51

Computed
Starting
Temperature C
32.8
27.5
22.1

In making up the problem, the value of 50 wt%
NaAc was chosen because the resulting calculations
gave the best match to the experimental tests. (By
phone a Prism staff member said the concentration
was between 50 and 55 wt%, but declined to say
exactly what the value was.)
The heat of crystallization was computed from
the data in reference 3.

REFERENCES
1. Prism Technologies, 3111 N. Knox, Chicago, IL 60641 (312-
685-0999)
2. International Critical Tables, E. W. Washburn, ed., Vol. 5, pg
100, McGraw-Hill, NY (1929)
3. Gmelins Handbuch der anorganischen Chemie 8. Auflage,
System Nummer 21, Natrium, Verlag Chemie, GmbH, Ber-
lin, pg. 822(1928)
4. Rossini, F.D., et al., "Selected Values of Chemical Thermody-
namic Properties," NBS Circular 500, pg. 470 (1952) 0

book review

PROCESS CONTROL: STRUCTURES AND
APPLICATIONS
by Jens Balchen and Kenneth Mumme
Van Nostrand Reinhold, 115 Fifth Ave., New York,
NY 10003; $59.95 (1987)

Reviewed by
Coleman B. Brosilow
Case Western Reserve University

This book aims to "bridge the long-standing gap
between process and control." Toward this end, the
second chapter reviews most control theory and con-
trol system design methods. Chapter 3 gives a mainly
qualitative description of many important chemical
and physical processes, ranging in complexity from
valves to crystallization and reaction processes.
Chapters 4 and 5 present alternate control struc-
tures for the processes described in Chapter 3. These
structures are combinations of PID, ratio, feedfor-
ward, and cascade controllers, along with arithmetic
and logic blocks which are standard in most distrib-

uted control systems. The book concludes by
presenting the control structures for several
integrated process systems such as a paper machine
and an ammonia plant. The discussion is mostly
qualitative.
The authors have undertaken to present an
immense amount of material to an extremely wide
audience; indeed, too much material to too wide an
audience. Chapter 2, by necessity, gives only the
most cursory overview of the topics covered. In some
places the need to be concise has led to inaccurate
and/or misleading statements as, for example, on
page thirteen where it is stated that in order for a
feedback controller to be effective, the loop transfer
function ho(s) must satisfy I h(s)l >>1. The discus-
sion on multivariable decoupling and predictive con-
trol completely omits treatment of control effort con-
straints. Such an omission is unforgivable in a text
that claims to bridge gaps.
Later chapters suffer from very uneven coverage
of subject matter. While most discussions describe
various pieces of equipment and how they work,
every so often the discussion gets very detailed. In
the discussion of compressors, for example, it is
pointed out that "it is important that the pressure
and temperature be such that the gas does not reach
the critical point." This somewhat imprecise state-
ment is then illustrated by PVT diagrams (page 103)
for water and carbon dioxide, with no explanation of
how to use the diagrams. In the discussion of chemi-
cal reactors, the reader is presented with a partial
differential equation model for the reaction A -> B in
a plug flow tubular reactor (pages 238-239). These
equations are then followed immediately by the state-
ment that if the heat transfer coefficient can be used
as a control variable, it can be expressed in terms of
a new variable which is the relative change in heat
transfer coefficient with respect to the steady-state
heat transfer coefficient. No justification is given for
the equation which follows nor is it clear why the
change of variable was even mentioned since the
subject is immediately dropped. This reviewer re-
mains confused as to why we would even wish to use
variations in heat transfer coefficient as a control
variable for tubular reactors.
In summary, it is difficult to know to whom to
recommend this book. It assumes too much chemical
engineering background for the average control en-
gineer and too much control background for the av-
erage chemical engineer. Perhaps, my academic col-
leagues will find useful some of the detailed process
descriptions and P&I diagrams. 0

Chemical Engineering Education

DEPARTMENT: U Mass
Continued from page 125.
microstructure and morphology in both flow systems and
porous materials. Winter studies structural development
in well-defined flows of different classes of polymeric sys-
tems, such as phase-separating block copolymers and
liquid crystalline polymers. Self-similar molecular struc-
ture is exhibited by cross-linking polymers at the sol-gel
transition. Malone studies the effect of flows on the mor-
phology and phase behavior of binary polymer blends.
Computer image analysis is used for characterization and
control of the process. Ng has shown by both simulation
and CAT-scan analysis that the liquid distribution during
flow through a bed of packing is a manifestation of local
flow features involving several particles. Because of his re-
search activities in the transport and reaction areas, his
work in process design has a strong focus on the under-
lying physics.
The morphology of amorphous and crystalline oxides
is a focus of several projects. Dynamic adsorption-desorp-
tion of liquid nitrogen or krypton, mercury porosimetry
and electron microscopy are three tools used to character-
ize morphology. Conner and Laurence study the effects of
pore size and porosity of silica-supported catalysts on the
fragmentation and yield during the initial stages of olefin
polymerization. In a similar vein, Conner has been col-
laborating with scientists at Brookhaven National Labo-
ratories to pioneer the development of X-ray synchrotron
computed microtomography and its application to charac-
terize the morphology of olefin polymerization catalysts.
Minimization of the pore size of supported microporous
inorganic films and of their penetration into the macro-
pores of the ceramic support are crucial goals in Harold's
synthesis of ceramic membranes.
One of the most successful programs developed in the
transport area is Julio Ottino's program in fluid mechan-
ics and mixing. His research has raised the level of under-
standing in mixing to the point where, for the first time, it
is possible to view many seemingly unrelated problems
within the context of a single theory.
Applied Theoretical Chemistry
In many new areas it is becoming critically important
to incorporate details of molecular-scale chemical physics
into engineering models. The department has research
efforts that address this need. Much of the work repre-
sents an emerging effort that will likely be a future core
strength for the department and the profession.
Michael Cook is developing and using density func-
tional methods for the study of point defects in materials.
An important application is to electronic device materials
such as silicon and III-V semiconductor alloys and com-
pounds. He is also investigating the nature of potential-
energy surfaces for free radical reactions as a means of
providing a more firm foundation for kinetic models. Peter
Monson's research is concerned with applications of fun-
damental statistical thermodynamics, especially in the
context of phase equilibria and the properties of interfa-
Summer 1991

cial systems. He has developed new approaches to study-
ing the influence of molecular shape and polarity upon
fluid phase equilibria. This work is now being extended to
prediction of solid-liquid equilibria. His group is also ex-
ploring the molecular basis of adsorption separations in
terms of the nature of the intermolecular forces and the
adsorbent microstructure. Fundamental theoretical stud-
ies of the molecular structure of fluid films on solid sur-
faces are also being carried out. Phil Westmoreland's re-
search stands at the interface between detailed molecular
theory and process reaction engineering. He co-developed
Bimolecular Quantum-RRK analysis to predict rate con-
stants and product channels for gas-phase association re-
actions in combustion. Westmoreland is exploiting this
method in pyrolysis, combustion, and plasma chemistry
while probing more complex potential-energy surfaces and
intermolecular energy transfer.

THE FUTURE
As this article is being written, the department is
in the middle of several new initiatives that promise
to significantly improve our programs. We are a
major participant in the University/Digital Equip-
ment Corporation PILGRIM project, which is a $6
million project to design, install, and test a network
of several hundred high-performance workstations
in the College of Engineering and in the Computer
and Information Science Department. So far the de-
partment has installed twenty workstations for re-
search purposes and has access to a workstation
classroom for teaching. Several courses will use work-
station-based software to complement lecture mate-
rial, including the design courses, the separations
course, and the statistical thermodynamics course.
The undergraduate program continues to evolve,
and it embraces a major commitment to upgrading
the lab. We began converting many of the laboratory
experiments to computer data acquisition and con-
trol some time ago with a generous donation of proc-
ess control computers from Analog Devices (see Chem.
Eng. Ed., 24, 106, 1990). Over the next two years we
will design and build new experiments on crystalli-
zation, process control, and polymerization kinetics.
Many of the older PCs used for on-line data acquisi-
tion and control will be retired and replaced by more
modern machines. We continue to explore ways of
inserting more chemistry and solid-state material
into the curriculum, and two of the faculty intend to
write books on these topics as that activity matures.
The department has grown into a vigorous,
vibrant place in only forty years of existence,
presently with eight of the thirteen faculty also at
forty or under. By the time we reach our half-
century in the year 2001, we hope to make our per-
spective a vital part of chemical engineering. 1

classroom

DEVELOPMENT AND USE OF

OPEN-ENDED PROBLEMS

PAUL R. AMYOTTE
Technical University ofNova Scotia
Halifax, Nova Scotia, Canada B3J 2X4

A t the 1987 summer school for chemical engineer-
ing faculty, sponsored by the American Society
for Engineering Education, a common theme was
the call for more open-ended problems in course
work. Suggestions for developing and using such
problems are presented in this paper. This is done
by considering various examples from courses on
mass and energy balances, communications, kinet-
ics and ideal reactors, and reactor design. The bene-
fits of using open-ended problems, from both in-
structor and student perspectives, are presented.
Difficulties which may be encountered by the in-
structor and students are also discussed. A rather
broad definition of open-ended is used here, namely
something which goes beyond the given this and
this, calculate that type of problem for which there is
typically only one answer.

PROBLEM DEVELOPMENT
Various avenues are available to obtain a variety
of open-ended type problems:
application of research findings
sharing problems with colleagues
selection of appropriate problems from the course text
consulting other reference texts
modification of traditional-type problems
development of new problems
The following sections contain several illustra-
tions of these different approaches. The examples
are open-ended to varying degrees and therefore

The examples are open-ended to
varying degrees and therefore represent
different levels of challenge for students. ... In
all cases, the intent is to promote and encourage
creativity and an inquisitive nature.

Paul Amyotte received his BEng from the Royal
Military College of Canada, his MSc (Eng) from
Queen's University, and his PhD from the Technical
University of Nova Scotia (TUNS). He is an associ-
ate professor and head of the chemical engineering
department at TUNS. His interests are fluidized-bed
drying, gas and dust explosions, and engineering
education.

represent different levels of challenge for students.
Some are intended to be fun and some are of a more
serious nature. In all cases, the intent is to promote
and encourage creativity and an inquisitive nature.
Application of Research Findings
From time to time, elements of the author's re-
search program on dust explosions have found their
way into the classroom in the form of tutorial discus-
sions and home assignments.
Briefly, explosion tests are conducted in a spheri-
cal vessel having a volume of 26 L. Dust dispersion
through a perforated nozzle is achieved by an air
blast from a 1-L reservoir. Prior to each run, the
explosion vessel is partially evacuated so that the
dispersion pulse brings the vessel pressure up to 1
bar at the time of ignition. Ignition is by a single
spark passed between two fixed electrodes or by a
more energetic chemical ignitor. Pressure develop-
ment over the course of an explosion is measured by
a piezoelectric transducer mounted flush with the
interior of the vessel.
Useful discussions (in the mass and energy bal-
ances course) on process variable measurement and
data analysis have arisen by asking the following
open-ended questions:
How might you record the pressure measurements from
the piezoelectric transducer?
[Pressure-time traces acquired by an oscilloscope
and by a personal computer are made available
either after discussion or to stimulate discussion
if required.]

Copyright ChE Division, ASEE 1991
Chemical Engineering Education

How could you determine the maximum rate of pressure
rise and the maximum explosion pressure from one of these
pressure-time traces? How accurate will these values be?
[These questions can lead to a discussion on
mechanical and computer methods for
determining slopes and maxima of curves.]
How could you determine the pressure required in the
explosion chamber prior to dust dispersal (so that the
pressure at the time of ignition is 1 bar)?
[Typical responses to this question have included
(a) by trial-and-error experimentation, and (b) by
consideration of the dispersion reservoir and
explosion vessel together as the system, with
application of Boyle's law to the initial (pre-
dispersion) and final (post-dispersion) states.]

Scanning electron micrographs of the same coal
dust before and after an explosion test have been
used in the kinetics and ideal reactors course to
initiate discussion on the nature of reacting hetero-
geneous systems. Two simple questions can accom-
plish this:
Do you see any similarities between the "before and after"
pictures?
[e.g., particle size]
Do you see any differences between the "before and after"
pictures?
[e.g., particle shape and degree of fragmentation]

The use of rupture disks and relief valves on
storage vessels and chemical reactors has been in-
troduced in the reactor design course by a walk
through our dust explosion research laboratory. The
vessel previously described is fitted with a rupture
disk, and thus is a good example of one method of
vessel or process protection. The discussion which
follows this tour is filled with what ifs (e.g., . the
rupture disk bursts? ... a dust with unknown explo-
sion parameters is being investigated?) and how
come's (e.g., .. the vessel has a rupture disk and not
a relief valve? ... the rupture disk is vented upward
into a fume hood?) which ordinarily might not have
arisen.
Sharing Problems with Colleagues

Many instructors have a collection of problems
contributed by their colleagues. One of the author's
favorites in the open-ended category is the following,
drawn from the mass and energy balances course:
Formaldehyde is made by the catalytic air oxidation of
methanol. When the process is operating properly, the
mole ratio of air to methanol in the feed is about 6:1, and
the conversion (moles of formaldehyde in product stream
per mole of methanol fed) is 30 mole %. There is an
unexplained drop in the conversion, and a complete analysis
of the product stream is ordered. The analysis gives the
following mole percentages: N2 (63.1), 02 (13.4), HO (5.9),
H2CO (4.1), CHOH (12.3), and HCOOH (1.2). The formic

Summer 1991

The use of rupture disks and relief
valves on storage vessels and chemical
reactors has been introduced in the reactor
design course by a walk through our dust
explosion research laboratory.

acid is formed by the undesired but unavoidable oxidation
of some of the formaldehyde. This phenomenon accounts
for the conversion of methanol to formaldehyde being only
30 mole % even under normal conditions. Calculate the
new conversion and suggest reasons for the sudden drop in
conversion.

The calculation of the new conversion (23%) is
relatively straightforward. On the basis of an air-to-
methanol feed ratio of 4.6 (instead of 6), the sudden
drop in conversion may well be due to a drop in the
air feed rate. However, the possibilities of a reduc-
tion in catalyst efficiency and a drop in methanol
feed rate cannot be ruled out entirely.

Selection of Appropriate Problems from the
Course Text

The following problem used in the kinetics and
ideal reactors course is taken from Fogler:'1'
The frequency of flashing of fireflies and the frequency of
chirping of crickets as a function of temperature are given
below:
For fireflies:
Temperature (C) 1 21.0 25.0 30.0
Flashes per minute 9.0 12.16 16.2
For crickets:
Temperature (C) 14.2 20.3 27.0
Flashes per minute 80 126 200
What do these two events have in common?

"The" solution from a kinetics point of view is
that the flashing and chirping frequencies both ex-
hibit an Arrhenius dependence with temperature,
and both have the same activation energy. However,
a simple linear relationship correlates each set of
data, as does the frequency as a function of tempera-
ture squared. Maybe an analogy with the specific
heat of a gas is in order. Perhaps a suitable question
to ask is: "Would more data on the two events help to
clarify the frequency/temperature relationship?"

Consulting Other Reference Texts

The following exercise was given in the commu-
nications course, but was drawn from the mass and
energy balances text (Felder and RousseauE[2):
I have given you the task of measuring the volumetric
flowrate of a liquid in a large pipeline. The liquid is in
turbulent flow, and a flat velocity profile may be assumed

(so that you need only measure the fluid velocity to
determine the volumetric flowrate). The line is not equipped
with a built-in flowmeter; however, there are taps to permit
the injection or suspension of devices or substances and
the withdrawal of fluid samples. The pipeline is glass and
the liquid is clear. Assume that any device you want to
insert in the pipe can be made leakproof if necessary, and
that any technique you propose can be calibrated against
known flowrates of the fluid.
Come up with several ways of performing the measurement
that might have a chance of working. (Examples: insert a
small salmon in the pipe, suspend a lure irresistible to
salmon upstream of the injection point, and time how long
it takes the fish to travel a measured section of the pipe;
or, use a laser Doppler velocimetry system.) The techniques
you propose must be substantially different from one
another; giving me a pitot tube with ten different
manometer fluids will get you nowhere. Good luck!

Student responses, reported in memorandum form,
included:
Use a vane anemometer, hot-wire anemometer, venturi
meter, rotameter, pitot tube, orifice plate.
Use the marker method, with blueberries or ping-pong
balls (negligible weight) as the marker.
Fill a small balloon with the same fluid as in the pipeline,
place it in the pipe, and note the time for a specific distance
travelled.
Insert a particle and measure its velocity with a radar
gun.
Insert a steroid-injected track star into the pipe, complete
with diving gear and speedometer. Have him run until he
feels no liquid pressure on his back and then measure his
velocity with the speedometer.
Install a small turbine and generator and measure the
energy output.
Tie a lump of sugar to a string and insert it into the
flowing liquid. Measure the time required to dissolve the
sugar.

Modification of Traditional-Type Problems

The prescribed text (Blicq'31) for our communica-
tions course contains several assignments which con-
sist of a descriptive passage followed by an instruc-
tion to write a specific type of report (incident, field
trip, etc.) based on the given scenario. These exer-
cises are helpful in establishing the fundamentals of
report writing, and they provide the students and
instructor with a given set of data with which to
work. On the negative side for the students is the
fact that these data are totally unfamiliar to them.
There is also the temptation to regurgitate the nar-
rative passage from the text in a slightly different
sequence.
A possible modification is to leave out the sce-
nario description, thus allowing the students to fill
in the details themselves. Consider the following
assignment:

Write an incident report (in memorandum form) on
something that has happened to you in the past year
or so.
The reports should be structured according to
the scheme of summary, situation, event, and out-
come, but the specific nature of each report will be
different. If a particular report is well-written, then
the instructor should have very few questions after
reading about an incident of which he previously
had no knowledge.

Here is another case of problem modification (from
the kinetics and ideal reactors course), this time by
leaving out a piece of information. The original prob-
lem from Fogler"El is:
The rule of thumb that the rate of reaction doubles for a
10C increase in temperature occurs only at a specific
temperature for a given activation energy. Show that the
relationship between activation energy and temperature
for which the rule holds is
T (10K)E/2
1 Rn2
Neglect any variation of concentration with temperature.

The problem can be reworded so that the exact rela-
tionship is not given and the students are not forced
down a pre-determined solution path:
There is a rule of thumb which states that the reaction
rate doubles for every 10C increase in temperature. This
is true, however, only at a specific temperature for a given
activation energy. Develop a relationship between
activation energy and temperature for which the rule of
thumb holds. Any variation of concentration with
temperature may be neglected.

Practically all students will start out with a ratio of
Arrhenius expressions:
k1 Aexp(-E/RT1)
k2 Aexp(-E/RT2)
where k = 2kI and T2 = T1 + 10K.

Some will stop at
(10K)E
T,(T1+ 10K)- (10K)E

A few will go on to solve the quadratic for T1. Only
a very few will approximate T,(T1 + 10K) by T2 to

arrive at

S(io1K)E
[Rfn2

An add-on statement to an existing problem can
sometimes provide a bit of an open-ended nature.
The following problem (mass and energy balances
course) from Felder and Rousseau"21 was modified by
the addition of part (b):
In the Deacon process for the manufacture of chlorine, HC1
and 02 react to form C12 and H20. Sufficient air (21 mole %

Chemical Engineering Education

02, 79% N2) is fed to provide 25% excess oxygen, and the
fractional conversion of HCl is 70%.
(a) Calculate the mole fractions of the product stream
components.
(b) Why do you think 25% excess oxygen is used in this
process?

Student answers to part (b) have included:
To provide additional flow material for intimate mixing
of the reactants
To help control the reaction
To increase the conversion ofHC1, which is the valuable
reactant, at the expense of air which is cheap and readily
available
To minimize the occurrence of undesirable side reactions
To control the reaction temperature
In a similar manner, this problem (mass and energy
balances course) from Luyben and Wenze114' was
modified by the addition of part (b):
A coal containing 81 mass % carbon and 6 mass %
unoxidized hydrogen is burned in dry air. The rest of the
coal is solid inert. The amount of air used is 30% more
than is theoretically required to completely oxidize all of
the carbon no CO2 and all of the hydrogen to H20.
(a) Calculate the number of kg of air per kg of coal, and the
composition of the stack gas leaving the furnace,
assuming this gas contains no CO.
(b) Is this a realistic coal?

Student answers to part (b) have included:
No; there should be some water content. A realistic coal
would also likely contain sulfur, nitrogen, and oxygen.
No; a realistic coal is more likely to undergo incomplete
combustion.
No; the majority of coals have some percentage of oxidized
hydrogen.
Yes; the general composition of the coal is of the order of
80-85% carbon and 4-5% hydrogen. However, the fact that
the rest of the coal is inert may be questionable.
It all depends; for run-of-mine coal, the inert solid (ash)
percentage is probably too low; for clean coal it's probably
too high.
It all depends; for an approximate mass balance
calculation, the coal composition may be alright. For any
detailed work based on the coal analysis, the coal should
not be considered realistic.
Development of New Problems

Tired of marking the same thing over and over,
the author gave the following assignment in the
communications course:
What bugs you? Respond in memorandum form.

The response was overwhelming, humbling, and
certainly enlightening. Replies ranged from the frivo-
lous to the serious:
Slow drivers in the fast lane
The quality of food services at some universities
Girlfriends who don't appreciate the amount of time an
engineering student must work

The lack of cartoon shorts before feature movies
Noisy roommates who don't attend summer term
Power outages during computer usage
Racism
Another example in this category is:
Pose and solve a short mass balance problem drawn from
everyday life. The concept need not be difficult; however, it
should be something which illustrates, in a non-technical
manner, the mass balance principle.

This question was given as part of a take-home
test and produced several interesting problems, such
as the one below.
A civil engineering survey showed that 1,000 vehicles enter
the Mic Mac Rotary (a local area of traffic congestion)
during the time period from 4:00 pm to 5:00 pm. Out of
every ten vehicles, one is a truck and the rest are cars. It is
Friday afternoon and all vehicles are coming from the new
bridge via the Circumferential Highway (the only source of
vehicles). Several civil engineers stood in the middle of the
rotary (they had nothing better to do) and counted what
vehicles used which exit. They then gave their data to a
chemical engineer who put them into the following table:
Prince Albert Road 100 vehicles
Circumferential Highway 500 vehicles (15% trucks)
(to Woodside)

Main Street

200 vehicles (5% trucks)

Waverly Road 186 vehicles (6.5% trucks)
NOTE: Trucks were not allowed to exit via Prince Albert
Road due to construction.
a) Draw the fully labeled flow diagram of the rotary.
b) What is the composition of each exit?
c) Is anyone lost in the rotary during this hour?
d) If yes, how many cars and trucks are lost? Why are they
lost?

The final example considered here is a mass bal-
ance problem involving data consistency checks which
was developed by the author and two of his col-
leagues (Furter, et al.151):
a) A process steam boiler (operating at steady state) at a
coal conversion plant fires coal gas from a continuous
vertical retort. The fuel analysis is given in Table 1 (see
Reference 5). An environmental test crew has made
measurements of the flue gas emissions in the stack; the
measured dry flue gas analysis is given in Table 2 (see
Reference 5). Over the duration of the testing, the molal
humidity of the combustion air supply was 0.05 mole
moisture per mole dry air. Using the law of conservation
of mass, check the consistency of the data.
b) The boiler described in part (a) operates at a thermal
input of 25 MW, and the higher heating value of the fuel
gas has been determined as 17.97 MJ/m3 at 15C and
atmospheric pressure. In addition to determining the dry
flue gas analysis, the environmental test crew has made
several other measurements. The temperature of the flue
gas was found to be 3250C. A particulates traverse
revealed negligible stack solids, a flue gas moisture
content of 38% by volume, and a stack gas velocity of 5.75
m/s. The chimney diameter is known to be 2.06 m, and

Summer 1991

the burners were thought to be operated with about 17%
excess air over the duration of the testing. Using the law
of conservation of mass, check the consistency of the
data.

In solving this problem, the student encounters sev-
eral questions:
What do you do when the left-hand side of a mass
balance expression does not equate with the right-hand
side?
Could the measured data be incorrect?
Is there a plausible explanation for the situation where
more of a component exits a system than enters?

PROBLEM USE

Incorporation

Some suggestions for incorporating open-ended
problems in a course include:
Offer exposure to open-ended problems in class
tutorials and home assignments before using them on
tests and exams.
For in-class and home exercises, gradually increase
the degree of difficulty and encourage students to
consult one another.
Get the class to brainstorm through a problem and
encourage volunteers to lead the discussion (several
helpful suggestions for developing a "group-based
Socratic approach" have been given by Felder[G6).
Give a problem to the class and let them go away and
think about it; start the next lecture by raising the
problem again.
Start out with low credit for open-ended problems,
and gradually increase the credit.
In addition to building the credit and difficulty of the
problems, increase the number of open-ended
problems as the course goes on.
Use open-ended problems in as many courses as
possible, and encourage colleagues to do the same.
Provide a very open-ended experience in design and
thesis courses.
Use closed-ended problems to establish the
fundamentals and allow the students to gain
confidence in their abilities.
Discuss problem-solving techniques and skills (see, for
example, FoglerD.J).

Difficulties

From a student's perspective, some potential
problem areas include:
* They are generally not used to dealing with open-
ended problems.
It is easy to be intimidated and become frustrated
(hopefully, only initially) by what appear to be "trick"
problems. There is also likely to be a feeling of "Boy, I

could never come up with that (i.e., the solution) by
myself' (which is quite often not true).
They want to ask the instructor many questions about
possible solutions. (The key is to get them to ask
themselves these questions.)
The students may not be used to having the following
conversation:
Student: "What's the right answer?"
Instructor: "I don't know. I don't think there is one."
From an instructor's perspective, some potential
problem areas include:
It can be time-consuming to develop open ended
problems, particularly from scratch.
It can also be time-consuming to grade solutions to
such problems.
The instructor must become almost a "cheerleader" at
times.
The instructor may not be used to having the
following conversation:
Student: "What's the right answer?"
Instructor: "I don't know. I don't think there is one."

Benefits

Among the many benefits of open-ended prob-
lems, the author has experienced the following:
Developing intangible communication skills such as
cogently expressing an opinion and thinking on one's
feet.
Appealing to various types of students, not just those
who are satisfied with number crunching and
application of formulas.
Giving the students a chance to be creative.
Allowing the students to write on topics which are
relevant to their daily lives.
Demonstrating that mass and energy balances are
more than just exercises in algebra.
Providing a lead-in to discussion of items such as
instrumentation and measurement accuracy.
Preparing the students for the open-ended type
problems they can expect in the future.
Educating the instructor as to the unique abilities of
some engineering students.

CONCLUSION
Various examples of open-ended problems and
ways to obtain them have been presented in this
paper. Suggestions for incorporating open-ended
problems and some of the benefits and difficulties
encountered in using such problems have been dis-
cussed. In the author's opinion, these benefits far
outweigh the difficulties. Open-ended problems are
invaluable for developing and fostering basic skills,

Chemical Engineering Education

once these skills have been established through
means such as closed-ended problems.

REFERENCES
1. Fogler, H.S., Elements of Chemical Reaction Engineering, Pren-
tice-Hall, Englewood Cliffs, NJ (1986)
2. Felder, R.M., and R.W. Rousseau, Elementary Principles of
Chemical Processes, second edition, Wiley, New York, NY (1986)
3. Blicq, R.S., Technically Write!, third edition, Prentice-Hall,
Scarborough, Ontario (1987)
4. Luyben, W.L., and L.A. Wenzel, Chemical Process Analysis:
Mass and Energy Balances, Prentice-Hall, Englewood Cliffs,
NJ (1988)
5. Furter, W.F., M.J. Pegg, and P.R. Amyotte, "A Practical Appli-
cation of Mass Balances," Chem. Eng. Ed., 23, 163 (1989)
6. Felder, R.M., "Stoichiometry Without Tears," Chem. Eng. Ed.,
24,188 (1990) O

book review

ELEMENTARY GENERAL THERMODYNAMICS
by M.V. Sussman
Reprint Edition with Corrections; Robert E. Krieger
Publishing Co., PO Box 9542, Malabar, FL 32902;
478 pages, $52.50 (1989)
Reviewed by
Amyn Teja
Georgia Institute of Technology

This is a reprint edition of the book first pub-
lished in 1972 by Addison-Wesley Publishing Co.
The new printing corrects a large number of typos in
the original edition and provides more exposure to
SI units. There are also a number of minor additions
to the text, such as a brief mention of the Design
Institute of Physical Properties Research (DIPPR)
publications and even references to estimation meth-
ods for thermodynamic properties. In all other re-
spects, however, this version of the book is identical
to the original.
The book is designed as a broad introduction to
thermodynamics and its many applications to engi-
neering and science. Thus there are the usual chap-
ters on the first and second laws (Chapters 2 and 3),
power and refrigeration cycles (Chapter 4), relation-
ships among thermodynamic properties (Chapter 6),
equations of state (Chapter 7), fugacity and activity
(Chapter 8), thermodynamics of mixing and compo-
sition change (Chapter 9), and chemical equilibrium
(Chapter 10).
In addition to the above, however, there are also
introductory chapters on statistical thermodynam-
ics (Chapter 5) and irreversible thermodynamics
(Chapter 11). Moreover, there are sections on nu-
clear energy, electrochemical processes, and fuel cells
Summer 1991

which are not generally found in introductory text-
books of thermodynamics.
Not unexpectedly, the breadth of coverage comes
at the expense of depth. Thus, the discussion on
cubic equations of state stops at the van der Waals
equation, with a brief mention of the Redlich-Kwong
equation but no mention of the other variants widely
used in chemical engineering process calculations.
Also, none of the modern analytic versions of the
corresponding states principle are described. More
importantly for chemical engineers, only the van
Laar equation is discussed as a solution to the Gibbs-
Duhem equation, and none of the recent activity
coefficient models are mentioned. The section on
fluid phase equilibria is therefore all too brief. Fi-
nally, statistical thermodynamics is only discussed
from the point of view of providing a molecular ex-
planation of entropy, and the reader is not given any
indication that it could lead to, for example, equa-
tions of state for real fluids.
Nevertheless, the book achieves reasonable depth
in many cases and offers a possible alternative to the
texts more specifically designed for chemical engi-
neers. It is particularly suited to students who are
introduced to thermodynamics in their sophomore
or even their freshman years. It appears to be suit-
able as a self-teaching text because it makes liberal
use of worked examples and certainly provides a
broader view of the applications of thermodynamics.
Perhaps it could serve as a supplementary text in
undergraduate chemical engineering thermodynam-
ics courses. Students will certainly find reading it
worthwhile. C

I books received

Understanding Process Integration II, by R. Smith; Hemisphere
Publishing Corp., 79 Madison Ave., New York, NY 10016-7892;
360 pages, $79.50 (1988)
Thermo- and Laser Anemometry, by Polyakov; Hemisphere Pub-
lishing Corp., 79 Madison Ave., New York, NY 10016-7892; 173
pages, $40.00 (1988)
Basic Concepts of Chemistry (Third Edition), by Leo J. Malone;
John Wiley and Sons, 1 Wiley Drive, Somerset, NJ 08875-1272;
682 pages, $42.50 (1989)
Chemical Information: A Practical Guide to Unilization, 2nd Edi-
tion, by Yecheskel Wolman; John Wiley & Sons, Inc., 1 Wiley
Drive, Somerset, NJ 08875-1271; 291 pages, $44.95 (1988)
Chemistry: Experiment and Theory, Second Edition, by Bernice
G. Segal; John Wiley & Sons, Inc., 1 Wiley Drive, Somerset, NK
08875-1272; 1008 pages, $49.22 (1989)
EngineeringApplications Software Development Using FORTRAN
77, by G. A. Moses; John Wiley & Sons, 1 Wiley Drive, Somerset,
NJ 08875-1272; 320 pages, $39.95 (1988)

curriculum

AN INTRODUCTION TO EQUILIBRIUM

THERMODYNAMICS

A Rational Approach to Its Teaching

PART 2: Internal Energy, Entropy, and Temperaturel

DONALD F. WILLIAMS, DAVID GLASSER
University of the Witwatersrand
Johannesburg, South Africa

n Part 1 of this paper, we introduced notation for
functions and their derivatives, and through
using this notation, we formulated a purely
mathematical background, based on the properties
of functions. We shall now show an approach that
may be used to introduce the fundamental ideas of
thermodynamics.
We start by explaining to the students that the
purpose of thermodynamics is to enable us to corre-
late and predict the behavior of real systems con-
taining matter. In doing this, we shall use the mathe-
matical background which was formulated in Part 1,
together with a knowledge of the behavior of matter
(which is studied in such subjects as physics and
applied mathematics).
Additionally, we will need to make some basic

9 A
n

1)

Donald Williams has taught at the University of the
Witwatersrand since 1967. He has a special interest
in teaching chemical engineering to students at the
junior end of the curriculum and has recently devised
a new course to be taught to first-year students. His
interest in improving the teaching of thermodynamics
was first aroused while being taught by David Glas-
ser in one of his earliest efforts.

David Glasser is a professor of chemical engineer-
ing at the University of the Witwatersrand. He holds
degrees from the University of Cape Town and Im-
perial College (London). His main areas of interest
are reaction engineering and mathematical model-
ing. He has been interested in teaching thermody-
namics ever since he first became involved after
being "made an offer" as the most-junior member of
the academic staff.

4N

I

I Part 1 of this paper, "Notation and Mathematics," was published
in CEE, Vol 25, No 2 (Spring 1991).

assumptions or axioms, which we have labeled be-
low as "postulates." There can be no a priori justifi-
cation or "proof' of such postulates, and some of
them may seem at the time to be rather peculiar.
The only reason for using these assumptions rather
than others is that the equations which result seem,
from experience, to be useful in our stated purpose
of predicting the behavior of matter-containing
systems.
This state of affairs is similar to the exposition of
Euclidean geometry, where we first had to accept a
number of axioms (such as "parallel lines never meet,"
and "vertically opposite angles are equal"). We could
then develop a succession of theorems (many of which
have results which now seem second nature to us)
which have proved to be useful in many areas of the
science of measurement. Alternative sets of axioms
(such as, for example, "parallel lines do meet") lead
to the development of alternative (non-Euclidean)
geometries, some of which are, in fact, found to have
uses in other areas.
Physical Background
We should agree, before we begin, that we have
an understanding from physics of the concepts of
length, time, and mass, to which we shall add the
chemical concept of the measurement of amount of
material in number of moles rather than mass.
The concept of length extends readily to give us
area and volume. Combined with time, it gives us
the concepts of velocity and acceleration. From mass
and acceleration (or from momentum, obtainable from
mass and velocity) we may obtain the concept of
force. From force and area we obtain pressure, and
from force and length we obtain work. We therefore
assume that we have a common agreed-upon under-
standing of these ideas, which we shall not bother to
Copyright ChE Division, ASEE 1991
Chemical Engineering Education

define more fully at this point.
We shall need to consider a number of "thought
experiments" involving these concepts. Some of these
we could actually perform; others are somewhat ideal-
ized, so that it might be difficult to set them up
exactly in practice. But we should have no difficulty
in envisaging the outcome of these procedures. In
some of them we shall need the concept of tempera-
ture. It is more difficult to agree upon an exact quan-
titative definition of temperature at this point, but
we should be able to agree that we have common
concepts of "hotter" (= higher temperature) and
"colder" (= lower temperature).
Conservation of Energy
Our basic primary axiom is that energy is con-
served. We can no more prove this than we can any
of the other postulates which we shall make below,
although we may perhaps take comfort in the suc-
cessful description of the behavior of matter in the
vast amount of science (in addition to thermodynam-
ics) which has as its basis the Principle of Conserva-
tion of Energy.
We now need to develop a quantitative mathe-
matical expression of this principle. We might start
by saying that if energy is conserved, the energy of a
body or system in state 2 must be the same as it was
in state 1, which we might express as
Ei = E2 (42)
Now, what terms go to make up the energy E? If
we consider experiments which we might make with
falling stones or moving projectiles, experiment would
lead us to conclude (in an idealized situation) that
the energy of these bodies was made up of the sum of
the two separately identifiable forms of energy which
we call kinetic and potential energies. Thus, we could
re-write Eq. (42) as
EK1 + Ep1 = EK2 + Ep2 (43a)
or
AEK + AEp = 0 (43b)
where we are assuming the usual definitions that
EK = mv2 and Ep = mgh.
Consideration of the state of affairs when we
raise our stones by hand (increasing their Ep with-
out changing EK) or proceed to throw them (increas-
ing their EK without decreasing Ep) shows that this
formulation is inadequate. We need to invent a con-
cept of the transfer of energy to the body (or system)
under consideration from an external source. Giving
this concept the symbol w, we may extend Eq. (43b)
to
Summer 1991

We start by explaining to
the students that the purpose of
thermodynamics is to enable us to
correlate and predict the behavior of real
systems containing matter.

AEK + AEp = w

(44)

(Of course, the Principle of Conservation of Energy
still applies overall since the corresponding equation
for our hand or other source of the energy term w
will be AE w = 0.) We find that Eq. (44) is now an
adequate description of these cases if we use a w
value calculated from

w = f dx

(45)

(where f is the force applied over distance x). We
may thus identify w with our prior concept of work.
But now consider what happens when our flying
objects hit the ground, or an immovable wall, losing
their EK and Ep without any w being apparent. We
are forced either to abandon the Principle of Conser-
vation of Energy, or (noting in passing that bodies in
such situations are observed to get hotter) to con-
clude that the energy which is "missing" from the
terms of Eq. (44) must still be present in another
form. We invent the concept of "energy of state" or
"internal energy" to account for this energy. Giving
this new concept the symbol U and extending Eq.
(44) to account for it, we obtain

AEK + AEp + AU = w

(46)

We shall not continue the argument further at
this point, but will merely note that further addi-
tions to the left-hand side of Eq. (45) may be neces-
sary in situations where energy is present in forms
which we have not accounted for. Terms such as
magnetic, electrostatic, or surface energies may need
to be introduced (or these may be regarded as an
extension of the concept of potential energy).
We find by experiment that if we put a fixed
amount of some specific material (such as oxygen
gas) into a well-insulated enclosure, we can totally
define the properties of the material if we know two
of the variables, such as the values of the pressure
and volume. That is, whatever happened before, if
we know the "state of the system" (i.e., the values of
the pressure and volume), then we know that the
values of other variables (such as density, refractive
index, and thermal conductivity) will be uniquely
determined. In other words, we know that these

other variables are a function of pressure and (spe-
cific) volume only.
It turns out in practice that not all pairs of vari-
ables are equally good for uniquely determining the
state of the system. For example, pressure and vol-
ume will not uniquely determine the state of liquid
water close to 4C, where the density goes through a
maximum. Thus, our postulates will later be made
in terms of specific pairs of variables which do not
have such problems associated with them.
Now consider an experiment such as the one
shown in Figure la. Material contained in a well-
insulated enclosure may be agitated by the stirrer or
acted upon by the piston. The movements of the
piston and the stirrer shaft both involve work which
we may measure in terms of our accepted concepts of
force-times-distance (or the straightforward exten-
sion to torque-times-rotation). The pressure and vol-
ume of the material in the container are also meas-
urable quantities.
Now consider the changes in P and V which we
may obtain in this apparatus. (For this purpose it
may be easier to first consider the contents to be a
gas-but similar, more complex, apparatus could at
least be envisaged for other materials.) By pushing
or pulling on the piston we may change the P and V
of our gas along curved lines such as those shown
in Figure lb. (If we had an ideal gas, these would
be the lines PVY = constant.) By rotating the
stirrer with the piston held fixed, we find that we in-
crease the temperature, and hence the pressure, at a
fixed volume.
By utilizing suitable portions of such paths, we
find that not only can we move (in one direction,
anyway) between any pair of points, but we can also,
in fact, do so by a variety of different paths. Figure
lb shows two of the infinitely many paths from point
1 to point 2. For each path, we may measure the sum
of the work done by the stirrer and the piston.
We find that, for fixed final and initial points, the
total work required is a constant, irrespective of the
path taken.

Now consider the energy conservation equation,
Eq. (46). Since there are no changes in the kinetic or
potential energies of our stationary apparatus, the
equation in this case reduces to

AU = w

initial and final states, not on the path. By choosing
some arbitrary reference state (say, Po,Vo) and as-
signing it a value of U (say, Uo = 0), we may by a
suitable experiment measure the value of U at any
other (P,V) point. Therefore we need have no further
"understanding" of the nature of our quantity U; it
is sufficient that we can measure it (and that it
will prove in due course to be a useful concept for
our purpose).
However, if we perform these experiments in an
apparatus that is not well insulated, all our care-
fully thought-out theory appears to collapse. Indeed,
in some cases an apparatus left in state 2 may re-
turn to another state without the performance of
any work w. Rather than abandon the Principle of
Conservation of Energy, we conclude that there must
be other ways than work of transferring energy to
the system. We give this means of transferring en-
ergy the symbol q, and Eq. (46) becomes

AEK + AEp + AU = w + q

(48)

We may obtain quantitative values of q from
experiments in an apparatus such as the one shown
in Figure 2. From experiments performed as in Fig-
ure 1, we may obtain the AU value for any change.
Thus (theoretically at least) we know the depend-
ence of U on P and V, which is the function UPV. The
energy balance for experiments conducted as in Fig-
ure 2 may be rearranged to give
q = AEK + AEp + AU w (49)

Experiments (or processes) for which Eq. (46) (or
Eq. 47) is an adequate description are termed
adiabatic processes and need to be surrounded by
perfectly insulating or adiabatic surfaces. Those in
which it is necessary to allow for the energy transfer
term q are said to be non-adiabatic, and the surfaces
which permit energy to be transported through them

(47)

Thus, it appears that our concept of "internal
energy" U is a useful one, in that U turns out to be a
"state function"; that is, AU depends only on the

Ca]

Cb

FIGURE 1. System with work terms.
Chemical Engineering Education

in this fashion are called diathermal.
We note from experience that the energy trans-
fer term q occurs when our (non-adiabatic, or un-
insulated) system and its surroundings are at differ-
ent temperatures, and we give q the name heat. One
should be careful about the fact that heat q is an
energy transfer mechanism, not a form of energy
itself. Once energy has entered a system in this
fashion, it is indistinguishable from energy that en-
tered as work. It is incorrect to expect to be able to
find the "heat" inside the system. Terms such as
"heat content" or "conversion of heat into work" are
misleading; they are based upon a misunderstand-
ing of the equivalent roles of heat and work as en-
ergy transfer mechanisms. Because of the fact that
both q and w refer to energy transfer processes rather
than to quantities of some substance (caloric!), it is
convenient to emphasize this by calling q "heating"
and w "working." This has the advantage of being re-
lated to the words used by other authors, but em-
phasizing the process aspect.
Neither q nor w is, of course, confined to adding
energy to the system. Both are also possible ways for
energy to leave the system. Thus, if the piston in
Figure 1 or 2 moves so as to increase the volume, it
actually has work done on it by the contents of the
apparatus, the energy of which therefore decreases.
We also know that if the non-adiabatic apparatus is
hotter than its surroundings, it will lose energy as
heat to the surroundings.
If we use different amounts of substance in our
experiments in order to determine UPv, we will ob-
tain different relations (or surfaces in U-P-V space).
We find, however, that we may reduce these all to
one surface by considering not volume V, but molar
volume, given by iV = V/N, where N is the number of

moles of material involved. This gives us values of
specific internal energy, or molar internal energy,

U = Uv

(50)

We say that U is an extensive property,
which depends on the amount of material present,
while U is an intensive property, which depends only
on the state (or condition) of the matter, not on how
much there is.
In Part 1 of this paper, we assumed a function
Usv and showed that this leads to Eq. (28)

(AU) = TdS- PdV= Q + W (28)
From our experiments, we have now obtained (for
processes where AEK = AEp = 0) the relationship

(AU)2 = q + w

(51)

Here we have used the subscript 1 to identify the
value from the equations of Part 1, and the subscript
2 to identify the physical values from our experi-
ment. The work term w results from the displace-
ment of the point of action of a force, or w = Jf-dx.
Suppose the process under consideration changes
under the influence of driving forces which are so
small that it is effectively in equilibrium at each
stage (such a process is termed reversible). It is then
easy to show from physical considerations that this
(force-times-distance) term may be expressed (in the
absence of work terms such as that for the stirrer in
Figure 1) as -JPdV.
We now choose to equate (AU)1 and (AU)2; that is,
we regard our internal energy U as the function Usv
of Part 1. This is in line with our experimental
finding that the state of a system depends only on
two independent variables. The ones we used before
were P and V, but once we have any two we can
easily change them to any other two with which
there is a monotonic relationship. (The reader need
not be disturbed by the fact that we have not yet
identified the variable S.) We may choose to identify
the V terms of both Part 1 and Part 2. Now consider
a series of experiments performed in the apparatus
of Figure 1, but without using the stirrer to increase
the internal energy. As we discussed in the previous
paragraph, the work done by (or on) the moving
piston is -IPdV. Thus the energy balance becomes

(AU)2 =-P2dV2 (52)
In these experiments, if dV2 is zero, it follows
that AU2 is zero. From Eq. (28), however, when dV1
is zero, we have

FIGURE 2. Apparatus for measuring q.
Summer 1991

(AU), = -J TdS1

(53)

It seems then, that whatever S represents is
constant during the experiments we are considering,
since (AU)1 must be zero as long as V is constant.
Thus we have, for these experiments,
(AU) = PdV1 (54)
Since we have equated the U and the V terms,
Eqs. (52) and (54) will only yield the required results
for all possible experiments if the P terms represent
the same quantity. We thus identify the variable P
which we defined in Eq. (16) by P = -Us' with our
physical concept of pressure.
It then follows that we may put

and hence

w = W = -PdV

q = Q = TdS

If the process is not at equilibrium at each
stage (that is, it is not a reversible process), then
w # JPdV. Thus for this type of process, w # W and
so q # Q. In practice, we seem to find that

w > W = -fPdV

so that

q< Q = TdS (58)

Predicting the Behavior of a System
Figure 3 shows an example of what we may re-
gard as the basic problem of thermodynamics; if we
can find a method for solving problems of this na-
ture, we shall in fact be well on the way to our
desired objectives. The diagram shows a container
constructed of walls which are
rigid so that the volume of the material which they
contain cannot change
adiabatic so that the transfer of energy to the contents of
the container by the "q" process is not possible
impermeable so that the material in the container cannot
penetrate the walls, nor can additional matter enter
through the walls
The container is divided into two sections by a
barrier, the material of which is also rigid, adiabatic,
and impermeable. The volumes on each side of the
divider contain material at specified conditions (na-
ture of the matter, amount of matter, temperature,
pressure, etc.). These conditions need not be the same
for each side.
We assume that each side of the apparatus is in
an equilibrium state, by which we mean that there

are no observable macroscopic changes in the state
of the matter in the system with time ("observable"
using whatever senses or methods of measurement
we might apply.) We shall further assume that we
are concerned with simple systems, which are chemi-
cally inert and homogeneous.
The problem which we wish to solve is this: Sup-
pose that one (or more) of the constraints imposed by
the barrier is removed. If we remove the rigidity
constraint, for example, we allow the barrier to move.
Removing the adiabatic constraint permits energy
to transfer as q through the barrier while maintain-
ing the other constraints. Removing the impermea-
bility constraint would permit material to pass
through the barrier, which would still be rigid and
adiabatic. (It is less easy to think of how this might
be achieved directly in practice, but that is no reason
for not considering the problem.) When any of the
constraints are removed, we can see that in general
some (at least) of the conditions in the two sections
of the apparatus will change. We wish to predict the
new equilibrium states that will result.
We know from experiments that if we release the
constraints, certain things will happen, but not the
reverse. For example, pressure, temperature, and
concentrations tend to equalize, while the reverse
does not happen. These statements in no way violate
anything we have said before, but neither do they
give us any information as to which states the sys-
tem will proceed to at equilibrium. In order to de-
scribe these experiments it is necessary to have fur-
ther postulates. Furthermore, while we have agreed
that we have some idea of what constitutes a con-
stant S experiment, we have not really defined ei-
ther S or T. Thus, what follows addresses the defini-
tion of these quantities, and gives us results which
are in accordance with our knowledge of the real
world.

V V2

N j Nj 2

FIGURE 3. Apparatus with internal partition.

FIGURE 3. Apparatus with internal partition.

Chemical Engineering Education

Solving the Problem: The Postulates
We shall accept that matter contained in a sys-
tem in an equilibrium state has an internal energy
U, and that this is an extensive property (so that it is
proportional to the amount of material present) and
an additive property (so that the total internal en-
ergy of the apparatus is the sum of the internal
energy of the two portions). We shall then make our
first postulate:
POSTULATE 1: Equilibrium states are completely
characterized by the values of U, V, and N -that is, by
their internal energy, volume, and number of moles of
various materials which they contain.
Note that this is entirely consistent with our
experimental knowledge that (for a fixed amount of
a given substance) the equilibrium properties are a
function of two variables. The two variables that are
chosen are a pair which do not give rise to the prob-
lems with uniqueness discussed earlier.
We now consider how to predict the state to which
our system will move when we relax (as discussed
above) one of the internal constraints. Will it, for
example, move to the state of lowest energy? This
idea might sound attractive; unfortunately, a little
further thought shows that the rigid, adiabatic na-
ture of the external walls (which constraints are not
going to be relaxed) means that both q and w will be
zero. Hence AU = q + w = 0; that is, the total internal
energy of the system is going to remain constant.
Thus, this suggestion is not correct. We need some
further postulates:
POSTULATE 2: Each equilibrium state of a simple system
has a property S, to which we shall give the name
entropy. This can be modeled mathematically by
S= SUV,[Nj](U,V,[Nj]) where SU'v[Nj >0 (59)

U 1U 2
V V
1 ,2 2

N l Nj 2

FIGURE 4. Alternative form of experiment.
Summer 1991

POSTULATE 3: Entropy S is extensive. That is, S = NS,
and for a composite system of n equilibrium states of
simple systems, the total entropy is additive; that is

S= sk (60)
k=1

Now let us consider the apparatus of Figure 3.
Suppose that we have the apparatus in an initial
state, with the contents of the two sides at different
conditions. The material in each side is in an equilib-
rium state. Suppose that for each side we know the
function S = S,VNj. We may therefore calculate the
entropies S1 and S2 of the two sides of the apparatus,
and from Postulate 3, the total entropy, which is
given by Stot = S, + S,
We now relax the adiabatic constraint imposed
on the internal partition. This means that energy
may move (as q) between the two sides of the appa-
ratus. We want to be able to predict the conditions
on each side of the partition when the apparatus
reaches its new equilibrium state (we shall call this
Experiment 1). The energy balance for either side of
the apparatus is of the form AU = q + w, but w = 0
since the barrier is rigid (AV = 0). Thus after energy
q has moved from one side to the other, the internal
energies will be U1 q and U2 + q, respectively. V1,
V, Nj, and N2j remain unchanged. We may there-
fore calculate new values for S,, S2, and Stot.
Consider now the alternative form of the experi-
ment shown in Figure 4 (which we shall call Experi-
ment 2). Here the adiabatic nature of the partition is
maintained, but some form of "energy exchange
machine" removes energy k from side 1 and adds
the same quantity of energy to side 2. Again, we
may calculate the total entropy Sk11, which by Postu-
late 3 equals S, + S2 for any value k of the energy
transferred.
We now postulate that the equilibrium state that
will be reached in Experiment 1 is the same as the
state of Experiment 2, at which Sktot has its maxi-
mum value. Notice that at each stage of Experiment
2, after transferring energy k, we have to wait for
the two parts of the apparatus to reach equilibrium
states before we can calculate S, and S2, since Postu-
lates 1 and 2 both apply only to equilibrium states.
It would therefore be wrong to say that in Experi-
ment 1 conditions change so that S goes to a maxi-
mum. While conditions in the apparatus are chang-
ing, it is obviously not in an equilibrium state, and S
is not defined. We therefore state our new postulate
as follows:

POSTULATE 4: The equilibrium state resulting after the
removal of an internal constraint is that possible
constrained state with maximum entropy. (We assume
that there is only one such constrained maximum.)
Let us now apply the theory we have stated to
the solution of the problem of Experiments 1 and 2.
We have
dU = TdS PdV + IgpidNi (61)

If we consider only small values of the differentials
dU, dS, dV, and dNi, then these small values on the
tangent plane will correspond to small changes in
the physical system. (If the changes are not small,
the values of the [derivatives] T, P, and gi of the real
system will change, so that the differentials [which
all lie on the tangent plane at a particular point] no
longer represent possible states of the real system.)
Identifying these small values by the symbol 6, we
may write
8U = T6S P8V + I i8Ni (62)

Since the partition retains its rigid and imperme-
able nature, we know that
5V1 = 8V2 = 0 (63)
and
6Nlj = 5N2j = 0 (64)
Thus
5U, = T18S1 and 8U2 = T28S2 (65)

or

Now

5S = 1 6U
1

and 5S2 = 16U2
T2

5Stot = 6S + 8S2 (67)

= 8U1 +25U2 (68)

For the whole apparatus, the energy is the sum of
that in the two portions; hence
Utot = U1 + U2 (69)
Since the exterior walls are rigid, impermeable, and
adiabatic, the total energy of the apparatus is con-
stant (q = w = 0), i.e.,

Hence

Thus

From which

Equation (73) follows from Eq. (9); although the 6
values are small, they are still differentials, since
they came from Eq. (61).
For a maximum of Su1, this derivative will be
zero. Thus, Postulate 4 tells us that at the new equi-
librium state we will have

1 1__0
T1 T2

or Ti = T2

(74)

Temperature
We may also consider what happens if we do not
allow the system to go all the way to this final
equilibrium state; that is, if we relax the adiabatic
constraint on the barrier for only a short time and
then reimpose it. This is the same as operating the
apparatus in Figure 4, but using the energy-transfer
machine to transfer a lesser amount of energy than
would maximize S.
Suppose that the initial state of the system is
such that when we relax the adiabatic constraint on
the internal partition, energy moves as heat from
compartment 1 into compartment 2. It follows that
U1 will decrease (and U2 will increase by the same
amount). These changes in U1 and U2 will cause a
change in Stot (as in Eq. 68) which must be positive,
since S must change towards its maximum. Con-
sider the graph of Sot versus U1, as shown in Figure
5. Since we have AU1 < 0 and AStot > 0, we have
moved from a point such as A towards a point such
as B, and along this curve
SU1
tot (75)
thus

1 1
^--<0
T1 T2

SLot

5Utot = 8U1 + U2 = 0

5U1 = -6U2

_1 i T2
U1
astot 1 1
uU1 T1 T2

or Ti > T2

(76)

U1

FIGURE 5. Maximum of SU
Chemical Engineering Education

By a similar argument, we can see that if the
heat flow is from compartment 2 to compartment 1,
AU1 will be positive, and we will be moving from
a point such as A' towards B'. Thus the derivative
of Eq. (75) will be positive, and we will conclude that
T, < T2.
Finally, we note that in Eq. (16) (or Eq. 75) we
defined T by 'v

T =U
which is exactly equivalent to the definition

T = Us V

(16)

system
S = K(NVU)1/3 (79)
where N is the total number of moles involved. From
this expression

from which

(77)

It follows that T is intensive, i.e., independent of the
amount of material we are considering.
We thus have for the quantity represented by our
symbol T that
it is intensive
at equilibrium, in the absence of any adiabatic constraint,
we find that T, = T2
prior to equilibrium, q moves from 1 to 2 when T, > T2
and from 2 to 1 when T, < T2
We thus see that T fulfills all our intuitive no-
tions of the concept of temperature, and we shall in
the future identify T with temperature. We may
further note that it was part of Postulate 2 that
SVN > 0
S '>O

hence

Us N = -1 > 0
U VNj
S

(78a)

T > 0 (78b)

Equations of State
Postulate 2 (Eq. 59) tells us that we may write
the entropy of a simple system in an equilibrium
state as a function of the internal energy U,
the volume V, and the number of moles of various
materials:

S = SU V'Nj
Now recall the definitions of T and P
T = v = Tsv
and
P = -USV = PSV

(59)

(18)

(16)

We may substitute for S in these equations from Eq.
(59) and then eliminate S between the resulting
equations to obtain a relationship between V, T, P,
and N.. As an example, suppose that for a particular
Summer 1991

_USv 352
as NVK3
SV 3
p aU S3
aV NV2K3

P2V = N T3K3
27

(80)

(81)

(82)

These relationships between P, V, T, and N are
the form of equation of state to which we are accus-
tomed in physics and chemistry. Notice that, unfor-
tunately, it is not in general possible to reconstruct
Eq. (79) or its equivalent from Eq. (82), the equation
of state, without further information. From Eq. (82)
we have

uSVv ( aUSV
WV 27 v-
27 [u8)

(83)

and we cannot obtain a solution to this partial differ-
ential equation without boundary conditions.
Units and Value for Temperature
If we consider our definition T = US', we see that
the units and value of T will depend upon those
which we ascribe to S. Working in the other direc-
tion, we may choose to give T arbitrary units of
degrees Kelvin. Since U must have energy units,
this means that we are assuming units of J/K for S,
or J/mol K for S.
For historical reasons, we are probably stuck with
this system. If we were free to start from scratch it
might be more logical to let S be dimensionless,
which would result in measuring temperature in
Joules per mole. In particular, it would be possible to
choose a temperature scale such that the ubiquitous
"gas constant" R = 8,314 J/mol K (and many other
possible equivalent values) had a dimensionless value
of 1. The time saved by chemists and chemical engi-
neers in units conversions involving R would surely
be enormous!
Other Versions of the Problem
We have considered only one version of the prob-
lem posed above. The reader should be able to pro-
vide the solution to other versions and show, for
example, that
relaxation of the rigidity constraint on the partition
leads to a final equilibrium state in which the pressures
in the two compartments are equal

removal of both the adiabatic and rigidity constraints
results in a final equilibrium state in which both the
temperatures and the pressures in the two
compartments are equal
removal of the adiabatic and impermeability constraints
gives a final equilibrium state in which the
temperatures are equal and pi = p12 for all i.
We may regard T as a "thermal potential," in
that a difference in T tends (in the absence of con-
straints) to cause energy to transfer as q. Similarly,
P is a "mechanical potential," tending to cause work
to be done (as an JPdV term). In the light of the third
result above, we name [t the chemical potential, since
a difference in i, produces a potential for the move-
ment of component i.
We note that in this approach it is not necessary
to "define" S by way of equations such as 6S = 6q/T,
where the value of 5q is so circumscribed that the
equation really has no meaning, and the student
ends up learning the subject (if at all) by a hierarchi-
cal process of learning what is or is not permissible.
The difficulty of trying to understand the "meaning"
of entropy is obviated by having a perfectly formal
way of defining it. Thus we only need to calculate its
value, not to understand it.

ACKNOWLEDGEMENTS
The two parts of this paper lean heavily on the
approach of our former colleague, W. F. Harris. He
introduced the thermodynamics course in this
form at our university, but unfortunately his inter-
ests turned elsewhere before he could produce the
definitive write-up we were always promised. It is
therefore true to say that the felicities of the
approach are his, and any faults in the detailed
development are ours. 0

REVIEW: Introduction to Rheology
Continued from page 131.
phenomena, to material functions, and to the impor-
tance of rheology in industrial processes. The text is
complemented by numerous tables and figures that
illustrate the behavior of a wide range of materials.
Theoretical and empirical relationships among ma-
terial functions are discussed in these chapters, and
well-known models for non-Newtonian viscosity (e.g.,
power law, Carreau, Bingham) and for linear viscoe-
lasticity (e.g., Kelvin, Maxwell, Jeffreys) are pre-
sented.
Each of the chapters mentioned above includes a

section describing the experimental measurement of
the material functions discussed in the chapter. This
emphasis on rheometry will be interesting and use-
ful to many readers, especially those involved with
theological characterization of materials. Measure-
ment techniques and configurations of commercial
rheometers and research instruments are surveyed,
and the suitability of particular types of instruments
for particular tasks is discussed. Theoretical prin-
ciples of measurements in various rheometer geome-
tries are presented, and excellent introductory dis-
cussions of the factors limiting the range and accu-
racy of measurements are provided.
While the first part of the book is concerned with
general aspects of rheology, the sixth and seventh
chapters are devoted, respectively, to the rheology of
polymeric liquids and the rheology of suspensions.
These chapters provide an overview of two impor-
tant areas of rheology, and also include introduc-
tions to topics of current research interest such as
liquid crystal polymers, reputation models, and nu-
merical simulations of suspension rheology.
The final chapter returns to continuum mechan-
ics, a topic no doubt dreaded by many of the in-
tended readers. But those who persevere are re-
warded by a concise statement, mostly in words
rather than equations, of the principles of contin-
uum mechanics that govern the formulation of con-
stitutive equations. A highly condensed survey of
the mathematical forms and theological predictions
of constitutive models is also included. This brief
chapter refers interested readers to many excellent
references for more detailed treatments of the sub-
ject.
Throughout the book, the authors guide the reader
toward more comprehensive sources of information,
and the reference list is excellent and up-to-date.
Although the treatment of many topics is necessar-
ily brief, it is authoritative, and beginning rheolo-
gists will not need to relearn the material as they
advance in their sophistication. The text is well writ-
ten, and it is infused with explanations of the his-
tory and development of rheology, which enhance
the reader's pleasure as well as his or her under-
standing. The book is very suitable as a textbook for
an introductory course in rheology. However, the
material is not presented in a problem-oriented style,
and some instructors may feel that the absence of
example and homework problems is a drawback.
The book is certainly well suited for individual study,
and I would recommend it highly to anyone seeking
a sound, but accessible, introduction to rheology. 0

Chemical Engineering Education

AUTHOR GUIDELINES

This guide is offered to aid authors in preparing manuscripts for Chemical Engineering
Education (CEE), a quarterly journal published by the Chemical Engineering Division of the
American Society for Engineering Education (ASEE).
CEE publishes papers in the broad field of chemical engineering education. Papers generally
describe a course, a laboratory, a ChE department, a ChE educator, a ChE curriculum, research
program, machine computation, special instructional programs, or give views and opinions on
various topics of interest to the profession.
Specific suggestions on preparing papers.
TITLE Use specific and informative titles. They should be as brief as possible, consistent
with the need for defining the subject area covered by the paper.
AUTHORSHIP Be consistent in authorship designation. Use first name, second initial, and
surname. Give complete mailing address of place where work was conducted. If current address is
different, include it in a footnote on title page.
TEXT Manuscripts of less than twelve double-spaced typewritten pages in length will be
given priority over longer ones. Consult recent issues for general style. Assume your reader is not a
novice in the field. Include only as much history as is needed to provide background for the
particular material covered in your paper. Sectionalize the article and insert brief appropriate
headings.
TABLES Avoid tables and graphs which involve duplication or superfluous data. If you can
use a graph, do not include a table. If the reader needs the table, omit the graph. Substitute a few
typical results for lengthy tables when practical. Avoid computer printouts.
NOMENCLATURE Follow nomenclature style of Chemical Abstracts; avoid trivial names.
If trade names are used, define at point of first use. Trade names should carry an initial capital
only, with no accompanying footnote. Use consistent units of measurement and give dimensions
for all terms. Write all equations and formulas clearly, and number important equations consecu-
tively.
ACKNOWLEDGMENT Include in acknowledgment only such credits as are essential
LITERATURE CITED References should be numbered and listed on a separate sheet in the
order occurring in the text.
COPY REQUIREMENTS Send two legible copies of the typed (double-spaced) manuscript
on standard letter-size paper. Clear duplicated copies are acceptable. Submit original drawings (or
clear prints) of graphs and diagrams, and clear glossy prints of photographs. Prepare original
drawings on tracing paper or high quality paper; use black india ink and a lettering set. Choose
graph papers with blue cross-sectional lines; other colors interfere with good reproduction. Label
ordinates and abscissas of graphs along the axes and outside the graph proper. Figure captions
and legends may be set in type and need not be lettered on the drawings. Number all illustrations
consecutively. Supply all captions and legends typed on a separate page.

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This year P&G will spend over $700 million in research
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	Front Cover
	Table of Contents
	Andreas Acrivos, of the City College,...
	University of Massachusetts
	Inventing multiloop control systems...
	Book reviews
	It goes without saying
	A novel freshman class to introduce...
	Errors: A rich source of problems...
	Determining the kinetic parameters...
	Chemical reaction engineering applications...
	Books received
	A simple heat of crystallization...
	Book reviews
	Development and use of open-ended...
	Book reviews and books receive...
	An introduction to equilibrium...
	Back Cover

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