Chemical engineering education

Material Information

Chemical engineering education
Alternate Title:
Abbreviated Title:
Chem. eng. educ.
American Society for Engineering Education -- Chemical Engineering Division
Place of Publication:
Storrs, Conn
Chemical Engineering Division, American Society for Engineering Education
Publication Date:
Annual[ FORMER 1960-1961]
Physical Description:
v. : ill. ; 22-28 cm.


Subjects / Keywords:
Chemical engineering -- Study and teaching -- Periodicals ( lcsh )
periodical ( marcgt )
serial ( sobekcm )


Chemical abstracts
Additional Physical Form:
Also issued online.
Dates or Sequential Designation:
1960-June 1964 ; v. 1, no. 1 (Oct. 1965)-
Numbering Peculiarities:
Publication suspended briefly: issue designated v. 1, no. 4 (June 1966) published Nov. 1967.
General Note:
Title from cover.
General Note:
Place of publication varies: Rochester, N.Y., 1965-1967; Gainesville, Fla., 1968-

Record Information

Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
01151209 ( OCLC )
70013732 ( LCCN )
0009-2479 ( ISSN )
TP165 .C18 ( lcc )
660/.2/071 ( ddc )

UFDC Membership

Chemical Engineering Documents


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Chemical Engineering Division, American Society for Engineering Education,
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ASEE Chemical Engineering Division, 11 DuPont Circle,
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University of Florida, Gainesville, FL 32611
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Department of Chemical Engineering
University of Florida
Gainesville, Florida 32611

Editor: Ray Fahien (904) 392-0857
Consulting Editor: Mack Tyner
Managing Editor:
Carole C. Yocum (904) 392-0861
Publications Board and Regional
Advertising Representatives:
Lee C. Eagleton
Pennsylvania State University

Past Chairman:
Klaus D. Timmerhaus
University of Colorado

Homer F. Johnson
University of Tennessee
Jack R. Hopper
Lamar University
James Fair
University of Texas
Gary Poehlezn
Georgia Tech
Robert F. Anderson
UOP Process Division
Lowell B. Koppel
Purdue University
William B. Krantz
University of Colorado
C. Judson King
University of California Berkeley
Frederick H. Shair
California Institute of Technology
Angelo J. Perna
New Jersey Institute of Technology
Stuart W. Churchill
University of Pennsylvania
Raymond Baddour
A. IV. Westerberg
Carnegie-Mellon University

Charles Sleicher
University of Washington
Leslie W. Shemilt
McMaster University
Thomas W. Weber
State University of New York

Chemical Engineering Education


The Educator
2 Klaus Timmerhaus of the University of Colorado,
Martin S. Barber

Department of Chemical Engineering
6 University of Maryland
T. W. Cadman, R. B. Beckmann

Views and Opinions
12 Cheating-An Ounce of Prevention... or the Tragic
Tale of the Dying Grandmother,
Richard M. Felder

22 Toward Encouraging Creativity in Students,
J. M. Prausnitz

18 A Simple Geometrical Derivation of the Spatial
Averaging Theorem, Stephen Whitaker
40 Extended Form of the Gibbs Phase Rule, Y. K. Rao
44 Simulation of Simple Controlled Processes with
Dead-Time, Keith Watson, Julius P. Wong,
Pradeep B. Deshpande

26 Computer-Assisted Laboratory Stations,
William J. Snyder, Michael E. Hanyak

30 A Sequential Design Laboratory Experiment for
Separating Particles by Fluidization
Principles, Donald D. Joye

36 A Resource-Based Approach to ChE Education,
R. B. Newell, P. L. Lee, L. S. Leung

II Editors Note
10, 17, 25, 29, 35, 45 Book Reviews
35 Letters
35 Books Received

CHEMICAL ENGINEERING EDUCATION is published quarterly by Chemical
Engineering Division, American Society for Engineering Education. The publication
is edited at the Chemical Engineering Department, University of Florida. Second-class
postage is paid at Gainesville, Florida, and at DeLeon Springs, Florida. Correspondence
regarding editorial matter, circulation and changes of address should be addressed
to the Editor at Gainesville, Florida 32611. Advertising rates and information are
available from the advertising representatives. Plates and other advertising material
may be sent directly to the printer: E. O. Painter Printing Co., P. O. Box 877,
DeLeon Springs, Florida 32028. Subscription rate U.S., Canada, and Mexico is $20 per
year, $15 per year mailed to members of AIChE and of the ChE Division of ASEE.
Bulk subscription rates to ChE faculty on request. Write for prices on individual
back copies. Copyright 1985 Chemical Engineering Division of American Society
for Engineering Education. The statements and opinions expressed in this periodical
are those of the writers and not necessarily those of the ChE Division of the ASEE
which body assumes no responsibility for them. Defective copies replaced if notified
within 120 days.
The International Organization for Standardization has assigned the code US ISSN
0009-2479 for the identification of this periodical.



Klaai 3. Ti/mw~ihauci

of the University of Colorado

University of Colorado
Boulder, CO 80309

T HERE ARE SEVERAL Klaus Timmerhaus's. There
is a patient, careful teacher much appreciated
by his students. There is a researcher with varied,
broadscale interests. There is a demanding, per-
fectionist administrator, somewhat abrasive
toward his superiors but not towards his sub-
ordinates. There is an active officer and member
of eleven professional and research societies known
to a host of friends for both technical papers and
analytic, what-is-ethically-required policy an-
alyses. And there is a paradox: in most of these
capacities Klaus appears to work full time!
In fact, Klaus's Spartan, efficient work schedule
would be well worth study by anyone interested in
maximum levels of human accomplishment. One
item after another moves across his desk; written,
edited, or marked for action with lead pencil in
a minute script that can put more than 300 words
on a page. Each item gets an allotted amount of
time; drafting is so precise that revision is seldom
His day at the desk is unbroken except for three
noon hours per week spent in equally efficient exer-
cise: he does not jog; he runs. A brown-bag lunch
at the desk later is not allowed to interrupt output.
An additional pile of work goes home with him
after a ten-hour day.

Klaus's research interests have
concerned ultra-high pressures, cryogenics,
or both. Since the energy crunch of 1973, they
have also turned toward energy economics and
conservation. His recent book, Energy Conservation in
Arid Lands, has drawn praise not only from
colleagues, but also from some American
Indians who inhabit arid lands.

O Copyright ChE Division, ASEE, 1985

L d~I~

"- --1

Said CU's former dean of engineering Max S.
Peters, himself a widely known and honored chemi-
cal engineer: "I have known Klaus since 1951 and
have worked closely with him for more than the
past twenty years, and I can honestly say that he
is the most conscientious and dedicated person I
have ever known. He truly is a great chemical
engineer in every aspect of our field in addition to
being a true friend and a wonderful person."
Klaus graduated from high school in Palatine,
Ill., winning three letters in track and serving as a
student editor and student body president. As a
chemical engineering student at the University of
Illinois he worked in a hospital and became an
ambulance driver and one of the few chemical
engineers who has ever delivered a baby.
During World War II he served as a radar in-
structor and coached championship track teams.
Back at the university after the war, he played
hockey and competed in four track events. A neck
fracture sustained in an auto accident in January
of his senior year slowed him only briefly; at the
end of April he was back in competition with a cast
on his neck and his arm in a sling, winning the first
race he entered. Later that spring he won the
National AAU Junior Championship in the 1500
meter event.


He still runs in senior events, recently taking
up speed walking at the urging of Max Peters and
taking first in his age category in his first 5-k race.
He has served for many years as an official in high
school and college track events.
Klaus earned his degrees at Illinois, participat-
ing with his graduate adviser, H. G. Drickamer,
and others on several papers-on high pressure
science, appropriately enough. He joined the Uni-
versity of Colorado faculty in 1953 after nearly
two years of employment by Cal Research (Stand-
ard Oil of California) in Richmond, California, as
a project design engineer. He became associate
dean of engineering in 1963. The College of Engi-
neering and Applied Science of the University of
Colorado is a three-campus organization, and
Klaus's responsibilities extend to all three campus-
es. Primarily, they concern graduate and research
activities, but in practice they involve most as-
pects of engineering education, from undergradu-
ate accreditation to faculty evaluation.
Klaus is also director of the three-campus
Engineering Research Center, whose grants in
force have increased from less than $200,000 in
1953 to more than $9 million in 1984, while gradu-
ate enrollment has grown from 90 to 550. These
research gains have involved extensive work with
faculty members to develop research ideas and lo-
cate suitable funding sources. Klaus scrutinizes
each research proposal that leaves the college,
working with faculty members to increase clarity
and ensure that each request tallies with the needs
of the funding agency to which it is addressed.
Not all possible projects are solicited: with the
rare exception of projects serving Colorado groups,
no research project is accepted unless it has clear-
cut educational value.
Klaus's research interests have generally con-
cerned ultra-high pressures, cryogenics, or both.
Since the energy crunch of 1973, they have also
turned toward energy economics and conservation.
His recent book, Energy Conservation in Arid
Lands, has drawn praise not only from colleagues,
but also from some American Indians who inhabit
arid lands.
As a cryogenic consultant, Klaus has been in-
volved with such projects as a major natural gas
liquefaction plant in the Mideast and the nation's
largest superconducting particle accelerator. Klaus
sees good opportunities and a new future ahead
for the chemical industries, even though he fore-
sees that oil producing nations will see that it is
not in their best interests to ship raw materials and

will build the chemical plants and oil refineries
that will permit them to export more valuable
finished products. "Chemical engineering needs to
diversify into many different industries that can
benefit from the specialized training given to its
graduates," he said.. "For example, biotechnology
holds great promise. It can produce chemicals,
pharmaceuticals, coatings, paints, and plastics
from renewable natural resources. These in-
dustries build on principles of mass and energy
balance of chemicals and materials which are the
heart of chemical engineering."
He recommends that some chemical engineers
look for careers in the solid state area. "Electrical

In fact, Klaus's Spartan,
efficient work schedule would be
well worth study by anyone interested in
maximum levels of human accomplishment. One item
after another moves across his desk ...

engineers have a big problem in obtaining ultra-
pure silicon wafers. This is a chemical engineering
problem and not an electrical engineering prob-
lem and should be taught by chemical engineers."
Similarly, he looks for chemical engineers to show
the way in developing new separation techniques,
augmenting dwindling energy reserves with
unique renewable energy processes, perfecting
new conservation approaches, developing greater
reliability and safety in consumer products, and
initiating entirely new manufacturing processes
in outer space. He has been a proponent in AIChE
of examining this situation and is active in the
New Technology Committee that has been set up
by AIChE to consider future directions and oppor-
tunities for chemical engineering. All in all, he sees
myriad new areas for chemical engineers.
Among Klaus's current research interests is
the thermal conductivity-convection relationship
in porous insulation materials. Recent consulting
experience has led him to believe that current
values for convection in these materials are too
conservative, and he is planning checks on the
data. He is also studying the effect of a number of
variables on the distillation efficiency of simple
hydrocarbon mixtures.
As an educator, he also has some concerns about
future trends in university research: "We should
keep in mind that the university is not just a re-
search facility: teaching is still our main function
and teaching is getting short shrift in many


As an educator, he also has some concerns about future trends
in university research: "We should keep in mind that the university is not just a
research facility: teaching is still our main function and teaching is getting short shrift in many
instances. We must keep a careful balance and not push the pendulum too far.

instances. We must keep a careful balance and not
push the pendulum too far." He believes that all
faculty should be involved in research to help them
in their teaching activities. He stresses, however,
that we need to be careful to maintain a balanced
"The better students will be successful in spite
of this trend; however, students who are less

Dean Timmerhaus and graduate student Hasan Dindi
check a fractional distillation column in which the
separation of simple hydrocarbons is being studied.

academically inclined and/or who are not interest-
ed in advanced degrees will be the mainstay of in-
dustry. We must keep them capable or we will all
lose out."
Some implications of the information revolu-
tion also concern him. "There exists among engi-
neers the recognition that more and more our im-
proving communications systems are transferring
more and more data, so that we are getting clogged

with information. We need to devise ways of sift-
ing and picking out what is pertinent.
"Computers can help with this problem, but
we need to avoid excessive reliance upon comput-
ers. A computer search is no better than the key-
wording that it is based upon. We need to remain
aware that what comes out is no better than what
is put in. Computer simulation also has pitfalls.
Flawed models can lead to accidents and catastro-
phes. Simulations need to be checked against
"I believe that computers must be brought into
education and integrated into it. We also need to
integrate in other new concepts. We must take a
new approach to teaching safety principles, and
also economics, as an integral part of chemical
engineering. Today, no part of a process or pro-
duct can be allowed to remain unsafe. There will
be serious and unpleasant consequences if we do
not face up to the requirements of safety. If we
are using a process that is unsafe because pressure
is too high, or flow is too great, or the temperature
is too high, we may need to change the process so
that it is safe.
"We are likely to trip up on what we cut out
for economy reasons. Safety relief valves should
be placed in the right places and in the right
numbers when the plant is designed-not after it
is built.
"Therefore, in our design courses we must
teach chemical engineering, safety, and economics
all in the same problems. Safety and economics are
subjects that we educators have wanted to leave
to industry, while they wanted to leave them to us.
Education is where they belong; if they are
learned then they will be more likely to stick."
Klaus himself is a member of the Advisory
Board for the National Institute of Occupational
Safety and Health (NIOSH) and is incorporating
what he recommends into a new book on cryogenic
processes that he is preparing with Thomas M.
Among Klaus's other achievements has been
preparing a proposal for and securing an NSF
matching grant worth $1.325 million (in 1966
dollars) for construction of CU's Engineering
Center. As chairman, cochairman, or the like he


has been involved with securing other grants with
a value of about $6 million. He has also managed
from time to time to serve as college safety officer,
acting chairman of the aerospace department, and
on more than 70 campus committee assignments.
His output of professional publications is some-
what awesome: He has edited 25 volumes of Ad-
vances in Cryogenic Engineering; 17 in the Inter-
national Cryogenics Monograph series; 4 of Low
Temperature Physics, and 2 of The Proceedings
of the AIRAPT International High Pressure Con-
ference. He is coauthor with Max Peters of two
editions of the very popular Plant Design and
Economics for Chemical Engineers.
He has also published more than 70 technical
publications in refereed journals, presented more
than 70 technical presentations at national profes-
sional society meetings and has given more than
100 presentations to national, regional, and uni-
versity audiences.
The variety of his service has nearly been
matched by the varieties of honors it has brought
him; if he doesn't hold the record for awards to
a chemical engineering professor he must be a top
He was one of three American academicians ap-
pointed as the first Foreign Corresponding Mem-
ber of the Verein Deutscher Ingenieure, has been
elected as a fellow of the American Society for the
Advancement of Science and AIChE, and a diplo-
mate of the American Academy of Environmental
Engineering. He is an elected member of the
National Academy of Engineering and the
Austrian Academy of Science. The 1981 Cryo-
genic Engineering Conference was dedicated to
him in recognition of his 25 years of service to
Among a few of his major awards are the
second Samuel C. Collins Award of the Cryogenic
conference, presented in 1967; the George West-
inghouse award (for outstanding teaching) pre-
sented at the Diamond Jubilee meeting of the
American Society for Engineering Education in
1968; the Alpha Chi Sigma Award of AIChE,
which has also awarded him its Founders Award
and named him in 1983 as an Eminent Chemical
Engineer. His most recent award (at press time)
was the Distinguished Public Service Award of
the National Science Foundation.
His awards from the University of Colorado in-
clude the Distinguished Engineering Alumnus
Award, even though he is not an alumnus of the

A familiar figure on the track.

University of Colorado, the Robert L. Stearns
Award for distinguished faculty service, and
numerous student-recognition awards for his
teaching and service.
Among the numerous professional society
offices he has filled have been the presidency of the
AIChE, membership on the National Science
Foundation Advisory Council, and a regional di-
rectorship of Sigma Xi. He has served for many
years on the U. S. National Committee for the
International Institute of Refrigeration, and is its
1982-85 chairman. He is a vice president of the
Scientific Council of the International Institute of
Refrigeration and a former president of the
Southwestern and Rocky Mountain Division of the
Klaus's wife Jean keeps their life organized
while he works, and accompanies him upon some
of his constant professional travels. Hobbies the
couple share include hiking and fishing in Colo-
rado's mountains. [




[0 department



University of Maryland
College Park, MD 20742

E ENGINEERING AT MARYLAND dates back to course
instruction in surveying and construction
given in 1859 within the Maryland Agricultural
College. From this historical perspective, chemi-
cal engineering is a relative newcomer to Mary-
land Formal degree programs in mechanical
(1894), civil (1900), and electrical (1908) predate
chemical engineering, as do a series of reorganiza-
tions which led to the University of Maryland
system and the College of Engineering as we
know them today.
Chemical engineering at the University of
Maryland began in 1937 when, under founder and
first chairman Wilbert J. Huff, the four year pro-
gram leading to the baccalaureate degree (BS)
was introduced. Graduate programs at the MS
and the PhD levels were initiated in 1938 and
1939 respectively, marking the first of the gradu-
ate degree programs within the College of Engi-
neering at the University of Maryland.
Today chemical engineering is one of eight pro-
grams within the College of Engineering and one
of three programs administered through the De-
partment of Chemical and Nuclear Engineering.
Approximately 80 BS, 12 MS, and 3 PhD candi-
dates graduate from the chemical engineering pro-
gram per year at the present time.
The University of Maryland is a comprehensive
public system of five campuses: The University
of Maryland at Baltimore (UMAB), the Universi-
ty of Maryland Baltimore County (UMBC), the
University of Maryland College Park (UMCP),
the University of Maryland Eastern Shore
(UMES) and the University of Maryland Uni-
versity College (UMUC). The College of Engineer-
ing is one of 16 colleges and professional schools

Copyright ChE Division, ASEE, 1985

in the university.
Prior to 1984-'85, the degree granting activi-
ties of the college were only at the College Park
campus. Effective this fall, undergraduate degree
programs in chemical engineering and mechani-
cal engineering are also offered at UMBC, and
plans have been approved which permit the initi-
ation of graduate engineering degree programs.
The programs at both UMCP and UMBC are co-
ordinated by the Dean of the College of Engineer-


The present is a time of
rapid progressive change at the
University of Maryland.... One of the
newest additions to the College of Engineering is the
Engineering Research Center, established to promote
industry-university interactions.

ing, George Dieter, residing at UMCP and Associ-
ate Dean Albert Gomezplata, residing at UMBC.
The college offers accredited four year BS degree
programs in designated fields of engineering, in-
cluding chemical engineering, as well as a co-op
plan of study and a BS in engineering with inter-
disciplinary areas of specialization.

As noted above, chemical engineering is offered
as an undergraduate degree program at both
UMCP and UMBC. Graduate degrees are offered
only at UMCP. College Park is home for the ma-
jority of the program's current faculty and activi-
ties. The campus is located in an urban setting,
triangulated by Annapolis (20 miles to the east),
Baltimore City (25 miles to the northeast), and
the White House in Washington, D.C. (10 miles to
the southwest). The chemical engineering, nu-
clear engineering, and engineering materials pro-
grams form the Department of Chemical and Nu-
clear Engineering. Collectively they occupy the
chemical engineering building on the northern
side of the campus adjacent to chemistry, mathe-
matics, physics and the other departments of engi-
neering. UMBC is located in Catonsville, just
southwest of the City of Baltimore. The campus
features modern architecture in a rural setting.
Research facilities at College Park feature bio-
chemical engineering laboratories, the laboratory
for aerosol mechanics, the laboratory for process
analysis and simulation, polymer characteriza-
tion and process laboratories and multiphase
flow laboratories. The nuclear engineering pro-
gram provides access to a Co-60 source, a LINAC,
a 250 kilowatt pool reactor and, most recently, a
300 psig, 1/3 scale thermal-hydraulic simulation
loop of a nuclear reactor system. Facilities in X-
ray analysis, crystal growth and materials testing
are available in the engineering materials pro-

The present is a time of rapid progressive
change at the University of Maryland. Under the

dynamic leadership of President John Toll and
UMCP Chancellor John B. Slaughter, with Dean
George Dieter at the helm for the College of Engi-
neering, the change has been particularly signifi-
cant for the college. Resources have been provided
for a major enchancement of engineering at Mary-
land. An undergraduate enrollment limitation plan
has been implemented on the College Park Campus
and, as noted earlier, engineering programs have
been initiated at UMBC.
One of the newest additions to the College of
Engineering is the Engineering Research Center
(ERC), established to promote industry-university
interactions. Under Director Herb Rabin, an engi-
neering extension service has been initiated to
serve throughout the state, areas of technology
have been identified for initial emphasis by the
center, and plans are being drawn for an incuba-
tor program directed to the fostering of entre-
preneurial activity.
The impact on chemical engineering has been
quite significant. A particular emphasis has been
placed on the enhancement of our biochemical
engineering research program. An important as-

The 14 liter computer controlled fermentor in the Bio-
chemical Engineering Laboratory.

pect of the enhancement is a co-operative under-
taking with the ERC which has identified bio-
chemical engineering as one of the areas for
initial emphasis by the center. Under the auspices
of the ERC, a 500 liter fermentor system together
with auxiliary analysis and separations equip-
ment has been ordered, with delivery expected in
March 1985. In addition, the ERC staff position
of Manager, Chemical Engineering Programs, has
been established to coordinate collaborative re-
search activities between the faculty and local


industry. As of this writing, candidates are being
interviewed for this position. Initial emphasis is
to be gven to biochemical engineering and the
closely related areas of process simulation and
control research within chemical engineering.
The equipment acquisitions of the ERC in bio-
chemical engineering are viewed as the first step
in the development of a pilot plant facility for
scale-up and developmental research on bio-
processes. The facility is to be located in the chemi-
cal engineering building, complementing the bench
scale fermentors, analytical equipment, and PDP
11/34 data acquisition and control system present-
ly in our biochemical engineering laboratories.
The emphasis on biochemical engineering with-
in chemical engineering and the ERC reflects but
one aspect of a university-wide emphasis on bio-
technology. At the university level, Vice-Presi-

Undergraduate Steve Ahnert putting the final touches
on a new liquid level module in the Undergraduate
Process Control Laboratory.

dent of Academic Affairs Rita Colwell has initiated
the formation of four centers emphasizing areas
of biotechnology. The first is to be the Center for
Advanced Research in Biotechnology (CARB),
representing a collaborative effort between Mont-
gomery County, the National Bureau of Stand-
ards and the University of Maryland. At the pres-
ent time a full-time director for CARB is being
recruited, and plans for a building for the activi-
ties of CARB at Shady Grove, Maryland, are being
The chemical engineering initiative at UMBC
as well as the emphasis on biochemical engineer-
ing faculty additions at UMCP will increase the
number of chemical engineering faculty in the
Program to nearly twenty in the next several
years and will provide unique opportunities for

interaction with faculty experts in the biosciences
at UMBC, UMCP and UMAB. The enrollment
limitation plan of the college is just beginning to
alleviate a very heavy undergraduate load in
chemical engineering, permitting the allocation
of more faculty time and resources to the ex-
pansion of the PhD program and the research ac-
tivities of the faculty. In addition to biochemical
engineering, the program has particular research
strengths in aerosol mechanics, process simulation
and control, multiphase flow, and polymers. Within
the department, polymers has been identified as a
primary area for development in the Engineering
Materials Program, directed by John D. Hoffman.
Adding to an already strong metallurgy program
under Richard J. Arsenault, the emphasis on
polymers will provide opportunities for collabora-
tion with the chemical engineering faculty work-
ing in the area. Overall, chemical engineering at
the University of Maryland is very much alive
and looking towards the future.

Chemical engineering faculty at the University
of Maryland currently number thirteen, with
eleven having primary duties at UMCP and two
at UMBC. Currently the program has two open
faculty positions at College Park and plans to add
three or four additional faculty at UMBC over the
next two years.
An ever-present pipe and a collection of owl
figurines are sufficient clues to identify Robert B.
Beckmann (Wisconsin, 1944). On the off chance
that one of the clues is missed, identity is insured
if a bow string tie, immaculate doodling, a print-
perfect style of written communication, or amus-
ing tales of horror from the senior design course
are detected. Bob served as chairman of the de-
partment in the early '60's, building the gradu-
ate program before moving on to a tour of duty
as dean of the college. Well known for his work on
behalf of accreditation across the country, Bob
provides the capstone on the design requirement
of the curriculum while annually adding to his
repertoire of anecdotes.
Theodore W. Cadman (Carnegie-Mellon, 1966)
serves as the department chairman and strives
to maintain his sanity with an active research
program involving process control innovations and
applications to fermentation operations and
modern process simulation techniques. He is also
an avid microcomputer enthusiast with a particu-
lar zeal for incorporating their use throughout


-9 a f -

The chemical engineering initiative at UMBC as well as the emphasis on
biochemical engineering faculty additions at UMCP will increase the number of chemical
engineering faculty in the Program to nearly twenty in the next several years and will provide
unique opportunities for interaction with faculty experts in the biosciences at UMBC, UMCP and UMAB.

the chemical engineering curriculum. To relieve
the stress and tensions of departmental adminis-
tration, Ted is an intrepid gardener, within cer-
tain constraints (anything planted has to be
hardy, perennial, and serve to minimize or lessen
lawn mowing), an inveterate do-it-yourselfer home
remodeler and, in case of severe frustrations, he
lays concrete block at his Chesapeake Bay retreat.
Richard V. Calabrese (Massachusetts, 1976)
has research interests in two primary areas:
turbulent two phase flow and the transport and
transformation of atmospheric pollutants. Turbu-
lent circulation patterns and drop/bubble breakup
correlations abound in his studies in the former
area. In the latter, Rich has been wide-ranging.
The prediction of polycyclic aromatic hydrocarbon
(PAH's) concentrations as a result of residential
wood burning is a current project. As is the conse-
quence analysis of nuclear reactor accidents, a seg-
ment of an Information System Study being com-
pleted by the Nuclear Engineering Program and
the University Research Foundation at Maryland.
With less than a year in the Program, Kyu-
Yong Choi (Wisconsin-Madison, 1983) is still
setting his feet at Maryland. A product of Wiscon-
sin at Madison, studying under Dr. Harmon Ray,
Kyu-Yong has selected polymerization reaction
engineering, with an emphasis on control, as his
primary research activity. Lately, he has been
particularly busy initiating his experimental pro-
Stowe Davison (Maryland, 1984) is the new-
est member of the faculty and the first to be hired
for the degree program at UMBC. A graduate of
Maryland, Stowe completed his doctorate under
James Gentry. He is an expert in computer ap-
plications and has selected the theoretical and ex-
perimental study of aerosol charging to begin his
academic research career. In addition to being a
gifted teacher, Stowe is quite at home in the
laboratory and lately has been putting his practi-
cal skills to the real test by virtually rebuilding
his home in College Park.
Interested in a new process? See Larry L.
Gasner (M.I.T., 1971). Larry has a practical engi-
neering bent which stands him well in all of his
activities. With primary interests in the develop-
ment and scale-up of bioprocesses, Larry is

anxiously awaiting the arrival of the 500 liter
fermentor system. Well, perhaps just a little less
anxiously than implied, since Larry is looking for-
ward to spending time in Germany with the vendor,
finalizing the plans for the system and reviewing
the construction progress.
James W. Gentry (Texas-Austin, 1969) brings
his scientific and mathematical skills to bear on
the study of aerosols. A prolific publisher of re-
search findings on the behavior of non-spherical
and ultrafine aerosols, Jim has an extensive col-
lection of books and classical records including the
collected works of 19th century mathematicians,
bound sets of Texas Football, and the collected
works of J. S. Bach.
Albert Gomezplata (Rensselaer ,1959) serves
as Associate Dean of Engineering with responsi-
bility for the activities at UMBC. As a member of
the chemical engineering faculty since 1958 and
a former chairman of the department, Al is well
equipped to initiate the programs at Catonsville
and to foster the development of chemical engi-
neering at the Baltimore County campus. On a
time available basis, Al crosses the street to his
sailboat on the waters in Annapolis and is an avid
do-it-yourselfer when it comes to keeping his
automobile (s) running.
Juan Hong's (Purdue, 1979) forte is biochemi-
cal engineering with a particular focus on biomass
and product formation and separation processes.
An avid experimentalist, Juan is equally skilled in
analysis and modeling techniques and, as many
a graduate student will attest, presents a mean
course in thermodynamics.
Although categorized under the nuclear engi-
neering faculty in the listings of the Department,
Yih-Yun Hsu's (Illinois, 1958) chemical engineer-
ing background and expertise in heat transfer and
two-phase flow make him a valuable contributor to
the program's activities. YY, as he is known, par-
ticularly enjoys teaching heat transfer to the
Junior chemical engineers.
Mention interaction analysis and one is assured
of attracting the attention of Thomas J. McAvoy
(Princeton, 1964). Together with strategies for
distillation column control and short-cut modeling
techniques, Tom brings a practical, enthusiastic
bent to process dynamics and control. In the ap-


propriate season, bluefish on the Chesapeake Bay
and ice hockey are known to be competitors. Tom
is director for the Center for Process Analysis,
Control and Simulation, promoting interaction
with industry in practical applications of control.
Among the center's activities are a biennial short
course, "Applications of Advanced Control in the
Chemical Process Industries," and a series of
videotapes featuring international experts on dy-
namics and control. In addition to his research ac-
tivities, Tom has modernized the undergraduate
process control laboratory using modular experi-
mental units featuring a liquid level system inter-
faced to an APPLE microcomputer data acquisi-
tion and control system.
Gregarious Thomas M. Regan (Tulane, 1967)
serves as the undergraduate advisor for the
chemical engineering program. In addition to
being a mainstay in undergraduate course in-
struction, including unit operations laboratory,
Tom has culinary skills which rate par excellence.
Wilburn C. Schroeder's (Michigan, 1933)
part time professorial position in chemical engi-
neering dates back to 1953. It has always been part
time and Will is always in every weekday, break-
ing precisely at 11:30 AM for lunch with several
of the faculty at a local restaurant. Lunch is well
worth the while to hear of his trips to Indonesia
to build ammonia plants, tales of his tour of
Germany immediately after World War II while
at the Bureau of Mines, or for a discussion of the
latest coal conversion technology-including the
Schroeder Process-or national politics and the
state of the market on the hour. Will's personality
and expertise in energy, coal technology, and eco-
nomics are particularly appreciated by the seniors
in his classes who are given a view of chemical
engineering that is not reflected in any text.
One of the quietest members of the Program
is Theodore G. Smith (Washington University,
1960). Ted's research interests are focused on the
study of polymer blends and the properties of
polymers, particularly mass transfer. This fall he
has also undertaken the particularly challenging
and interesting task of using microcomputers in
the introductory sophomore class. With funds pro-
vided by the university and the college, 24 Zenith
150 microcomputers have been purchased for the
undergraduate program. Microcomputers were also
purchased for use in the introductory freshmen
courses taught within mechanical engineering, so
Ted should find his task somewhat easier the
second time around.

Nuclear Engineering Program: Kazys K.
Almenas (Warsaw, 1968); Dick Duffey (Mary-
land, 1956); Mohammed Modarres (M.I.T., 1979);
Frank J. Munno (Florida, 1964) ; Gary A. Pertmer
(Missouri-Columbia, 1978); Marvin L. Roush
(Maryland, 1964); Joseph Silverman (Columbia,
Engineering Materials Program: Richard J.
Arsenault (Northwestern, 1962); John D. Hoff-
man (Princeton, 1949); Marc L. Mansfield (Dart-
mouth, 1981).

The review by Thomas M. Regan is greatly

book reviews

2nd Edition
By F. A. Holland, F. A. Watson and J. K. Wilkinson
John Wiley & Sons, 1983, xv: + 346 pages. $21.95.
Reviewed by V. W. Uhl
University of Virginia
The scope of this book exceeds the title term
"process economics" as generally understood. The
latter half of the book treats topics which deal
with management techniques and business con-
siderations. Overall, the level and content put the
work in the double category of an undergraduate
text and an introduction for engineers in industry
to economic evaluation and management topics.
The book will first be generally characterized.
After the contents are delineated, there is a de-
tailed commentary and then a thumbnail appraisal.
The treatment, although orderly, is uneven
with respect to writing quality, intensity of the
text, and the mode of demonstrating concepts and
techniques. Some handling is inadequate while
other material appears extraneous. The wide dis-
parity in the quality of the style-stodgy in the be-
ginning, felicitous later-suggests that each
author may have written different sections, and
they did not collaborate on editing. Some concepts
are artfully and thoroughly developed; then es-
sentials such as assets and depreciation are im-
properly presented and clumsily explained. In the
last half some listed topics, such as cost benefit


analysis, are barely more than mentioned. The
figures lack distinction and clarity, the tables are
typed and many lack titles. The references are
up-to-date, but many expected attributions to
sources are not given.
Part one, titled "Elements of Profitability As-
sessment," surveys within a logical structure:
time value of money; items of cost, including their
handling, e.g., depreciation, and breakeven an-
alysis; use of profitability measures; estimation
of capital investment; and the prediction of an-
nual operating expenses. In scope it corresponds
almost to the first (1974) edition. Chapter 3
thoroughly considers a range of methods for as-
sessing probability (twelve in fact). Chapter 4,
which deals with uncertainties in profitability
estimates is out of place; it should have been co-
ordinated with related material in the last half
of the book.
"Elements of Decision Making" is the designa-
tion for the second half, doubled in length from
the 1974 edition. The topics are properly classi-
fied by the two chapter headings as numerate
methods and management considerations. The
nine sections in the first of these chapters in-
clude: statistics and probability; curve fitting and
trend analysis; utility functions; linear pro-
gramming; forecasting; learning curves; and
profit-volume analysis. The last three are new.
The final chapter on management considerations
looks at matters such as: types of accounting;
price and cost trends; value engineering; cost-
benefit analysis; marketing; risk and insurance;
and inflation (an addition to the new edition).
The treatment of engineering cost analysis is
comprehensive. Each chapter has several ap-
propriate problems which serve to fulfill the
books's role as a textbook. The concept of con-
tribution, especially as the contribution to sales
ratio (CSR), proves useful in the analysis of sales
data. The subject of capital cost estimation is well
done, and it is on an international basis. Note-
worthy treatments in the second half of the book
deal with utility functions and learning curves.
The book fails in its poor expression of some
concepts, limited scope, and inadequate reflection
of current practice. The manner in which the
cardinal concept of "cash flow" (net profit after
income taxes plus depreciation) is expressed is in-
direct and therefore confusing. Also, attempts to
correlate technical economics (for prediction)
with financial accounting (for historical record)
are unorthodox and hence confusing. For instance,

Due to a steady increase in the number of papers sub.
mitted in recent years, CEE was faced last year with a two-
year backlog of papers. We accordingly took steps to 1) in.
crease the number of pages of editorial matter in each issue,
2) reject papers of lesser quality, 3) request the shortening of
papers of considerable length, and 4) solicit fewer papers.
As a result, with the publication of this issue our backlog
has nearly been cut in half.
We appreciate the patience of our prospective authors during
this period and encourage our readers to continue to send us
papers of high quality
Ray W. Fahien

assets are incorrectly perceived; gross profit is
equated to net profit; the latter is taken as income
before taxes which is contrary to the common ac-
counting definition, at least in the U.S. The
practices for handling depreciation are limited.
For instance, the Accelerated Capital Recovery
System (ACRS) enacted by U. S. federal legisla-
tion in 1980 is not mentioned. Only discrete inter-
est is used for the computation of net present value
(NPV) and internal rate of return at a time
when the employment of continuous interest and
the half-year convention is common and growing.
The wider view of "engineering economy" is ig-
nored, one which considers choice between alter-
natives which are of the nature of plant addi-
tions, process modifications, and equipment re-
placement. And the optimization of processes,
either by mode of operation or sizing in design
(often termed Economic Balance) are not con-
Several topics in the second half, such as ele-
mentary statistics, have no place because of their
elementary character. Others, such as cost-benefit
analysis and marketing are treated in a summary
fashion, so they constitute a mere mention of these
subjects. And inflation is handled in too cursory
and incomplete a way to be useful.
Unfortunately the awkward presentation of
the first half of the material, further burdened by
a clumsy and needlessly extensive nomenclature,
renders this basicly simple subject arcane. The
work is also lacking in judgments. For instance
no critique was offered for the dozen methods of
profitability assessment described. Readers seek
guidance and a rationale.
Overall the book is limited in scope, is mislead-
ing in places, and makes an essentially simple dis-
cipline difficult to master and tedious to consid-
er. D


Views and opinions


... or the Tragic Tale of the Dying Grandmother

North Carolina State University
Raleigh, NC 27695

Note: The material in this paper was presented
at an orientation program given by North Caro-
lina State University to new faculty members and
teaching assistants. The formal misconduct pro-
cedure discussed in response to Question 12 of
course varies from one university to another, but
the philosophy underlying the procedure is rela-
tively standard.

IN THESE PAGES, I talk about cheating-how to
minimize its occurrence (preventing it com-
pletely is generally too much to hope for), what
to do when you suspect it, and what to do when
you can prove it. I don't claim to be an expert on
the topic-I'm not sure there is such an animal-
but will simply offer a few ideas for consideration.
Ultimately, all instructors must develop their own
philosophies on cheating, based on their individual
senses of justice, morality, and humor.
Here, then, are some questions a course in-
structor might ask about this uncomfortable sub-
ject, and some suggested answers.

1. I'm going to be teaching a (small, large)
(undergraduate, graduate) course. Is there
likely to be cheating?
It may reflect the spirit of our times, or a de-
cline in student morality, or the unchanging nature
of the human species, or anything else you choose

The sad fact is, however,
that as long as grades are important
to students-as they probably will
be-some students will do whatever they can to
get the highest possible grades.

Copyright ChE Division, ASEE, 1985

Richard M. Felder is a professor of ChE at N. C. State, where he
has been since 1969. He received his BChE at City College of
C.U.N.Y. and his PhD from Princeton. He has worked at the
A.E.R.E., Harwell, Exxon Corporation, and Brookhaven National
Laboratory, and has presented courses on chemical engineering
principles, reactor design, process optimization, and radioisotope ap-
plications to various American and foreign industries and institutions.
He is coauthor of the text, Elementary Principles of Chemical Processes.

to see in it. The sad fact is, however, that as
long as grades are important to students-as they
probably always will be-some students will do
whatever they can to get the highest possible
Clearly, the likelihood of cheating varies from
one classroom situation to another. If you are
teaching an advanced graduate course with eight
excellent students, it is probably safe to leave the
room during a test. On the other hand, if you
teach a sophomore course with 200 students in a
room that seats 200, and no one cheats or attempts
to do so, you should nominate the class for the
Guinness Book of World Records.
You may as well resign yourself to the fact
that some students, impelled by desperation or a
flexible moral code, will try to beat whatever sys-
tem you impose, and guide yourself accordingly.

2. Why should I be all that concerned about
cheating ?
Most obviously, when students cheat and get
away with it, it penalizes honest students, in some
cases forcing them to cheat as well just to remain


competitive. More than this, however, it cheapens
the value of the degree and adds to the probability
that students will be officially declared qualified in
fields in which they have no competence whatever.
These incompetents could end up building our
bridges, designing our nuclear reactors, removing
our appendices, and possibly most serious of all,
teaching our children.

3. What forms does cheating take?
There are two major categories: (a) cheating
on homework and (b) cheating on tests. I'll take
them up in turn.

4. How do students cheat on homework?
Cheating on homework involves getting solu-
tions from somewhere other than one's own head,
and turning them in as original. The sources in-
clude other students' solutions (either stolen or
freely shared), back solutions in files (popular
among fraternity members), and stolen textbook
solution manuals. These are all traditional sources,
known and loved for generations.
The current generation's contribution to the
field is the stolen computer file. Instructors who
store homework solutions on hard disks (as op-
posed to personal floppy disks) never know when
some budding software wizard with an eye toward
academic or financial gain might gain access to
their files and copy and possibly reproduce and
sell the solutions. Also, when the assignment in-
volves writing a computer program, copying an-
other student's solution file is often a trivial exer-
cise for someone who knows his way around an
operating system.

5. How should I deal with homework cribbing?
One way is to change the assignments each
time the course is given, so that back files become
useless. This imposes a tremendous additional
work load on the instructor, however, and in the
case of such things as laboratory courses may be
The instructor or grader can go through all
the papers, looking for sets of identical solutions.
However, it is difficult or impossible to prove any-
thing in such cases. Students can always claim
that they worked independently and coincidentally
came up with identical answers, and you have no
way of disproving them. If a student hands in a
photocopy of a page from the solution manual,
you would of course have a pretty good case

against him. However, the chances are that anyone
that stupid will probably flunk out in the natural
course of events, so that no extraordinary action
may be called for.
My own solution for this problem is relatively
simple, although it is strictly applicable only to
technical courses. To the greatest extent possible,
eliminate the requirement that homework be done
independently. In fact, I always encourage
students to work together, although I require them
to hand in their own solutions. By working with
others, students often learn how to solve problems
that would have stumped them as individuals.
Of course, some students will get free rides
this way, simply copying solutions without under-
standing them. However, these students will al-
most invariably be weeded out by the course tests.
To be assured of this, include material of the type
in question on the tests; ask questions about the

On almost every test
some students will not show up and
will later appear in your office with stories that
will astound you with their inventiveness,
pathos, and sheer chutzpath.

conduct of the experiments and the analysis of
data in laboratory courses, and give brief pro-
gramming exercises in courses that involve com-
puter homework.

6. How do students cheat on tests?
Let me count the ways.
THE SNEAK PREVIEW: Students get copies of
the test before it is given, and come to class with
the solutions already worked out.
THE EYES HAVE IT: They copy from neighbors'
papers-usually those adjacent or in the row ahead,
sometimes in the row behind. (The latter requires
more agility than the average engineering student
possesses, and sometimes results in severe whip-
prewritten slips of paper, notebook covers, or easily
accessed portions of their epidermis.
out of the examination room during the test, osten-
sibly to the bathroom, and either look up the
answers or get by with a little help from their
worked out solutions intended for distribution after
the tests have been collected, and hastily correct
their own solutions before handing their papers in.
Since most students taking a test invariably wait
until the last second to hand their papers in, and the


instructor is usually distracted by the mob around
the front desk at this point, he can easily miss the
student in the middle of the crowd pulling this par-
ticular stunt.
hand in their test at all if they feel they have done
poorly, then claim the grader lost it.
THREE-PAGE MONTE: They substitute correct
solutions for incorrect ones after the graded tests
have been handed back, and claim that the grader
made a mistake.
solutions to previous examinations and simply write
them down when the same questions reappear.

Any instructor lazy enough to use the same
tests semester after semester invites the last of
these activities. I do not consider it cheating, but
a legitimate exercise for the enterprising student.
The other methods cited above are a different
story, however. As much as possible must be done
to guard against them.

7. How do I prevent cheating before the exami-

The key word is security.
Don't leave a copy of the test on your desk, or on
your secretary's desk, or stored in your word pro-
cessor where someone else can get access to it, or
on the photocopy machine, or in a wastebasket in
your office or the department office.
When work is not being done on the test, keep all
existing copies locked away in a safe place, like your
personal file cabinet.
Don't let work-study students photocopy a test-do
it yourself, or have your secretary or teaching as-
sistant do it, and immediately seal the copies in an
envelope or folder and lock them away.
Know how many copies were run off, and count
them before the test is given. If the count is wrong,
make up a new test, or see the following story.

A professor in our chemistry department once
gave a test for which the answer page was the
test paper. Before giving the test, he counted the
copies, and found that he was short by two. He
took the papers to the department office, used a
paper cutter to remove about 1/8 inch from the
bottom of each sheet, and then gave the test. After-
wards, he collected the solutions, stacked them
vertically, pulled out the two that were longer than
all the others, and invited the students they be-
longed to into his office for a little chat. I don't
know what happened from there, but you get the

8. How can I minimize cheating during the

Most obviously, by keeping your eyes open. Be sure
the examination is proctored at all times, and be on
the lookout for suspicious behavior. (Keep the cold
hard staring to a minimum, however-too much of a
police-state atmosphere can intimidate students to
a point that they become incapable of showing what
they really know.)
If there is room, request that students sit in alternate
seats. If this is not possible, and if you have reason
to believe that copying may be a problem in a par-
ticular class, you may find it convenient to make up
and distribute alternate versions of the test to ad-
jacent students. (Shuffle the order of the questions,
or use different sets of numbers if calculations are
If someone's eyes are obviously wandering during a
test, silently call his attention to the fact that he is
being observed. If you can't catch his eye, you might
announce (humorously, if you can manage it) that
group solutions will not be accepted, and look pointed-
ly at him when he looks up. In extreme cases, you
can quietly ask him to move to a more isolated loca-
Don't hand out worked-out solutions until you are
absolutely certain you have collected all the test
papers. One way to guarantee this is to hand them
out in the period following the one in which the
test was given.
Before grading the papers, log them in, so you will
know immediately who did not submit one.

9. How can I minimize cheating after the exami-
If possible, use examination booklets, so that sub-
stitution of corrected pages for original ones is made
more difficult.
Make copies of all graded solution papers, or of
some of them if there are too many to copy them
all, before handing them back. Then, if a student
comes to you and complains that the grader made a
mistake, comparing his paper with the copy will
tell you whether he was really misgraded, or whether
he's trying to pull the old switcheroo on you.
Note the names of all students who present question-
able claims of misgrading. If you can't disprove their
claims, give them the benefit of the doubt, and
change their grades-but on subsequent tests, be
sure to copy their graded solutions before handing
them back, even if you copy no others.

10. Does the type of test determine how likely
students are to cheat on it?

To a considerable extent, yes. The tests which
are most likely to be cheated on are those with
answers that are easy to copy (e.g. true-false and
multiple choice tests), and those which seem un-
fair to the students. Generally speaking, if you
want to construct an engineering course test that
is both pedagogically sound and difficult to cheat
on, I recommend the following:


Require full problem solutions, not just simple
answers, and be liberal with partial credit.
Give only open-book tests.
Give tests that are easy to read and possible to
If the answer to a question is "true" or "(d)"
or 675C, it is a trivial matter to ascertain this fact
from the adjacent student and get full credit,
while on a problem that takes several pages to
work out the cheater's task is much more arduous.
Requiring detailed solutions and giving partial
credit makes life more complicated for the in-
structor and the graders, but it helps assure that
students who understand the course material are
not unduly penalized for careless mistakes, and it
minimizes the chance of a student getting full
credit for copying a correct answer without having
the vaguest idea of how to do the problem.
I have strong feelings on the question of open-
book versus closed-book tests. What I want to
know is whether my students can take the material
I have given them-course notes, worked out prob-
lems, and a course text-and use it to solve prob-
lems; I really do not care how much data they can
cram into their short-term memories the night
before the quiz. An open book test allows me to
find out what I want to know; it tests the students'
understanding, not their memory, and it also pro-
vides a closer simulation of the tests that await
them in their careers. As a fringe benefit, open-
book tests eliminate the usefulness of inscribing
or scotch-taping facts, formulas, and conversion
factors on shirtsleeves and under socks.
There is no question but that a poorly con-
structed test invites cheating. I know a professor
who seems to delight in making up test questions
that even his faculty colleagues cannot decipher.
In some cases the problems are trivial; the only
trick is to figure out what is being asked. Students
faced with this sort of thing tend to panic, en-
visioning zeros on the quiz since they do not even
know how to get started, and they often take what-
ever measures they can to get out of their di-
Another feature of some tests that drives
students up the wall is the mistake-ridden problem
that either has absurd solutions or cannot be
solved at all. Such problems almost invariably ap-
pear when the instructor makes up the quiz at the
last minute and does not bother to work out the
solutions himself. If this is a chronic occurrence
in a course, students tend to be much more in-
clined to share solutions than they might otherwise

Finally, we have the instructor who likes to
make up tests for which the average is in the
20's or 30's. Rightly or wrongly, students regard
such tests as basically unfair, and they often
feel little remorse about cheating on them. I be-
lieve that tests like this are little more than ego
trips for the professor-they do not serve any use-
ful pedagogical purpose.
The closest I have ever come to cheating on
a test was on my graduate school thermodynamics
final. The whole course was a disaster-the text
spoke about one body of material, the lectures
about completely unrelated material, there were
no quizzes-and the final examination had no ap-
parent relation to either the book or the lectures.
Fortunately, I was not led into temptation be-
cause there was no one to copy from-we were
all in the same boat. I got a 9 on the exam (out
of a possible 100). It was good enough for a B in
the course; two hot-shots who got 12 and 11 got
A's. However, I truly believe that if I had cheated
on this travesty, God would have forgiven me.

11. What about students who miss tests?
On almost every test some students will not
show up and will later appear in your office with
stories that will astound you with their inventive-
ness, pathos, and sheer chutzpah. "My alarm
didn't go off," is probably the most popular story,
followed by, "My car wouldn't start," and com-
plaints of every malady known to medical science
and some that medical science has yet to catch up
All instructors hate make-up tests. It's hard
enough to construct a fair test that covers every-
thing you want to cover, that discriminates be-
tween students who are excellent, good, fair, and
poor, and that can be finished within the allotted
time slot. Having to do it twice is one of the great
pains of higher education. To avoid it, some in-
structors allow no excuses except certified doctors'
notes, and in the absence of such documentation a
test grade of zero is assigned. (This approach is
particularly appropriate if the instructor makes a
practice of dropping the lowest test grade.) Others
give students the benefit of the doubt and routine-
ly give make-up tests, often taking them from pre-
vious years.
I tend to fall into the latter category, but I
have my limits. Two students who missed a quiz
last year came into my office and indicated that
they had to go back home to stay by their dying
grandmother's bedside. Since I had already given


one of these students a make-up test earlier in the
semester (it seems his alarm clock had failed to
go off, and then his car wouldn't start), I was a
trifle skeptical, so after they left my office I called
his home and inquired. There was no dying grand-
mother. The two students got zeros on the quiz,
and they can expect to be watched with hawk's
eyes for the remainder of their academic careers.

12 What should I do when I suspect a student of
It depends strongly on the grounds for your
suspicion. Unless you have fairly clear evidence,
the best procedure is to do nothing. It is better to
miss an occasional violation than to subject an
honest student to implications of dishonesty and
possibly to public embarrassment.
If a student's paper shows evidence of foul play
-it duplicates another paper too closely, for
example, or it indicates ability completely inconsis-
tent with previous performance, or it seems to
have been tampered with after being graded and
returned-calling the student into your office and
asking him to discuss it with you is a first step.
You might say you are not clear about how he ar-
rived at his answers, and ask him to go over what
he did. Or you can point out the things that make
you suspicious and ask for explanations.
If the student denies all wrongdoing (as he
usually will) and you have no way of proving con-
clusively that he cheated, give him the benefit of
the doubt and drop the matter. If in fact he cheat-
ed, the fact that he was called in may be enough
to keep him honest thereafter.

13. What should I do when I have clear proof that
a student cheated?
All universities have administrative policies
and procedures for dealing with this situation.
Briefly, the N.C. State academic misconduct pro-
cedure involves confronting the student with the
charges against him; filing a report on the case
with the Department of Student Development if
the student admits guilt; or referring the case to
the Student Attorney General for a formal hear-
ing if no admission is forthcoming.
Unless the instructor filing charges recom-
mends a stronger sanction, a student who admits
guilt or is found guilty by the hearing panel is
given a zero on the assignment or test he cheated
on and is placed on academic misconduct probation
for the remainder of his career at the university.

A record of the incident is placed in his permanent
file, but does not appear on his transcript. A
second violation results in suspension.
In most cases, instructors choose to avoid this
procedure, either to keep students from getting
black marks on their records or to avoid time-
consuming red tape. They may take individual
action ranging from assigning a grade of zero on
a particular test to failing the student in the
course, and in some instances recommending or
demanding that he drop out of the curriculum.
Quite obviously, individual discipline is risky:
a student may claim that his rights have been vio-
lated, and the instructor may find himself involved
in much more red tape than he ever would have
had to deal with by proceeding through official
channels. The safest procedure is to adhere to the
university policy-and it is mandatory to do so
when penalties more severe than low test grades
are involved.
The first step of the academic misconduct pro-
cedure is confronting the student with the charges
against him, and requesting an admission of guilt.
Before doing this, however, you should reread the
university policy and inform the student of the
consequences of admitting guilt and of denying it.
Make a written transcript of the proceedings and
have the student sign it attesting to its accuracy.
A copy of the transcript can serve as the report
to the Department of Student Development.
Finally, make sure that you retain copies of any
incriminating evidence, so that if a formal hearing
is necessary you will be able to substantiate the
charges that led to the procedure being initiated.
Finally, if a student in one of your courses has
been proven guilty of cheating, I believe you should
make your departmental colleagues aware of it.
I once caught a student who tampered with a
graded test and failed him on the test. Attempting
to be fair to him, I said nothing about the incident
to anyone. He managed to pass the course, made his
way through the rest of the curriculum, and gradu-
ated. Subsequent to his graduation, it came out
that almost every instructor who had him in their
courses experienced difficulties of a similar nature,
and all of them did what I did. He literally cheated
his way through college and is now certified to
practice chemical engineering, which is a frighten-
ing thought to me.
If my colleagues and I had just talked to each
other, we would have been on the lookout for this
type of behavior from him, and when it occurred,
we would have known enough to proceed through


the university judicial system. He would have been
placed on misconduct probation, and there is a
good chance that his academic career would have
been appropriately terminated. As it is, we can
only hope that he is not now in a position to do
too much damage.
These are distasteful things to have to write. I
like and admire most students-if I didn't, I would
find another profession. I detest the thought that
I have to undertake the precautions outlined in
this paper, which in a sense tar all students with
the same brush.
I started my teaching career filled with an
idealistic humanitarianism which held that if you
assume the best in people they will reward you by
living up to your expectations. Unfortunately, I
quickly found out that it does not always work
that way. My idealism was interpreted by the dis-
honest students as a license to cheat with impunity

and by the honest ones as a sign that I didn't care
about the cheating that they all knew was going
on. I eventually concluded that taking precautions
against cheating, regardless of the implications of
these precautions, and dealing firmly with proven
cheaters, were the fairest things I could do for
my students.
Most students are basically honest. Most cheat-
ing incidents do not reflect chronic behavior pat-
terns, but slips resulting from momentary panic.
As an instructor, you should keep this in mind:
always give students the benefit of the doubt when
a reasonable doubt exists, and do all you can to
avoid blackening their records and jeopardizing
their futures by overreacting to minor ethical slips.
At the same time, make it quite clear to your
students that cheating is unacceptable, and back
your words up when it becomes necessary to do
so. By so doing, you will be serving the interests
of the students, yourself, your faculty colleagues,
and the university as a whole. D

gl book reviews

FLOW. Book I: Inertial Flows
By S. W. Churchill; Etaner Press,
Thornton, PA 19373 (1980)
Reviewed by
David G. Thomas
Oak Ridge National Laboratory

The selection of words and their order in the
title of this text describe the emphasis and ob-
jectives of the author. To accomplish this, simple
derivations from first principles are used to ex-
plain practical problems that occur in single phase
compressible and incompressible flows. The basic
physics of the flow phenomena is retained even
when developing approximate models which often
are of sufficient accuracy for engineering applica-
tions. More to the point, because empirical models
are avoided whenever possible, increased confi-
dence in the generality of the result is developed.,
This is an unusual book in several respects. It
is not listed in the 1983-84 edition of Books in
Print. Under the umbrella of the general title are
included 7 books, of which the one under review

is the first. Other titles in the series are:
II One-dimensional Laminar Flows
III The General Equations of Motion
IV Unconfined Multidimensional Flows
V Confined Multidimensional Laminar Flows
VI Confined Turbulent Flows
VII Flows Through Dispersed Media
The division of subject matter indicated above
results in an unusual grouping of topics on both
compressible and incompressible flow in Book I.
For instance, successive chapter titles are: Ch. 1,
Reversible Expansions and Compressions; Ch. 2,
Expansions at Low Velocity; Ch. 3, Maximum Re-
versible Rates of Flow for a Gas; Ch. 4, Jet Pro-
pulsion Engines; Ch. 5, Maximum Rate of Flow
of Gas Through a Pipe; Ch. 6, Sudden Expansions
and Contractions; Ch. 7, Shock Waves; Ch. 8,
Detonation Waves in Gases; Ch. 9, Surface Waves,
and Ch. 10, Cavitation, Incipient Vaporization and
Aerodynamic Heating. There are an average of
20 problems for each chapter and it would be es-
sential to solve the majority of them to gain full
benefit from the approach selected by the author.
Not only do the problems require an understand-
ing of the basic principles but some developments
of importance are deferred to the problem sets.
Numerical methods are avoided. This book is suit-
able for a senior or first year graduate course. E


o classroom



University of California
Davis, CA 95616

T HE CHEMICAL ENGINEERING approach to trans-
port phenomena usually begins with the study
of fluid mechanics, moves on to heat transfer, and
completes the introductory sequence with a study
of diffusion and mass transfer. This sequence is
normally restricted to single phase transport phe-
nomena, or situations in which the influence of
the second phase is represented only in terms of a
boundary condition. The beginning sequence is
often treated with great care as the Navier-Stokes
equations slowly evolve [17, Chap. 5], the thermal
energy equation rises from the morass of Cartesian
tensor analysis [10, Sec. 10-1], and the complexi-
ties of multicomponent transport phenomena [3,
Sec. 18.3] complete the initial foray into the world
of partial differential equations. What follows is

p .

Steve Whitaker received his undergraduate degree in chemical
engineering from the University of California at Berkeley and his
PhD from the University of Delaware. He is the author of three
books: Introduction to Fluid Mechanics, Elementary Heat Transfer
Analysis, and Fundamental Principles of Heat Transfer and has re-
search interests in fluid mechanics, interfacial phenomena and multi-
phase transport phenomena. He has taught at U.C. Davis, North-
western University and the University of Houston, and in 1982 he
received the Magnar Ronning Award for Teaching Excellence and the
Tau Beta Pi Outstanding Teacher Award in the College of Engineer-

The key mathematical theorem used
in these three studies is known as the spatial
averaging theorem, and it was presented
independently by the above workers in
1967. In each study a different route to the
averaging theorem was used ...

crucial to chemical engineering: multiphase trans-
port phenomena. However, the disparity between
the precise analysis encountered in single phase
transport phenomena and the qualitative treat-
ment of multiphase transport phenomena often
causes our students to question the efficacy of
engineering science and encourages faculty mem-
bers to adopt the position that it simply is not
worth the trouble. Clearly, the transition from
axioms and well-posed problems to applications
and ill-posed problems deserves our attention.
The connection between single phase transport
phenomena and multiphase transport phenomena
is easily accomplished by means of the spatial
averaging theorem. This approach was originally
developed by Anderson and Jackson [1] who de-
rived the equations of motion for a fluidized bed,
by Slattery [15] who studied the problem of visco-
elastic flow in porous media, and by the author
[18] who used the method to derive a dispersion
equation for mass transport in porous media and,
more importantly, to outline a method of closure.
The key mathematical theorem used in these three
studies is known as the spatial averaging theorem,
and it was presented independently by the above
workers in 1967. In each study a different route to
the averaging theorem was used, and since 1967
there have been numerous other treatments of this
mathematical problem [2, 8, 11, 19]. The process
is not yet terminated, for in recent papers Cush-
man [6, 7] has raised the issue of the need for time
and space-dependent averaging volumes, and
Veverka [16] has commented on possible limita-
tions of the averaging theorem. Howes and

Copyright ChE Division, ASEE. 1985



7 -Phase -Phasi

FIGURE 1. A two-phase system

Whitaker [13] have examined the questions raised
by Veverka and find them to be unimportant for
cases of practical interest. The objective of this
paper is not to produce a new result, but merely
to provide a route to the averaging theorem that
can be used in our undergraduate classes.

In Fig. 1 a two-phase system is illustrated with
the continuous phase identified as the p-phase
and the discontinuous phase identified as the a--
phase. One could think of this system as a bubble
column or as a fixed bed reactor. We direct our
attention to the p-phase and note that the species
continuity equation can be expressed as
t A = RA
Here cA represents the molar concentration of
species A, the molar flux is given explicitly by

NA = CAVA (2)

and the molar rate of production per unit volume
of species A owing to homogeneous chemical re-
action is represented by RA. It should be clear that
we are thinking of the p-phase as a fluid and the

The objective of this paper is not
to produce a new result, but merely to
provide a route to the averaging theorem that
can be used in undergraduate classes.

o--phase can be either a non-porous solid, a porous
solid, a liquid, or a gas. It will be sufficient for
our purposes to consider only the mass transfer
process in the p-phase.
Obviously we are unable to determine the de-
tails of the concentration field in the p-phase and
some type of averaging procedure is in order. The
method of volume averaging is based on the as-
sumption that a local average concentration and a
local average rate of reaction will suffice for design
purposes. To this end, we associate with every
point in space an averaging volume such as the
sphere illustrated in Fig. 1. We designate the aver-
aging volume by v and average values computed
on the basis of this volume are assigned to the
centroid of the volume. Since there is an averaging
volume associated with every point in space, i.e.
in both the p and the -c-phases, we can generate a
field of average values of the concentration,
temperature, etc.
In the method of volume averaging there are
numerous types of averages. This is perhaps best
illustrated in a recent paper dealing with diffusion
and reaction in a micropore-macropore model of
a porous medium [22, 23]. In that work one finds
four different volume averages and eleven differ-
ent concentrations for a single species. In general,
there are two averages that one needs and the
first of these is referred to as the phase average
which is defined by

V cA dV

Here Vp(t) represents the volume of the p-
phase contained within the averaging volume
which can be expressed as

v = V (t) + Vo(t) (4)

Note that while the individual volumes,
Vp(t) and V,(t), may be functions of time and
space, the averaging volume is not.
When the point concentration of species A is
constant, we see from Eq. 3 that the phase average


concentration is not equal to that constant value.
Because of this, we usually prefer to work with
the intrinsic phase average concentration which
is defined by


These two average concentrations are related by

= E
in which ep is the volume fraction of the P-phase
given by

eB VB(t)/V (7)

The averaging procedure is best initiated in
terms of the phase average, and thus we integrate

Use of the traditional nomenclature illustrated by
Eq. 3 leads to the form

CA\ + = N a _/ -

Here it is clear that we must be able to interchange
differentiation with respect to both time and space
with time-dependent spatial integration if we are
to obtain a governing differential equation for the
average concentration. The general transport
theorem [17, Sec. 3.4] will allow us to treat the first
term in Eq. 9 in a precise manner, and what is
needed here is a rule for interchanging spatial
integration with spatial differentiation. Clearly
we seek a three-dimensional form of the Leibnitz
rule using the same simple approach currently
available in the derivation of the general transport

In general we require an averaging volume to
contain many "pores" or "particles" of both phases
in order to obtain smooth and representative values
[5, 19]. Such an averaging volume is illustrated
in Fig. 2 in which we have clearly identified V and
Vp (t). The volume of the P-phase is bounded by
two surfaces that we identify as

A (t)
A e(t)

FIGURE 2. Averaging volume for a two-phase system

Eq. 1 over the volume Vp(t) and divide by v to

Sa dV + V. A dV = RA dV (8)

Vg(t) V(t) V1(t)

interfacial area
area of entrances and exits

and for the purposes of our derivation it is
sufficient to consider the simple system shown in
Fig. 3. There we have illustrated two averaging
volumes with the centroids separated by a distance
As along a straight line, the orientation of which
is designed by the unit vector X.
The objective here is to derive the three-
dimensional Leibnitz rule which can be expressed

J CA dV = VcA dV nocA dA

V (t) Vg(t) Ao(t)

Rather than deal directly with the gradient, it is
more convenient to begin with the directional
derivative [17, Sec. 7.4] and use the definition of
the derivative to write


of the general transport theorem [17, Sec. 3.4] in
order to evaluate the integrals on the right hand
side of Eq. 12. Each point on the surface of the
averaging volume v (s) is translated a distance
As in the X-direction in order to construct the
volumes Vi(As,t) and V1 (As,t), and the details
of the geometry are illustrated in Fig. 4. Our
next step in this analysis requires that we repre-
sent the volume integrals over Vi(As,t) and
Vu(As,t) in terms of the surface areas AI and
A,. These two areas are identified by the unit
outwardly directed normal vector np shown in Fig.
3, and as As0- these two areas will be coincident
with the area of entrances and exits, Ape (t). When
the averaging volume undergoes a displacement
As, an element of the surface will generate a
cylinder as illustrated in Fig. 4. The differential
volume elements illustrated in Fig. 4 can be ex-
pressed as

dVI = As dAcs

FIGURE 3. A uniform translation

d f
*V cA dV cA dV

cA dV cA dv

V (s+As,t) V (st)
= lim -(s't) (11)
As+o As

Clearly the intersection of the two integrals
will cancel in Eq. 11 so that we obtain

where dAes represents the cross-sectional area of
the cylinder under consideration. The cross-
sectional area is related to the surface area element

dAcs = -XB dA
dAcs = hB dA

over All
over AI


These relations allow us to express the volume
Continued on page 50.

ds dV = lim

j cA dVi CA dV
V1(At) (As,t)

Since the two volumes, VI(As,t) and V (As,t),
tend to zero as As*0, we can use the simple geo-
metrical arguments presented in the derivation


- V (s.As)

Lu,. ~sj


views and opinions


University of California
Berkeley, CA 94720

T HE WORD "CREATIVITY" has been much abused
because it is difficult to define precisely. In
common speech, it is often used for a negative
purpose: educators, politicians and administra-
tors are criticized for "not being creative" but,
upon further investigation, that criticism often
means only that the critic doesn't approve of what
the educator, or politician or administrator, is
doing. In American society, where we tend to
worship whatever is new and where we tend to
condemn whatever is old, the word "creative" is
a positive adjective, a word of praise, while the
more-commonly-used phrase "lack of creativity"
is a sign of condemnation.
The dictionary doesn't help much. Webster's
Unabridged Dictionary refers, on the one hand,
to creativity as "making something out of nothing"
as in the Bible where God created the earth, and

John M. Prausnitz obtained a BChE degree from Cornell University
(1950), and a MS from the University of Rochester (1951). His PhD
is from Princeton University (1955), where he also served as Lecturer
in ChE. In 1955 he joined the ChE department at the University of
California, Berkeley. Although his initial professional work was pri-
marily in reactor design, he soon turned his attention to applied
thermodynamics, with particular emphasis on phase equilibria in
fluid mixtures. He is the author of Molecular Thermodynamics of Fluid
Phase Equilibria and the co-author of Properties of Gases and Liquids
(with R. C. Reid and T. K. Sherwood), in addition to numerous articles
and monographs.

on the other hand, to social or legal acts, as in
government where Congress creates a new law,
or to artistic acts where a painter or sculptor
creates a work of art.
None of these definitions are satisfactory when
we consider creativity in science or in the educa-
tion of scientists and engineers. Within that con-
text, I much prefer a definition which I once heard
from a psychologist: A creative act is one where
two ideas or concepts, previously believed to be
totally separate, are for the first time, shown to be
closely related. A creative act, in other words, is
to show that two apparently distinct ideas or con-
cepts are, in truth, not distinct but are merely
two aspects of some more general unifying idea or
concept. This definition helps us to find ways for
encouraging creativity in chemical engineering
students, especially graduate students.
Let me now illustrate this definition of creativi-
ty by some examples from the history of science
and then indicate how that definition suggests
some possibly useful procedures for educating
creative scientists and engineers.
A striking example is provided by the history
of thermodynamics. Until about 1870, thermody-
namics (as the name implies) was the science
of heat engines, a science concerned with the
principles which govern the conversion of heat
to mechanical work and vice versa. The research
of Mayer, Joule, and Carnot showed that this con-
version can be quantitatively described through
simple mathematical relations which, however, are
characterized by a lack of symmetry; the rules for
converting work to heat are not the same as those
for converting heat to work. It was this lack of
symmetry which led Clausius to the concept of
entropy and toward quantitative formulation of
the first and second laws of thermodynamics.
While this theoretical development of thermo-
dynamics was proceeding, there was at the same
time significant experimental development in
chemistry where the early pioneers of what we
now call physical chemistry were measuring

Copyright ChE Division, ASEE, 1985



Through his invention of a unifying concept-the chemical potential-Gibbs constructed a
theoretical framework which has tremendously influenced and advanced many fields of science, with
particularly beneficial effects in chemical engineering. Gibb's unifying action, showing the relationship
between apparently separate fields of inquiry, is a striking example of what we mean by creativity.

yields of chemical reactions and distributions of
components in mixtures among two or more
phases. Until about 1870, no one recognized that
there was a fundamental connection between what
we now call chemical equilibria and phase equilib-
ria. More important, no one had seen any connec-
tion between these chemical phenomena and the
scientific principles of heat engines. Now, more
than 100 years later, we recognize a connection
because of our notions of asymmetry and irreversi-
bility: it's easy to convert work to heat but it's not
easy to go back again; it's easy to make water and
carbon dioxide from methane and oxygen but it's
not easy to do the reverse; it's easy to mix water
and alcohol but, having mixed them, it's not easy
to separate them to their former condition.
We all know that it was Gibbs who first recog-
nized the connection between physical chemistry
and thermodynamics, two sciences which, prior
to Gibbs, had been believed to be unrelated.
Through his invention of a unifying concept-the
chemical potential-Gibbs constructed a theoreti-
cal framework which has tremendously influenced
and advanced many fields of science, with par-
ticularly beneficial effects in chemical engineer-
ing. Gibbs' unifying action, showing the relation-
ship between apparently separate fields of inquiry,
is a striking example of what we mean by
Gibbs' creative work related one science to an-
other; he used the scientific principles of heat
engines to obtain a theoretical treatment of equi-
librium in chemical systems. However, the essence
of creativity-tying together two separate ideas-
need not be limited to those cases where both
ideas come from the world of science. Creative
acts interconnect intellectual ideas regardless of
origin or classification. For example, Sigmund
Freud's autobiographical writings indicate that
psychoanalysis was born from the interaction of
two major factors. First, as a young man, Freud
worked in a psychiatric hospital in Paris where
he treated women afflicted by hysteria; second,
Freud had read the philosophical works of Fried-
rich Nietzsche and had been impressed by
Nietzsche's observation that human behavior was
only superficially conditioned by the rational rules

of society, while in its essential acts, human be-
havior was governed by deep-seated, irrational
motives. Freud saw a connection by establishing
the now well-known concepts of id and super ego
which allowed him to interpret hysteria as a conse-
quence of emotional suppression, usually dating
back to early childhood; once the patient recog-
nized the source of her problem, she could, with
counseling, find an accommodation which often led
to a cure. Freud's creative act was to apply to
medicine what at that time was far-out, radical
A third and final example is provided by the
physicist Niels Bohr whose complementarity
theory is now accepted by most scientists as one
of the basic cornerstones of physics. This theory,
also known as the Copenhagen interpretation of
quantum mechanics, is a concept of nature which
believes that duality is not an apparent, but a
fundamental feature of natural phenomena: light
is not uniquely corpuscular nor is it uniquely a
wave; it is both, such that, depending on what ob-
servation we want to interpret, one is more evi-
dent and sometimes the other. If duality is funda-
mental, then classical causality and determinism
are not possible, as shown by Heisenberg's un-
certainty principle. According to the Copenhagen
view, probability and statistics are not just ap-
proximations which follow from our inadequate
knowledge; they are the fundamental laws which
govern natural phenomena.
Bohr tells us that his theory of complementari-
ty has two roots: spectroscopy and the philosophy
of Soren Kierkegaard, a Dane like Bohr, who
bitterly opposed the deterministic philosophy of
Hegel that dominated Europe during the nine-
teenth century. Hegel's famous sequence (thesis,
antithesis, synthesis) expressed the notion that
with time, like a pendulum, a particular idea (or
thesis) generates its opposite (antithesis) and
that with more time, the two opposed ideas merge
to form a new idea (synthesis). Kierkegaard was
a deeply religious Christian who doubted that
man could ever attain absolute knowledge; such
knowledge was reserved for God. Kierkegaard
denied that with time one idea is followed by its
opposite; he stressed instead his belief that two


opposed ideas exist simultaneously. Opposites co-
exist and if we examine any one deep truth, we
find its opposite to be true as well. Kierkegaard's
view is succinctly expressed by the title of one of
his books, Either/Or.
Bohr studied Kierkegaard in his youth, shortly
before he became interested in interpreting transi-
tions of electronic energy states, as measured by
spectroscopists. Before Bohr, most physicists had
never heard of Kierkegaard and, even if they had,
it would not have occurred to any one of them
that Kierkegaard's highly abstract criticism of
Hegel had any connection with electronic transi-
tions. But Bohr saw the connection. His creative

If we accept the definition of
creativity that I have indicated, then we
must see to it that our students are exposed to
a variety of subjects, including some that are
remote from chemical engineering.

act was to establish an interpretation of physical
phenomena using concepts from what was (and
still is) obscure philosophy.
What do these examples suggest toward foster-
ing creativity in education? If we accept the
definition of creativity that I have indicated, then
we must see to it that our students are exposed to
a variety of subjects, including some that are re-
mote from chemical engineering. If the essence of
creativity is to do something new or to do some-
thing in a new way, then we should give our
students the intellectual tools that are needed for
novelty; to do that, our students should become
familiar with modes of thinking and with pro-
cedures of inquiry which are different from those
we use in common chemical engineering. Simply
put, creativity is likely to be stimulated by intel-
lectual breadth.
The most common argument for breadth is,
that for professional success, a chemical engineer
must not only be technically competent but must
also be familiar with economics and with all those
humane skills that allow him to interact positively
with a variety of co-workers and that, in general,
lead to good citizenship. A further argument is
that our alumni are not only chemical engineers
but also intelligent human beings who seek to fill
their leisure hours with satisfying enjoyment, and
therefore it is proper to include music, art and
literature in a chemical engineering curriculum.
Without in any way subtracting from the weight

of these arguments, I would add that breadth is
necessary for creativity, not necessarily to pro-
duce a Gibbs or Freud or Bohr-because that is
unlikely-but to provide our alumni with a broad
attitude toward problems they are likely to en-
counter, to give them the capability to think be-
yond common chemical engineering when they face
those new challenges-as they surely will-which
cannot be solved by the conventional wisdom that
is contained in standard chemical engineering.
In any one field of human endeavor, progress
is inevitably attained by borrowing from another.
The great advances recently made in medicine
and in biology have come about primarily because
of progress in experimental physics and analytical
chemistry. Today, doctors can diagnose previously
hard-to-detect pathology because of the CAT
scanner which utilizes sophisticated x-ray tech-
nology combined with computers. Further, while
recent discoveries in molecular biology promise to
produce cures for serious diseases, they are only
possible because of powerful electron microscopes,
refined chromatographs and sensitive detectors of
isotope radiation. Similarly, regardless of what
opinions we may have of modern art and modern
music, we recognize that the new art forms that
are appearing in the United States and Europe
are increasingly influenced by the encounters that
our artists and musicians have with non- Western
cultures, notably African, and with electronic
tools and gadgets, including the computer. I
mention all this only to emphasize once more that
progress results from cross-fertilization and to
stress that in any area of human activity, signifi-
cant novelty is only achieved by going beyond the
frontiers of that area through adoption of achieve-
ments from other areas.
Let me close by reflecting briefly on how these
general ideas of breadth and creativity can be put
into practice, given the inevitable boundary con-
ditions under which we must operate. In under-
graduate programs, our primary educational ob-
ligation is to impart professional competence such
that our alumni, within a year or less, can make
productive contributions to their employers. To
achieve that end in a reasonable number of se-
mesters, we tend to believe that we must fill the
curriculum with numerous required courses, leav-
ing little room for breadth. I suspect that we have
gone too far in specific course requirements and
that at least a few required courses are in our cur-
riculum not because they are truly necessary but
because of tradition (because the professors re-


sponsible for the curriculum took these courses
when they were students) and because every pro-
fessor in the department insists that his particular
specialty must be taught to everyone, essentially
because he likes to teach it.
If we are serious about encouraging creativity
for undergraduates, we must open up the curricu-
lum and encourage at least our better students to
become familiar with intellectual concepts and
tools that are not now common in chemical engi-
neering. Clearly, not all students will benefit from
such exposure, and therefore we should have
flexibility such that our average students will do
more or less what they do now but where the
student with unusual potential is permitted and
encouraged to deviate from the norm and to direct
at least a part of his imagination toward other
intellectual disciplines.
For graduate education, where the curriculum
is less rigid, we should insist that our students take
some high-level courses in other departments. By
high-level, I mean courses with significant intel-
lectual content; that is, courses taken by majors in
other fields, and not survey courses designed for
general education. Further, we should encourage
independence and develop self-confidence by insist-
ing that in their second year of graduate study, our

Q o book reviews

by Peter C. Powell
Chapman & Hall, 733 Third Ave., New York;
$49.95 HB, $25 PB (1983)
Reviewed by
James M. McKelvey
Washington University
Engineering with Polymers by Peter C. Powell,
Mechanical Engineering Department, Imperial
College, London, is a text designed for final year
undergraduate students in mechanical engineer-
ing. It assumes no prior knowledge of polymer
science or chemistry on the part of the student.
It is the author's stated intent to present the
"minimum useful knowledge of engineering with
polymers within a mechanical engineering degree
There are four main sections to the book: (1)
The first four chapters provide an introduction to
the language, terminology, and technology of
polymers. This includes an introduction to polymer

PhD students pass an oral proposition examina-
tion where the candidate proposes an original re-
search project on a subject remote from his PhD
thesis. The student must defend his proposal to a
committee of professors that should include one or
two colleagues from departments other than chemi-
cal engineering. Except for remoteness from his
thesis, there should be no restriction concerning
the subject of the proposed research. The im-
portant point is that the student must choose the
proposed research topic himself, that he receive
minimum guidance in preparing his defense and
that in judging the proposal, the examining com-
mittee insist on high intellectual standards, regard-
less of utility.
Given the job-oriented goals of the chemical
engineering curriculum, it is not likely, nor is it
desirable, that there be a major shift in the intel-
lectual menu for most chemical engineering
students. But for those students who have creative
potential, I hope that we can relax our sectarian
interests and expose them to intellectual vistas that
at present have nothing to do with contemporary
chemical engineering but that some day, through
the inventive genius of our younger colleagues,
may broaden and enrich the domain of our pro-
fession. O

physics, polymer materials science, and polymer
processing. (2) Two chapters provide an intro-
duction to the mechanical behavior of polymeric
materials, one on stiffness and the other on
strength. (3) One chapter outlines the mechanics
of fiber reinforced composites, and (4) Two
chapters provide an introduction to polymer fluid
flow, heat transfer and the effect of processing on
Given the mechanical engineering orientation
and purpose of the book it is not surprising that
the book's most comprehensive treatment is given
to the mechanical behavior of polymers and the
mechanics of composites. The treatment of polym-
er processing is largely descriptive and somewhat
superficial. A valuable part of the book are the
problems associated with each chapter and an
outline of the solutions, which makes the book
well suited for self-study. The sections on polymer
and composite mechanics would be a useful adjunct
to a first course in polymers for chemical engineers,
which would probably provide a more compre-
hensive introduction to property-structure re-
lationships and processing. O


lao laboratory


Bucknell University
Lewisburg, PA 17837

RAPID INCREASES IN technology, computer liter-
acy requirements, and the current trend to
achieve the BS degree in four years or less, create
heavy academic pressures on engineering students.
With laboratories occupying approximately one
third of the student's scheduled time, it is essential
that this time be used efficiently by both students
and faculty. Current students are demanding more
participation in the practical aspects of chemical
engineering [1]. However, universities are un-
able to provide the type of equipment used in in-
dustry because of budget constraints, and thus
most academic engineering equipment dates from
the 1950's. An article in Chemical Engineering
News [2] describes the deteriorating quality of
chemical engineering education as a result of
faculty shortages and equipment obsolescence.

1 k

William J. Snyder received his BS, MS and PhD degrees at Penn
State. He worked for R. W. Coughlin as a postdoc at Lehigh Uni-
versity before moving to Bucknell University. His chemical interests
are in thermodynamics, kinetics, polymer science and computer-aided
design. He is currently performing research on polymer degradation
and chemical sensors. (L)
Michael E. Hanyak received his BS at Penn State, MS at Carnegie-
Mellon and PhD at the University of Pennsylvania. After working at
Air Products for three years on developing a steady-state process
simulator for cryogenic systems, Dr. Hanyak moved to Bucknell in
1974. His chemical engineering interests are in computer-aided design
and thermodynamics. (R)

... universities are unable to provide the
type of equipment used in industry because of budget
constraints, and thus most academic engineering
equipment dates from the 1950's.

Also, in the university environment, increased
demand on scholarly development by the faculty,
larger enrollments, and the low priority of labora-
tory development have exacerbated the problem.
One way of alleviating some aspects of this
problem while increasing the effectiveness of
laboratory time is to implement the concept of
computer-aided laboratory stations (CALS).
By augmenting the laboratory with computer
stations for data acquisition and control, many
advantages are obtained, such as
Increasing the efficiency of student laboratory time
Providing necessary training for skills needed in
Increasing the student's capability of performing
complex and complete data analysis
Providing students with the opportunity to analyze
real problems, exercise engineering judgment, and

Contents of a Laboratory Station

* Apple II Plus System-48K
* Disk II Floppy Disk & Interface
* Language System with PASCAL
* Second Disk II Drive
* Thermal Printer
* 80-column Video Board
* FORTRAN Compiler Software
* IMI ADALAB Add-On Package
* IMI ADA-AMP Instrumentation Amplifier
* IMI VIDICHART, Scientific Plotter, and Curve Filter
* Secure Equipment Cart
* Electronic Hardware
-Two Prototyping/Hobby Cards
-Three Transformers
-Filters & Circuit Breakers
-Rack panels & Mounting chassis
-Nine Relays
-Thermocouple Jacks & Plugs

Copyright ChE Division, ASEE, 1985



1 I

FIGURE 1. Computer Assisted Laboratory Station

express creativity
Increasing faculty efficiency, but not at the cost of
student interaction.

A laboratory station must be able to receive
analog or digital data from sensors, to condition
signals, and to either create a display or store the
data. Students need to interact with the station by
programming in higher level languages such as
BASIC, FORTRAN, and PASCAL instead of as-
sembly language. The station should be linked to
a mainframe computer by a high speed modem
for long term data storage, statistical analysis,
and text or graphic output. For the control of
laboratory processes, the station must be able to
send digital or analog signals to stepping motors
and voltage controlled instrumentation. The sta-
tion should provide a visual status report upon
request, contain alarms, and produce good hard
copy. Finally, because of space limitations the
station is restricted to the size of a small desk or
carrel and should be of modular construction.

The critical state of laboratory instruction
clearly dictates the focused use of the computer
for data acquisition and control. Realizing the ad-
vantages of CALS, the Chemical Engineering De-
partment at Bucknell designed and constructed

two portable stations at a cost of approximately
$6000 per station (1981 prices). Each station con-
tains an Apple II Plus computer, a television
monitor, two disk drives, a language card, a
thermal printer, an 80-column video board, a
micromodem, and the ADALAB system from
Interactive Microwave, Inc. (IMI). Table 1 de-
scribes this equipment in more detail. In addition,
software in BASIC from IMI is provided for data
acquisition, control and data analysis.
All the equipment, including manuals and disk
storage racks, is contained in a mobile 3' x 5' x 2'
security cabinet. The portable CAL (Fig. 1) al-
lows students to roll the station to their experi-
ment, plug in wires that monitor temperature,
pressure, or composition and to run software to ac-
quire data. Also, the students can write programs
to control the experiment. For powerful data;
analysis, students can transfer the data from
Apple diskettes to Bucknell's time-sharing com-
puter using the micromodem. In addition, the
student has access to a small graphics tablet (Fig.
2) connected to the Apple for digitizing data that

FIGURE 2. Digitizing Station

is not convenient for data logging but is needed in
a computer file.

The characteristic response is an important
consideration when selecting or specifying sensors.
For example, accurate control of humidity is often
required in chemical processes and in heating-
ventillation-air conditioning systems (HVACs).
A knowledge of sensor response time over a range
of operating conditions is necessary for the de-
termination of a transfer function with humidity


S. the work load on the faculty is reduced without sacrificing quality. The
use of the CAL concept for a portable station provides flexibility and ease of operation without
expensive duplication of equipment. Educational laboratories now can
simulate industrial environments at a minimum cost.
r- 1

FIGURE 3. Diagram of Humidity Chamber

as the measured variable. The objective of this ex-
periment is to determine the response times of a
solid state humidity sensor at various humidity
conditions and to develop an empirical model for
the sensor.
The sensor used in this experiment is a small
(0.5 cm) fast response solid state device. Figs. 3
and 4 show an environmental chamber for sub-
jecting the sensor to step changes in humidity.
The humidity in each well-mixed chamber is con-
trolled by varying the temperatures of saturated
salt solutions. The sensor is mounted on a sliding
rod and can be rapidly transferred from one
chamber to the other. The voltage output from the
sensor (0-3 volts dc) is sent to an ADALAB

FIGURE 4. Humidity Chamber

system which is controlled by the Apple com-
puter. Use of the VIDICHART software enables
data acquisition of sensor voltage. Typical sensor
response data expressed in terms of a first order
time constant are shown in Table 2 and Fig. 5.


Personal computers, when configured for
laboratory use, not only increase the efficiency of
students but provide an exciting experience for

Calculated Sensor Response Data

Soln. Temp Air Temp. Trial 1 Trial 2
Salt 0C 0C RH, % t, secs. t, secs.

Run #1
Potassium Flouride 31.5 30.4 26.5 75.0 75.2
Sodium chloride 24.0 28.4 75.5 82.8 82.5
Run #2
Lithium chloride 11.7 25.4 11.0 12.2 12.5
Potassium sulfate 10.8 25.8 98.1 15.8 15.8
Run #3
Lithium chloride 24.1 25.3 11.5 1.4 1.3
Potassium sulfate 23.8 25.2 97.3 9.0 9.1




91.00 -





0 12.50

13.00 13.50 14.00


FIGURE 5. Sensor Output

J P book reviews

by H. V. Tyrrell,, and K. R. Harris.
Butterworths (1984). 448 pages, $75.00.
Reviewed by E. N. Lightfoot
University of Wisconsin
This book, originally conceived as a revision
of Tyrrell's "Diffusion and Heat Flow in Liquids,"
is intended to give the non-specialist a balanced
summary of the literature on both theoretical and
practical aspects of diffusion in liquids, of sufficient
depth to provide effective access. Both translation-
al and rotational diffusion under the influence of
arbitrary driving forces, in binary as well as multi-
component systems, are discussed. It was deemed
that heat flow could no longer be included in a
book of reasonable length without undue sacrifice
of depth.
The first four chapters are used to establish
the foundations of transport theory, starting with
the classical phenomenological description. The
phenomenological introduction is followed by a
summary of non-equilibrium statistical mechanics
which permits, at least in principle, the calculation
of transport properties from molecular parameters.
The primary purpose of these chapters is to pro-

*I *I* **I**K*



them. Since students enjoy computers, they are
easily motivated to expand their ideas beyond the
laboratory time and gain valuable skills by self-
study. Because hardware and software to inter-
face the Apple Computer to laboratory experi-
ments is commercially available, the work load on
the faculty is reduced without sacrificing quality.
The use of the CAL concept for a portable station
provides flexibility and ease of operation without
expensive duplication of equipment. Educational
laboratories now can simulate industrial environ-
ments at a minimum cost. O


We would like to thank Robert J. Murcek for
his ideas and time in implementing the GALS.

1. Lipowicz, Mark A., and Roy V. Hughson, "Putting
College Back on Course," Ch.E., 90, 19, p. 48, Sept.
2. Worthy, Ward, "Chemical Education Falls on Hard
Times," C & EN p. 43, Feb. 9, 1983.

vide a unified treatment adequate for understand-
ing modern methods of interpreting experimental
Chapter 5 provides rather detailed descrip-
tions of the most widely useful techniques for
gathering data, and Chapters 6 to 8 are devoted
to interpreting experimental results in terms of
kinetic theory and physical models.
Translational diffusion coefficients have been
measured for well over a century, and many classic
techniques have been highly refined and are still
widely used. Among those described by the authors
are optical techniques based on Gouy and Ray-
leigh interference phenomena (much improved
in the last decades by the availability of lasers),
diaphragm cells, use of Taylor dispersion (which
has become important because of its speed), and
light scattering.
Photon correlation techniques have made light
scattering methods particularly important for
macromolecules such as proteins, but effective use
of these methods requires understanding of the
underlying physics, as does the use of nuclear
magnetic resonance for description of rotational
diffusion. Largely because of this need Chapter 5
is rather long and detailed.
Chapter 6 is devoted to the interpretation or

Continued on page 49.

Ei laboratory




Villanova University
Villanova, PA 19085

O NE OF THE MOST frequent activities of practic-
ing chemical engineers is design-in one form
or another. Yet the laboratory rarely, if ever, pro-
vides experience in this area. Many good reasons
exist for this, but these will not be discussed here.
Rather, one experiment will be discussed in the
hopes of stimulating similar experiences for
chemical engineering students in laboratory.
The laboratory experiment in sequential de-
sign was organized around a central problem-to
separate a mixture of essentially two kinds of
particles by fluidization principles. Fluidization
had only been touched upon briefly in a previous
course, so the subject matter was new but not com-
pletely unfamiliar. The problem was defined as
follows: in certain processes solid particles are
treated to expand their structure or create large
internal pore volume. Not every particle is suc-
cessfully treated, and the need exists for separat-
ing the untreated or poorly-treated particles from
those that meet the product requirements. The
particles differ in density and size, so that some
fluidization or elutriation technique can be used
for the separation. The overall objective of this
semester-long exercise was to design, build, and
operate an apparatus to solve the problem.
Fluidization laboratory exercises have been de-
scribed previously [1] but not in the sense of a
design problem with the goal of building a func-
tioning unit.

The particles differ in density and
size, so that some fluidization or elutriation
technique can be used for the separation. The overall
objective of this semester-long exercise was
to design, build, and operate an apparatus
to solve the problem.

Copyright ChE Division, ASEE, 1985

Donald D. Joye is currently Assistant Professor of chemical engi-
neering at Villanova University. He joined the staff at Villanova in
1981 after previous teaching and industrial experience. He received
his BSE degree in chemical engineering from Princeton University in
1967 and his MS and PhD from Lehigh University in 1969 and 1972,
respectively. Dr. Joye's research interests are in fluid mechanics and
related fields, heat transfer, and the unit operations. He is a register-
ed patent agent and has particular interests in teaching problem
solving skills and the innovation process.

Each lab group worked on a separate step of
the design in a sequence selected by the instructor
in a manner similar to the way a design team
might function. All lab groups were required to
read and understand basic fluidization principles
as described in standard textbooks such as Foust,
et al. [2], McCabe and Smith [3], etc. Each group,
when its time came for the lab, was given an as-
signment and shown why that particular job
needed to be done.
Students working in the early stages needed
to characterize the particles with respect to size
(equivalent diameter) and true density, in order
to calculate terminal speeds and fluidization veloci-
ties. The particles were highly irregular, which
made the job somewhat challenging. Particles of a
given kind were not all the same size, so some
statistics [4] were used to quantify expected vari-
ations. Other lab groups tested these results by
finding terminal speeds experimentally. Fluidiza-
tion theory was then used by subsequent groups
to select an appropriate fluid velocity that would
carry the light particles out with the fluid and


leave the others behind. Design of the column and
selection of the prime mover from materials avail-
able in the lab (a design constraint) were then
carried out. Several groups then participated in
constructing and testing the unit. Finally, opera-
tion of the equipment to achieve the desired ob-
jective was undertaken-with all groups watching
the final test runs.

Fluidization theory and drag force phenomena
on particles are well-known and well-documented
[5]. Irregularity of the particle shape, however,
creates some interesting problems for the students.
What is the diameter of an irregularly shaped par-
ticle? Would a shape factor be appropriate? Neces-
sary? How does one measure true density when
the geometry cannot be characterized clearly? Most
of these questions were answered by application
of fluidization principles and problem solving
Calculation of terminal speed also involves un-
knowns. Air was selected as the fluid due to the
nature of the particles. The terminal speeds of the
particles in air could be calculated after the regime
of fall was known. The trial-and-error method of
Foust et al [2] or the K-factor approach of McCabe
and Smith [3] could be used here. Then the ap-
propriate terminal speed equation could be select-
ed. For example, if the fall of the particle through
air were in the Newton's Law region where the
Reynolds numbers are relatively high, e.g. greater
than about 500 but less than about 200,000, the
terminal speed can be calculated by

vt = 1.75 Vg D,(p,-p)/p (1)

where vt = terminal speed
g = acceleration of gravity
D, = (equivalent) diameter of particle
pp = density of particle
p = density of fluid.

The minimum fluidization velocity is the gas
velocity at which fluidization begins. Prior to this
condition air would pass through a bed of particles
without disturbing them (packed bed). Once the
minimum fluidization velocity is exceeded, the bed
expands and is said to be fluidized, up until the
terminal speed is reached. At this point the par-
ticles are carried along with the fluid, and a stable
bed of particles no longer exists. The Ergun equa-
tion [2, 3, 5] can be used with a substitution for
the pressure drop term to give an equation from

The overall design concept was
that of a vertical column of a certain height
and diameter connected to an air blower
with the appropriate pressure drop-
throughput characteristics.

which the minimum fluidization velocity can be
calculated [3]
1.75 D,2 P2 v2 + 150 Dp (1-EM) Vo
e EM3 1L2 02 EM3 /1
D,) gp (PP-p) = 0 (2)
Z 0 (2)

where 4 = shape factor
Em = packed bed porosity
vo = superficial (average) velocity.
In this case the shape factor was set equal to
1.0, because the geometry of the particles could
not be quantified by well-known methods. The bed
porosity was measured experimentally.
Once the terminal speed and minimum fluidiza-
tion velocity have been determined, a porosity dia-
gram (shown in the next section) can be con-
structed for both kinds of particles. From this dia-
gram an appropriate air velocity can be selected.
In addition, this diagram shows what will be
happening to the other kinds of particles at the
selected operational air velocity.
Design of the column reduces to selecting an
appropriate column diameter considering the
particle diameters and the fact of fluidization.
Blower sizing can then be done on the basis of
volume throughput and pressure drop. The pres-
sure drop through the fluidized bed can be esti-
mated by equating the force exerted on the solids
to the force of gravity minus the buoyant force
of the displaced fluid [3]
AP = ghM (1 er) (p p) (3)
where AP = pressure drop
h, = height of packed bed of solids
This pressure drop is essentially constant for
batch fluidization (prior to entrainment). When a
mixture of particle types is present, and one type
is being entrained while the other is not, it becomes
difficult to calculate the bed pressure drop ac-
curately and some estimate must be used.

Twelve lab groups participated in this experi-
ment. The first six groups worked on preliminary
design calculations, and the last six worked on the
design, construction, operation, and checking of


The first lab group determined an average
diameter and density for the relatively dense and
non-porous particles. This was accomplished by
weighing sets of particles and dropping them into
a graduated cylinder partly filled with oil, so that
the volume change could be observed. The fluid
used in the cylinder was oil, which would slow
down or prevent absorption of the liquid by the
particles. The average density was found to be
1.23 g/cc. The total volume of a known number
of particles was then used to calculate a volume-
average diameter based on spherical geometry.
This diameter was 0.574 cm. The methods of
achieving the assigned objectives were left to the

more porous particles. These particles were very
porous and much more irregular than the others.
Volume displacement techniques were much more
difficult to perform. These particles were also
more fragile than the dense ones. One group de-
cided to take ruler measurements of the longest
and shortest diameter they could measure and
average the results. This gave an arithmetic aver-
age diameter of 1.47 cm with a standard deviation
of 0.34 for a sample size of 50. The second group
decided to measure diameter by terminal speed
experiments. This gave 1.19 cm for the diameter
with a standard deviation of 0.21 for a sample
size of about 20. One group calculated a density
based on weight of the particle, the arithmetic

The separation was successfully effected by the last group, and a
good time was had by all at the demonstration. What material was used for
the particles? Popped and unpopped popcorn kernels. Needless to say,
the students consumed the data with enthusiasm.

group members with little input from the instruc-
The second lab group also worked on the dense,
nonporous particles. They used a similar technique
for density measurement but with water as the
working fluid. Their density was 1.31 g/cc, slight-
ly higher than the previous group's value. This
could be explained in part by water absorption re-
ducing the displaced volume, and in part by vari-
ation in samples taken from the broad particle
population. An overall average density of 1.27 was
used. To find the equivalent diameter this group
decided to try a terminal speed experiment. They
first dropped spheres of known diameter and
weight into a heavy mineral oil to determine its
viscosity (Reynolds numbers were in the Stokes'
Law region [2, 3]), then dropped particles into the
same oil, measured the terminal speed, and used
the Stokes' Law terminal speed equation to calcu-
late a diameter (Reynolds numbers for this case
were just less than 1.0 and Stokes' Law could be
used). This projected diameter was found to be
0.476 cm, which is less than the previous estimate.
The particles were not spherical and apparently
slightly elongated, so that the smaller cross-
section would be perpendicular to the flow di-
rection in free-fall experiments. This group also
calculated the packed bed porosity by volume dis-
placement (of oil this time) and the minimum
fluidization velocity from Eq. 3. Packed bed
porosity, EM, was 0.36, and the minimum fluidiza-
tion velocity in air at 23C was 1.13 m/s.
The next two groups worked on the less dense,

average diameter and spherical geometry. The
average density was 0.042 g/cc with a standard
deviation of .022, quite a large spread. The aver-
age terminal speed of these particles in air was
measured to be about 3.5 m/s with a standard
deviation of 0.31. Distance of fall was about 4 m,
so true terminal speeds were probably a bit high-
The following two groups completed the pre-
liminary calculations by determining the terminal
speed in air of both dense and light particles, find-
ing minimum fluidization velocity and packed bed
porosity of the light particles and evaluating the
distance vs. speed relationship in free fall to es-
tablish the reliability of terminal speed experi-
ments. One of these groups calculated density and
porosity by pouring oil into a beaker filled with
particles. A screen was used to keep the particles
submerged. Weights and volumes were recorded.
They reported a density of 0.08 g/cc and a porosity,
E,, of 0.68. This density was considered to be too
high because of absorption of oil and compaction
and breakage of the particles, so an average of the
two density estimates was used. The calculated
minimum fluidization velocity for the light
particles was 1.04 m/s in air at 23C.
The terminal speed of the more dense particles
falling through air was also measured experi-
mentally. In the early measurements, however, the
particles fell so rapidly through 4 meter distance
that accurate timing could not be done. Thus, an-
other group needed to establish what distance was
needed to reach terminal speed, and what distance


was required to get an accurate measure for
terminal speed. This can be carried out by a
graphical integration of the force-balance equation
as discussed by McCabe and Smith [3] when
distance is set equal to the integral of vdt. The re-
sults showed that the light particles needed about
2.75 m to reach 95% of terminal speed, while the
more dense particles needed about 22 m to reach
95% of their terminal speeds. Terminal speed
experiments for the light particles were then re-
peated, subtracting out the distance required to
reach terminal speed and timing the fall from this
point on. The results were not significantly differ-
ent than before. For the more dense particles a
place greater than 22 m tall and still safe for
students to be running an experiment could not
be found on campus, so the students decided to
settle for the stairwell of a building five stories
high and time the fall for the last two stories. The
average terminal speed was calculated from 45
runs to be 16.2 m/s with a standard deviation of
The results for preliminary calculations are
summarized in Table 1. This information can be
used to construct a bed porosity chart as shown in
Fig. 1. The data points on the figure are from ex-
perimental tests discussed subsequently.

During the remainder of the semester six
other groups worked on the design of the separa-
tor using the information provided by the first six
groups. The overall design concept was that of a
vertical column of a certain height and diameter
connected to an air blower with the appropriate
pressure drop-throughput characteristics. Two
groups rummaged about the lab looking for suit-
able equipment. Eventually a plastic column .203 m
(8-inches) nominal diameter and about 1.2 m long
was found and deemed suitable. Squirrel cage blow-

Summary of Results of Preliminary
Design Calculations

Estimated diameter, cm
Terminal speed diameter, cm
Average density, g/cc
Packed bed porosity, EM
Min. fluidization
velocity, m/s
Terminal speed in air, m/s

0.574 1.47
0.476 1.19
1.27 0.06
0.36 0.68

1.13 1.04
16.2 3.5

0.8 I 2 4 6 8 10 20

FIGURE 1. Porosity diagram for light and dense particles
with experimental results.

ers were considered and discarded on the basis of
insufficient throughput and probably not enough
pressure drop. Finally a 0.75 kW (1 hp) centri-
fugal blower was decided upon. Estimations were
made rather roughly in this stage. A safe design
velocity was chosen to be about 4.5 m/s, at which
point over 90% of the light particles would be en-
trained, and the dense particles would be in a
fluidized state. The bed height could only be guessed
at, since the amount of dense particles in the feed
was not precisely known. The percentage of dense
particles (by number) in the feed was estimated
to be 10% 5.
The third group constructed the apparatus.
Some modifications were, of course, necessary. A
screen was placed at the bottom of the column to
prevent material from entering the blower. It was
decided to operate batchwise given the constraints,
and an adaptor had to be fabricated to connect the
.203 m (8-inch) diameter column to the .127 m (5-
inch) diameter blower outlet pipe. Of course no
specifications were available for the blower, so the
students had to determine the throughput experi-
mentally. The inlet side of the blower contained a
throttle plate and an orifice-manometer setup to
do just that. A schematic of the apparatus is shown
in Fig. 2. It soon became obvious that a means for
collecting the entrained particles was required. A
fourth group designed a collector, but after con-
sidering the effort required to build it, decided to





orifice and

centrifugal blower
and motor
FIGURE 2. Apparatus

make do with a large plastic trash bag with holes
punched in it.
The estimated pressure drop was about 5 cm
(2 inches) of water; the required throughput was
0.13 m3/s (280 cfm) of air at 23'C, and the input
power required was about 0.1 kW (.125 hp). With
a blower of .75 kW (1 hp) rating, the (installed)
maximum throughput was found to be 0.2 m'/s
(425 cfm), which was plenty adequate, if not a
bit oversized.
The last two groups operated the column. One
group checked the predicted porosity diagram, and
the other group operated the column for separa-
tion. From the data points shown in Fig. 1, the
predicted porosity curve was closely approximated
in the case of the light particles. In the case of
the dense particles, the experimental results were
nowhere near the predicted curve. One could
easily see the reason for this during the operation
of the unit when the dense particles alone were
present. Air from the blower was not uniformly
distributed across the column cross-section. In
fact it appeared that circulation currents were
present, such that half the bed was not even
fluidized, while the other half was shooting about
inside the column. Only a crude estimate of the
bed height could be made. This situation was
clearly different from textbook expectations and
gave the students a real insight into the difficulties
of maintaining fluidized beds. The light particles

were larger, less dense and required a lower veloci-
ty for fluidization, such that the above phenomena,
though still present, was much reduced in intensi-
ty. Designing an air distributor could have been
undertaken at this point to overcome the problem
-but wasn't because of lack of time. This would
have brought the experimental data for the dense
particles more in line with expectations from
The separation was successfully effected by the
last group, and a good time was had by all at the
demonstration. What material was used for the
particles? Popped and unpopped popcorn kernels.
Needless to say, the students consumed the data
with enthusiasm.


The foregoing has presented the details of an
unconventional laboratory exercise which brings
design experience to the students in a laboratory
setting. In addition the exercise has proved power-
fully supportive of the following teaching values:
How to deal with the unexpected.
How to deal with constraints.
How to make engineering decisions where precise
measurement is impossible or when good informa-
tion is not available.
How to size and modify equipment.
How to accomplish an overall objective by breaking
down the larger job into smaller parts and working
to solve one part at a time.
The value of checking back and evaluating past work.
Gives students satisfaction at seeing the job done
successfully and understanding where their part fit
into the whole effort.
Challenges the students with a real-world problem
that has an achievable solution reasonably within
their grasp.
It was fun, something students could relate to easily.
Stimulated students to think beyond the immediate
solution, for example several students recognized that
the apparatus would not do for home application! E

1. L. T. Fan, "Fluidization as an Undergraduate Unit
Operations Experiment," J. Chem. Educ., 37 (7), 259
2. A. S. Foust, et al., Principles of Unit Operations, 2nd
ed., J. Wiley and Sons, NY, 1980.
3. W. L. McCabe and J. C. Smith, Unit Operations of
Chemical Engineering, 3rd ed., McGraw-Hill, NY,
4. Chemical Engineers' Handbook, R. H. Perry, et al.
(eds.), 5th ed., McGraw-Hill, NY 1973.
5. D. Kunii and 0. Levenspiel, Fluidization Engineer-
ing, J. Wiley & Sons, NY, 1969.


BEbook reviews


By J. T. Oden and G. F. Carey;
Prentice-Hall, Englewood Cliffs, NJ 07632
(1983) $29.00 Cloth

Reviewed by
Bruce A. Finlayson
University of Washington

The finite element method is becoming in-
creasingly popular as a method for solving differ-
ential equations in chemical engineering. Conse-
quently, students are demanding information
about it even if their professors obtained their
training before finite element methods were well-
known. For this reason, short concise books on the
finite element method are especially welcome. This
book is Volume IV in a series of six books by the
authors. Each book is a succinct book on this sub-
ject. Since chemical engineers may be more inter-
ested in the other volumes in the series the topics
are listed here: Volume I-An Introduction; Vol-
ume II-A Second Course; Volume III-Computa-
tional Aspects; Volume V-Special Problems in
Solid Mechanics; Volume VI-Fluid Mechanics.
Volume IV begins with the chapter on nomen-
clature, defining Sobelov spaces for example. This
beginning chapter emphasizes to the reader that
it is the mathematical aspects of the theory that
are to be presented. The next chapter on interpola-
tion theory shows the best error estimates that
can be achieved since a finite element approxima-
tion to solutions of differential equations can never
be better than the interpolation of the exact solu-
tion. Then 3 remaining chapters deal with elliptic
boundary value problems: the regular approach, a
mixed method, and a hybrid method. In the mixed
method one solves for the function and derivative
(like temperature and heat flux) while in the hy-
brid method one relaxes interelement continuity
and adds a Lagrange multiplier constraint.
In all three chapters, the variational theory
is first presented, thereby changing the differential
equation to a variational statement. Then error
estimates are provided for the finite element ap-
proximations of these problems and theorems are
proved under which they apply. Finally example
applications are given usually to the Poisson equa-

tion or the heat conduction equation with a known
generation term.
A book such as this is heavy going unless the
reader has some exposure to functional analysis,
although the theorems are clearly identified and
can be used without studying the proof. Some of
the conditions of the theory (Babuska-Brezzi con-
dition) could not be used, though, without a func-
tional analysis background. Thus this book will
appeal to a small segment of the chemical engi-
neering audience, but is a welcome companion to
the other volumes in the series. O


Dear Sir:
Since I think it is important that you know
this, I take great pleasure in informing you that
on July 4, 1984, the "Universidad Nacional del
Litoral," in the city of Santa Fe, Argentina,
granted the first doctoral degree in Chemical
Engineering in this country, the thesis work
having been carried out at the Institute of Techno-
logical Development for the Chemical Industry
(INTEC). The second doctoral degree, this time
conferred to a woman, was also granted by UNL
and INTEC.
Sincerely yours,
Dr. Alberto E. Cassano

books received

Machine Design Fundamentals: A Practical Approach,
U. Hindhede, J. R. Zimmerman, R. B. Hopkins, R. J.
Erisman, W. C. Hull, and J. D. Lang; John Wiley and
Sons, New York, 10158; 642 pages, $43.95 (1984)
Handbook of Industrial Water Conditioning, Eighth
Edition; Betz, Trevose, PA 19047; 437 pages (1983)
Coal Liquefaction Products, Vol. 1. Edited by H. D.
Schultz; Wiley-Interscience, NY 10158; 415 pages, $65.00
Plastics Products Design Handbook, Part B: Processes
and Design for Processes, Edited by Edward Miller;
Marcel Dekker, Inc., NY 10016; 392 pages, $55.00 (1983)
Pascal Applications for the Sciences: A Self-Teaching
Guide, Richard E. Crandall; John Wiley & Sons, New
York; 246 pages, $14.55 (1984)





University of Queensland
St. Lucia, Qld, 4067

T HERE IS A GRAVE need to modernize chemical
engineering education within universities. This
contribution presents the current problems and
describes the proposed plan of the Queensland de-
partment to implement a scheme for resource-
based education in chemical engineering. The
financial cost over the period 1984-1989 is esti-
mated to be as high as half a million dollars. Ad-
ditional efforts of dedication and self-sacrifice by
staff are necessary but cannot be quantified.

The traditional mode of instruction in chemi-
cal engineering over the past forty years has
mainly been lectures supplemented by some prob-

lem and laboratory classes, and yet outside the
university a major information revolution has
taken place. In the light of these changes the time
is prudent to evaluate whether better use of new
resources can alleviate the problems that are per-
ceived by this department. These problems are
touched on in the following paragraphs.
Content. The content of the degree course is
expanding in response to rapid growth in both the
breadth and depth of engineering knowledge. The
rapidly expanding base of engineering knowledge
tends to submerge and confuse students' under-
standing of fundamental principles.
Structural Changes. The graduate in industry
has at his command a vast resource of information
in databases and computer software packages. He
is no longer expected to carry out routine engineer-
ing calculations but, rather, has to select the
correct computer package and critically evaluate
the results. To perform these tasks a student

Bob Newell received his B.Sc.
App. and B.E.Chem. from Queens-
land and his PhD from the Uni-
versity of Alberta, Canada. He
also has a Dip.Ed. in Tertiary Edu-
cation from Monash. He joined
the staff at Monash University in
1974, and moved to Queensland
in 1980, where he is currently a
Senior Lecturer. His early research
was in the multivariable control
of a pilot plant evaporator, un-
stable steady state control in a
CSTR and multilevel heirarchical
optimization. Current interests in-
clude optimization of the Australian oil refinery and transportation
system, combined fuzzy and deterministic control, and selftuning and
adaptive control of heat recovery systems. (L)
Peter Lee is a Lecturer in ChE. He received his B.E.Chem. from
RMIT in Melbourne and his PhD from Monash University in 1980. He
worked in the design and commissioning of computer control systems
for both continuous and batch plants for three years before coming
to Queensland. His early research was on the control of the unstable
steady state in an exothermic CSTR. His interests include multivari-
able self-tuning and adaptive control of fermentation and heat re-
covery systems. He is also involved in industrial projects involving

waste-water treatment, grinding circuits, and mineral flotation. (C)
Ming Leung holds a Personal Chair and is currently Head of De-
partment. He graduated from Imperial College (BSc) and Cambridge
University (PhD). Prior to joining the University of Queensland he
spent several years in the oil and chemical industries. His research
interests are in gas-solid flow and fluidization. He was the recipient
of the Distinguished Lecture Award at the Fourth International Sym-
posium on Freight Pipeline Conference at Atlantic City, and a keynote
speaker at the third Engineering Foundation Fluidization Conference
at Henniker. He has served as a consultant in the USA, Europe, South
Africa, and Australia, mainly on standpipe flow. (R)

Copyright ChE Division, ASEE, 1985



I 1986 I 1987 I 1988








should be thoroughly grounded in fundamentals
and exposed to various software packages.
Laboratory. Much of the laboratory equipment
and many experiments in the Queensland Depart-
ment of Chemical Engineering are becoming ob-
solete. As a result, some of the skills students are
being taught are increasingly irrelevant in a
modern industrial environment. Indeed, in many
areas industrial practice is far in advance of our
laboratory experiments.
Student/Staff Ratio. The increasing student/
staff ratio means less feedback to students in
terms of comments on tutorial problems and
practical reports. We need to promote more inter-
active teaching practices and more efficient use of
student-staff contact time, i.e. more opportunity
for individual contact and discussion and fewer
formal "one-way" lectures.
Literacy. In the age of electronic media, in-
coming students are less inclined and less able to
extract information efficiently from books. While
we may decry this trend, we must nevertheless
adapt to it. Course notes, directed reading, and
information databases are some possible aids in
this area.
Motivation. The changing social environment
and the secondary school environment are no long-
er producing students who are "automatically"
motivated. We need to introduce instructional
techniques to instill motivation as well as concepts

and knowledge. Course and subject objectives and
the increased use of interactive media and personal
contact will assist.


To meet the challenge of educating chemical
engineers for the 1990s, a fundamental evaluation
of the curriculum and the mode of instruction is
being carried out in the department. It is recog-
nized that the traditional mode of instruction needs
to be reviewed, together with curriculum re-evalu-
After much discussion in the department
during 1983, a plan has evolved to change the
mode of instruction towards a resource-based and
partly self-paced learning environment.
The plan is to implement the new mode pro-
gressively from 1985, after a detailed curriculum
re-evaluation and writing of aims and objectives
for the course and individual subjects has been
carried out. Fig. 1 shows the current planning
diagram for the project. The main features of the
new scheme are described in the following para-
1. Reducing the total number of lectures
given in the course and reserving the remaining
lectures to concentrate on fundamental principles.
Currently there are a large number of lectures
and students are often unable to discriminate be-



1984 I 1985

1o C-A -/I

The traditional mode of instruction in chemical engineering over the past forty
years has mainly been lectures supplemented by some problem and laboratory classes, and yet
outside the university a major information revolution has taken place.

tween fundamental principles and the vast amount
of factual material presented.
2. Setting up self-paced laboratories, with
long opening hours attended by academic staff. The
laboratories will be refurbished to modern engi-
neering standards and experiments will be de-
signed to meet specific objectives. Written or video
tape aids will be available to assist students in
carrying out experiments. The objectives of these
experiments may be (i) teaching of experimental
design, (ii) demonstration of difficult to under-
stand concepts, and (iii) simulation of experiments
carried out in industry. Currently, students are
required to carry out specific experiments at
scheduled classes. In a class-like atmosphere with
many students working at one time, staff-student
contact often takes the form of staff advising
students what to do rather than discussion of the
results and underlying precepts. By providing
better guidance on how experiments should be
conducted, more time will be available for discus-
sion of results. The quality of staff-student con-
tact will improve.
3. Setting up a laboratory of demonstration
experiments. They will be very simple and easy
to operate experiments for illustrating basic
principles and a variety of observed phenomena.
Many will be transportable to lecture or tutorial
and all will be accessible to students whenever
they wish. The ability to observe phenomena in
the laboratory without the usual long preparation,
procedures, and reporting and being able to choose
their own time and pace should provide students
with motivation and a valuable complement to
other resources.
4. Setting up a self-paced computer-aided
learning (CAL) laboratory with long opening
hours attended by academic staff. Only material
specifically suited for CAL will be taught in this
mode. Some CAL courseware will be prepared by
our own staff and where possible some will be pur-
chased. To significantly reduce the time required
for preparation of CAL lessons, the lesson will
be prepared with the understanding that a tutor
will be available nearby to provide assistance to
students. The staff member will be in attendance
during opening hours to discuss problems with
students providing effective personal contact. Cur-

rently a student is taught through lectures, often
at a pace not appropriate to him and at a time
when he may not be receptive, and with little or
no opportunity for review.
5. Making available a comprehensive range
of chemical engineering software packages, physi-
cal and chemical properties data package, com-
puter-aided design packages, etc. We are in the
process of building up such a library of packages.
Students will be exposed to resources comparable
to those available in industry. They will be trained
in the use of computer databases for access to
reference knowledge and in critical evaluation of
computer results in a manner required of them as
practicing engineers in industry.
6. Making available audio-visual reference
material. Much industrial training is presented
today with the aid of professional audio-visual
aids. Some of these quality aids are also ideal
university teaching aids and an attempt will be
made to obtain such materials wherever possible.
Audio-visual materials, particularly video-tapes,
offer the opportunity of bringing the industrial
environment to the student when the student re-
quires this information. Presently the student re-
ceives this information only from field trips or
printed media, the timing of which may not coin-
cide with the need for such knowledge.

In redesigning a course, as opposed to starting
from nothing, there are certain pragmatic con-
straints. In the present case, the department
controls only the second to fourth years of the
course. This period has been divided into:
Background science subjects whose content is general-
ly determined by many votes.
Core chemical engineering subjects which define the
basic graduate requirements.
Elective subjects which will be used to enable the
student to gain some breadth and also some depth
in a particular specialist area.
The elective specialist areas are mainly de-
termined by the expertise of the staff. The other
elective subjects are a "smorgasbord" of subjects
offered within and outside the department. The
current review is of the core chemical engineering


Course Aims. The development of aims for the
core course is following the traditional systems
approach by starting with a small number of
general aims for the graduate:

Given the task of making a product from given raw
materials with the maximum economic return, the
graduate should be able to synthesize a suitable inte-
grated set of unit operations (ability to synthesize
an integrated process).
Given the task of designing or analyzing a unit
operation or process, the graduate should be able
to formulate a model in terms of the basic mechan-
isms involved (fluid mechanics, thermodynamics,
heat transfer, mass transfer, reaction kinetics) and
to solve the resulting equations to determine con-
ditions for optimum performance or performance for
given conditions (ability to design or analyze parts
of a process).
Given a process plant and a set of environmental
constraints, the graduate should be able to determine
the optimum conditions for operating the process and
to design a measurement and control system and/or
operating strategies to maintain the process at the
optimum conditions despite disturbances (ability
to operate a process).
Given a task to perform and sufficient resources, the
graduate should be able to plan and organize the re-
sources to complete the task in minimum time
(ability to perform).
Given a message to communicate, the graduate
should have the written and oral skills to effectively
communicate with those above, at, or below his/her
level of responsibility and/or expertise.

These global aims have been hierarchically de-
composed into about 80 more specific aims.
The next stage was to assign some weighting
or importance to each aim. The professional engi-
neering institutions have certain requirements in
this regard. Therefore the aims were grouped ac-
cording to their guidelines which defined some
group weightings. Individual aims were then
weighted within these groups by staff consensus.
The aims were then reordered into six groups
(two semesters each of three years) taking into
account the fact that many are prerequisite for
others, the available contact hours (which varies
somewhat by semester), and the natural grouping
by content. This defined subjects each with 2 to 5
aims and a weighting which could be converted
into a credit point figure.

Subject Objectives. There is a large literature
on objectives and on their preparation, typified by
texts such as Rowntree [4] and Briggs [1]. They are
generally prepared by hierarchical decomposition
and then ordered and represented as flowcharts,

network diagrams, logic diagrams, etc. Himmel-
blau [2] has done this very nicely and this text is
used as the basis of an introductory second year
In the present project, academic staff will be
given half-years off their normal duties to prepare
objectives and then instructional material for
subjects in their area of expertise or knowledge.
Eventually each of the core chemical engineering
subjects will be defined by a set of objectives re-
lating back to the course aims.
It is hoped that such detailed subject specifica-
tions will avoid the overlap and gap problems
which usually develop in courses over the years. It
is also more likely to succeed in core subjects
where knowledge is not at the forefront of research
and is reasonably static.
Teaching Strategies. The core section of the
course will be resource-based and will combine
the strategies of guided discovery and of conver-

After much discussion in the
department during 1983, a plan has evolved
to change the mode of instruction towards a
resource-based and partly self-paced
learning environment

national learning as defined by Pask and Lewis
Both these strategies consider the student to
be a problem solver and consider knowledge to
be an elaborate structure or network of concepts.
The extent of the structure or network will be
defined by the subject objectives.
The guided-discovery strategy has the teacher
defining the knowledge structure and dividing it
to set the students a series of sub-goals which they
explore using resources and problems supplied by
the teacher. For example, the teacher may define
a sub-goal by a lecture and supply a study guide,
laboratory experiment, and problem sheets as re-
sources and then assess progress individually in
tutorials and by a test. Using this strategy, a
typical subject might be divided into six two-
week modules, each started with a lecture and
followed by two tutorials and a test.
The conversational-learning strategy has the
teacher defining the knowledge structure, but al-
lowing the student much more freedom. The
student decides upon the order in which material
is covered and is free to use supplied resources and
Continued on page 50.


Ls971 classroom


University of Washington
Seattle, WA 98195

Phase rule can be used to determine the degrees
of freedom possessed by a system consisting of
several species which partake in one or more
chemical reactions.
f = (N-r-s) -p + 2-t + u (1)
where f = degrees of freedom
N = species
r = independent reaction equilibria
s = stoichiometric constraints
p = phases
t = special or additional constraints
u = special or additional variables
A species is defined as a chemically distinct
entity. For instance, in a system comprised of
HO(g) and H20(I) the number of species is but
one. On the other hand, in the H2(g)-02(g)-
H20(g) system, there are three species. In any
system, once the species that occur have been

Y. K. Rao is professor of metallurgical engineering at the University
of Washington in Seattle. He received his PhD degree in metal-
lurgical engineering from the University of Pennsylvania in 1965. Be-
fore joining the University of Washington in 1976, he was an associ-
ate professor of mineral engineering at Columbia University. He has
published over eighty papers on thermodynamics, kinetics and catalysis,
metal extraction, carbon reactions, reduction and chlorination pro-
cesses, and vapor-phase epitaxy of optoelectronic materials. He is
the author of the forthcoming text, Stoichiometry and Thermodynamics
of Metallurgical Processes (Cambridge University Press).

identified then the corresponding atom matrix can
be constructed. For this purpose, each species
is represented by a line vector of atom coefficients.
For the said H,(g)--O0(g)--H20(g) system we

The resulting atom
echelon form utilizing
This gives


0 -+-

matrix is reduced to an
standard procedures [1].

1/2 E

The rank of the echelon matrix E, defined as
the number of non-zero rows, is seen to be 2.
This also happens to be the rank of the parent
matrix. Thus

c* = rank of the atom matrix = 2.

It is well to note that underlying this system,
there are but two kinds of atoms-namely H and
0. Thus, the above findings with regard to the
rank of the atom matrix may appear to be entire-
ly predictable; and it may be supposed that c* is
equal to k where k is defined as the kinds of atoms
that comprise the species present in the system.
However, careful examination uncovers the fallacy
of such a supposition. The following example il-
lustrates the point. In the CaCO3(s)--CaO(s)--
CO2 (g) system, it is clear that there are three
kinds (Ca, C, and 0) of atoms. The corresponding
atom matrix is constructed as follows:

Ca C 0
CaCO, (s) 1 1 3
CaO (s) 1 0 1
C2 (g) 0 1 2
This is reduced to the echelon form in the usual

O Copyright ChE Division, ASEE, 1985


The stochiometric constraint is a unique constricting relationship between the mole
fractions of two or more species occurring in a given phase. It is well to note that the scope of the
stoichiometric constraint does not extend beyond the particular phase that is under consideration.

1 1 3 1 3
1 0 1 0 1 2 = E
0 1 2 0 0 0
Thus, the rank c* of the atom matrix is only
2 despite the fact that there are three kinds of
atoms underlying the species. In general,
c* < k (2)
The number of independent reactions that
occur in a system comprised of N species is linked
to the rank of the atom matrix in accordance with
the Gibbs stoichiometric rule [2].
0 < r < (N-c*) (3)
The equality sign gives r* the maximum number
of linearly independent reactions that are re-
quired to describe the system. Therefore, f*, the
minimum number of degrees of freedom the system
possesses becomes equal to
f* = (*-s) -p + 2-t + u (4)
where c* = (N r*), and r* is the maximum
number of linearly independent reactions oc-
curring in the system.

The number of components (c) of a system is
the smallest number of chemical species (or con-
stituents) that must be specified in order to com-
pletely define the composition of the phases in-
volved in the equilibrium. For a phase composed
of a constituents, in the absence of stoichiometric
constraints, one must specify (a 1) mole
fractions in order to fully define its composition.
The last remaining mole fraction can be obtained,
by difference, from the equation
XL + X + ...... + Xa-2 + Xa-1 + Xa = 1.0 (5)
The number of components is not necessarily
the same as the number of elements, or chemical
species, or compounds present in the system.
The number of components can be greater than,
equal to, or less than the number of initial sub-
stances from which the equilibrium system is
synthesized in the laboratory. The number of com-

ponents, c, is not necessarily equal to the rank of
the atom matrix constructed with the species oc-
curring in the system under consideration. In
c < c* < k (6)
where c* and k have the same meaning as before.
It will be noted that in the absence of any stoi-
chiometric constraints, c = c* = (N r*).
It is important that we have a clear under-
standing of the concept of stoichiometric con-
straint. The stoichiometric constraint is a unique
constricting relationship between the mole
fractions of two or more species occurring in a
given phase. It is well to note that the scope of the
stoichiometric constraint does not extend beyond
the particular phase that is under consideration.
The constraint can be formulated in terms of mole
fractions, as mentioned earlier, or in terms of
partial pressures; and sometimes it is also ex-
pressed in terms of numbers of moles of species.
Despite the fact that the numbers of moles of
species are extensive variables (whereas the phase
rule is a relationship between intensive variables),
there is no internal inconsistency in this approach
because the moles of species occurring in a given
phase can be readily converted into mole fractions
by division with total moles in that phase.
There is a distinction to be made between the
stoichiometric constraint (in the present sense of
the word) and the material balance equation; this
distinction is most apparent in heterogeneous
systems. A relationship that links numbers of
moles of species from two or more phases ceases
to be a stoichiometric constraint and simply be-
comes a material balance equation. This does not,
however, preclude the reduction of two or more
material balance equations into one or more stoi-
chiometric constraints by appropriate algebraic
operations. Also, one cannot write a stoichiometric
constraint for a given phase that is in violation of
the material balance equation for the larger
The number of components (c) in the system
is given by
c = c*-s = (N r* s) (7)
where s is the number of stoichiometric con-


straints totaled over all the phases present in the
The existence of the stoichiometric constraint
can be demonstrated quite rigorously by the use
of the concept of "extent of reaction." A stoichio-
metric constraint is said to exist (i) if the atom
ratio in a particular phase is equal to a ratio of
two small integers, or (ii) when a simple relation-
ship can be written linking two or more atom
ratios in a particular phase. The following
examples are instructive.
Suppose a system is prepared by placing an
arbitrary amount of NHCl(s) in an evacuated
vessel. The temperature is raised, causing a
portion of the salt to decompose into gaseous

While the method of extent of
reaction is satisfactory for the purposes of
formulating the stoichiometric constraints in a system,
a simpler procedure may be advantageous
in some instances.

products. The species present in the system in-
clude NHCl (s), NH2, HC1, N2, H2, and Cl,. Since
the rank of the atom matrix is 3, it follows that
there are three linearly independent reactions.
These reactions and the corresponding extents of
reaction are


NH, + HC1 ; E
1/2 N2 + 1 + 1/2 H ; E
1/2 H2 + 1/2 Cl2 ; E3


The number of moles of each species can be
written in terms of the initial values and the ex-
tents of reaction.
n(NHCl) = n(NH4C1)-E
n(NH3) = 1- 2
n(HC1) = e -E3
n(N2) = 0.5 e2
n(H2) = 1.5 E2+0.5E3
n(Cl2) = 0.5 E,
There are five "new" species, all occurring in
the gas-phase. The numbers of moles (or mole
fractions) of these five new species are seen to be
expressed in terms of three extents of reaction.
This means that only three of these quantities are
independent. This can be demonstrated quite
readily by the matrix methods.


E2 E3
-1 0
0 -1
0.5 0
1.5 0.5
0 0.5

1 -1 0
0 1 -1
S0 0 1 =E
0 0 0
0 0 0

The echelon matrix (E) shown on the right
has a rank of 3 indicating that only three inde-
pendent vectors exist. Thus, intuitively, we antici-
pate the existence of two stoichiometric con-
straints. For the g.atoms of each element in the
gas-phase, we have
N = n(NH3) + 2n(N2) = E1
H = 3n(NHs) + n(HC1) + 2n(N2) = 4E
Cl = n (HC1) + 2n(C12) = El
Two independent atom ratios can be written be-
tween these three elements. Thus

H 4e1 4
N E 1 '
Substitutions provide

H 4E1 4
Cl E 1

n(HC1) + 2n(H2) = n(NH3) + 8n(N2)
3n(NH,) + 2n(H2) = 3n(HC1) + 8 n(Cl2)

Division by the total number of moles of gaseous
species yields

x(HCI) +2x(H2) = x(NH,) +8x(H2)

3x(NH,) + 2x(H2) = 3x(HC1) + 8x(Cl2)

where x(i) is the mole fraction of the ith species
in the gas-phase. Thus, we have uncovered two
stoichoimetric constraints (applicable in the gas-
phase) for this system. That the atom ratios H/N
and H/C1 in the product-gas mixture will be equal
to 4/1 can be readily surmised by an inspection of
the stoichiometry of the original NH4Cl (s) species
from which the gas-phase has evolved.
We can determine the number of components
in this system by the application of Eq. (7). It will
be noted that

N = 6 (one solid + five gases) ;r* = 3 ;c* = 3
s = Number of stoichiometric constraints = 2

Substitutions yield
c = (6-3-2) = 1

We may now consider a variation of the fore-
going illustration. Suppose that the system is pre-
pared by placing a mixture of arbitrary amounts
of NH4Cl(s)/NH. (g) in an evacuated vessel and
at equilibrium there are present HC1, N2, H2, and
Cl2 in addition to the two initial substances. It is
readily seen that in this particular example, the
atom ratios H/N and H/C1 of the gas-phase are
not equal to 4/1. However, there does exist a simple


There is one kind of
special constraint that resembles a
stoichiometric constraint. This emanates from the
condition of electroneutrality in ionic systems...

relationship between the atom ratios. Since the
initial mixture is composed of arbitrary amounts
of the two constituents, let us suppose that it con-
sisted of q moles of NHs per mole of NHCl(s).
Since the four new species are generated from
these two compounds, we can write
NHCI N, 4H, Cl
q NH -- qN, 3qH
S= RNL = 1 + q RHL = 4 + 3q
Cl Cl
where RNL and RHL are atom ratios in the gas-
phase. By eliminating q, we obtain the following
relation that links the two atom ratios:

RHL = 3RNL + 1


In light of this, we can conclude that there indeed
exists a stoichiometric constraint in this system.
The same conclusion can also be reached in a slight-
ly different way. In terms of extents of reaction
n(NH4Cl) = no(NH4C1) E
n(NH3) = no(NH3) + 1-E2
n(HC1) = E 4
n(N2) = 0.5 E
n(H,) = 1.5 E, + 0.5 E3
n(C1,) = 0.5 E
Since the last four equations involve only
three independent parameters, viz., E,, E,, and
E3, it is clear that only three of these equations are
truly independent. The remaining can be obtained
by a linear combination of the others. It is a
relatively simple exercise to show that
3n(N,) = 1.5 E = n(H,) -n(Cl2)

3 x(N,) + x(Cl,) = x(H2)


which is the stoichiometric constraint for the
system. The very same relationship can also be
deduced by starting with Eq. (13).
In this system also we have N = 6, c* = 3,
and r* = 3. Furthermore, s = 1. This provides
c = Number of components = c* s = 2
The systems NH,Cl(s)/HCl(g), NHCl(s)/
N,(g), NH4Cl(s)/H2(g), and NHCl(s)/C12(g)

can be treated in a similar manner. In each of
these, one can write a simple relationship with the
atom ratios from which the stoichiometric con-
straint can be derived.
Let us consider a system that is prepared by
placing MgSO,(s) in an evacuated vessel and is
allowed to equilibrate. The species present include
MgO (s), SO, SO., SO, 02, S, S2, S, S,, S, 5S, S, ,
and Ss in addition to the original MgSO,(s). The
atom matrix has a rank of 3 and the maximum
number of independent reaction equilibria is 11.
The concentrations of the 12 new gaseous species
generated in the system can be expressed in terms
of 11 independent extents of reaction. Thus, there
exists one stoichiometric constraint in the gas-
phase. It can be easily shown that
0 3
S 1
3n(S03) + 2n(SO) + n(SO) + 2n(O,)
n(SO,) + n(SO2) + n(SO) + ijn(Sj)
This translates into the following stoichiometric
x(SO2) + 2x(SO) + 3 jx(Sj) = 2x(02)
Additionally N = 14, c* = 3, r* = 11 and s = 1.
Substitutions yield
c = c*-s = 2
This result is correct despite the fact that the
system was prepared from a single substance.
While the method of extent of reaction is satis-
factory for the purposes of formulating the stoi-
chiometric constraints in a system, a simpler pro-
cedure may be advantageous in some instances.
Suppose that a homogeneous system is prepared
from I number of constituents. At equilibrium,
this single-phase system contains N species of
which I are the initial constituents. The rank of
the atom matrix of N species is c* and a maximum
of r* reactions are required to describe the system.
We have

J = N-I


where J is the number of "new" species generated
by the r* reactions. The number of stoichiometric
constraints s present in the system is given by

s = J r* = N I r* = c* I


This relationship is directly applicable to single-
Continued on page 46.





University of Louisville
Louisville, KY 40292

T HE STUDY OF SYSTEMS with dead-time in under-
graduate process control is important due to
the fact that a large number of chemical process
systems exhibit apparent dead-time characteristics
and that the dead-time is detrimental to control.
The topic dealing with the determination of
closed-loop response of processes containing dead-
time is typically not covered in under-graduate
process control, possibly because the solution by
Laplace transforms requires the use of Pade ap-

Keith R. Watson is currently with E. I. DuPont de Nemours Co., in
Midlothian, Virginia, where he is working in the area of applying
digital computers for process control. He obtained his Master of
Chemical Engineering degree from the University of Louisville in 1982.
(Not pictured)
Julius P. Wong, professor of mechanical engineering at the Uni-
versity of Louisville, obtained his PhD from Oklahoma State University
in 1966. He has worked at the Energy Controls Division of Bendix
Corporation and at the Avionics Division of Honeywell, Inc. His cur-
rent research interests are in the area of finite element analysis and
computer-aided design. (L)
Pradeep B. Deshpande, professor of chemical engineering at the
University of Louisville, has over fifteen years of academic and full-
time industrial experience and has published over thirty technical
papers. He is co-author of the text Elements of Computer Process
Control with Advanced Control Applications, and author of the text
Distillation Dynamics and Control. His research interests are in the
area of process dynamics and control. (R)

rtJ ~-I;---l~'~b,---- -


FIGURE 1. Typical sampled-data control system.

proximation for dead-time which makes the pro-
cedure lengthy and tedious. In this paper a com-
puter-aided method is described which simplifies
the procedure.
The method is based on the premise that the
closed loop response of a sampled-data control sys-
tem shown in Fig. 1, approaches that of the equiva-
lent analog system (i.e., one without samplers and
zero-order hold) as the sampling period is reduced.
Thus, by suitable selection of the sampling period,
the conventional (analog) control system can be
analyzed by the z-transform method.

The scope of the program described in this
paper is limited to the analysis of simple processes
containing one or two time constants, a gain, and
a dead-time element.
The closed-loop pulse transfer function of the
sampled-data control system shown in Fig. 1 is
D (Z) GhGp (Z) R (Z)
1 + D(Z) GhoG,(Z)
1 + D(Z) GoG,(Z) (
The terms in Eq. (1) are indicated in Fig. 1.
The sampled-data system can be analyzed
either for set point changes or for load changes.
For set point changes, the expression for R (Z) is
of the form
a + b Z-1 + cZ-2
R(Z) d + eZ-' + fZ-2 (2)

O Copyright ChE Division, ASEE, 1985


fe '-V *VO

The method is based on the
premise that the closed loop response of a
sample-data control system ... approaches that of
the equivalent analog system ... as the
sampling period is reduced.


PROCESS : Kp=I,ed= 146,T=334
,I' CONTROLLER: K = 2-61, Ti = 2512,T=O 628
SET POINT : R(t) = 5(1-e'"l

FIGURE 2. Set point response of the equivalent analog
control and sampled-data control systems.
where a,b,c,d,e,f are user selected constants.
The appropriate expressions for D and Gp are
inserted in Eq. (1) and the resultive equation is
simplified to give

S( C1 + C2 Z-1 + C2 Z- + ... (
C(z) D+D2Z-+DZ+... (3)
D, + D, Z-1 + D, Z-2 () .
The constants in Eq. (3) are functions of the
process parameters (K,, O(a, T or Kp, 0d, T1, T ),
controller parameters (K,, T7, Td) and the sampling
period, T. Eq. (3) upon inversion by long division
gives the closed-loop response at the various
sampling instants. The load response of the pro-
cess can be similarly evaluated [1].

A digital computer program written in double
precision Fortran to solve Eq. (3) has been de-
veloped and tested. A listing of the program is
available from the authors upon request. The
user must specify as inputs the parameters of the
process and controller, whether set point response
or load response is desired and the sampling period.
The closed-loop response of an illustrative pro-
cess is shown in Fig. 2. Also shown is the digital
computer solution based on fourth-order Runge-
Kutta integration and the analog computer solu-
tion based on the fourth-order Pade approxima-
tion. The sampling period for the z-transform-
based solution is 0.01 time units. It may be ob-
served that the sampled-data system approximates
the conventional system well.

The z-transform based computer program
should be useful in undergraduate process control.
The undergraduate student, of course, will prob-
ably not be able to handle z-transforms. However,
all that the student needs to know for the purpose
of executing the program is the nature of the in-
put data needed and the format of the results to
be expected. O

Deshpande, P. B., R. H. Ash, Elements of Computer Pro-
cess Control with Advanced Control Applications, ISA,
1981; Prentice-Hall, 1983.

p book reviews

Second Edition
By Max S. Peters, McGraw-Hill Book
Company, NY (1983) $32
Reviewed by E. V. Collins
Iowa State University

The text covers the traditional topics of stoi-
chiometry, unit-operations, chemical technology,
and plant design. A complete nomenclature table
is found at the beginning of each chapter where
appropriate. Since this text is intended for
students with no calculus background, there is no
coverage of unsteady-state conditions.
This text is very well suited to a freshman
level over-view course of the field of chemical
engineering. We have used the first edition of
this text in a survey course for other engineering
disciplines. Worked out example problems are well
chosen and used liberally throughout the text.
Homework problems are available where appropri-
ate, covering rather a wide spectrum of difficulty.
Five homework problems are indicated as appropri-
ate for computer solution. These cover a variety
of applications, e.g. look-up table preparation, an
iterative solution for a fluid flow system, and a
matrix solution for a material balance problem.
The author used parallel solutions to example
problems in first the American engineering system
and then the SI system of units. It is unfortunate
that the physical properties tables in the appendix
are all given in American engineering system of
units. This perpetuates the use of the American
engineering units, since all data must be convert-
ed to the SI system of units. O


Continued from page 43.
phase systems only. For the more complex sys-
tems involving several phases, the more detailed
'extent of reaction method' should be employed.
The number of stoichiometric constraints in
any particular phase is equal to the number of new
chemical species (as distinguished from the 'old'
or 'initial' species from which the system is pre-
pared) occurring in that phase less the maximum
number of linearly independent reactions required
to describe the system. The number of components
is equal to the rank of the atom matrix less the
total number of stoichiometric constraints summed
over all phases.

In contrast to the stoichiometric constraints
which are preordained by the particular stoi-
chiometry of the reaction system, the special con-
straint 't' has something of an arbitrary quality.
One particular form this constraint often takes is
that of specifying the pressure. For example, the
total pressure of the system may be specifically
fixed as in the case of equilibrium phase diagrams
for alloy systems which are determined at a con-
stant pressure of 1 atm. Alternatively, the partial
pressure of a gaseous species (or the activity of a
component in a condensed phase) may be spe-
cifically set at a particular value. Each such spe-
cific choice constitutes a special (or additional)
constraint and results in a parallel loss in the de-
grees of freedom enjoyed by the system under con-
There is one kind of special constraint that re-
sembles a stoichiometric constraint. This emanates
from the condition of electroneutrality in ionic sys-
tems: the total charges on cationic species must
exactly match those on the anionic species. In some
systems, the electroneutrality constraint can be
redundant because it may simply be a linear com-
bination of independent stoichiometric constraints.
So a check must always be made on the linear inde-
pendence of the constraints before they are im-
posed on the system.
The effect of the special constraint on the
number of components in a system is of some inter-
est. When the imposed special constraint relates
to phase-composition (i.e., mole fraction, partial
pressure, or activity) it reduces the number of
components in the same manner as does a stoichio-
metric constraint.

The discussion of the extended form of the
Gibbs phase rule will not be complete without a
consideration of its application. Each of the follow-
ing examples is designed to illustrate a specific
feature of the extended rule.


H2 (g) -O2 (g) -H20 (g) system

This is prepared by filling the vessel with a
mixture of hydrogen, oxygen and water vapor.
The system is allowed to equilibrate. It is seen
that N = 3 and c* = 2; hence r* = 1. The lone
independent reaction equilibrium is

H2(g) + % 02O(g) = HO2(g)


There are no stoichiometric or special con-
straints; and no special variables are involved.
Furthermore this is a single-phase system. Substi-
tutions give

f = (3-1-0) -1 +2-0-0 = 3
c=2-0 =2

We can specify (1) temperature (2) total pres-
sure and (3) a composition parameter such as
the H/O atom ratio of the gas-phase.

H 2n(H,) + 2n(HO0)
0 n(H20) + 2n(02)
2P(H,) + 2P(H20)
P (H20) + 2P(02)
where n(i) and P(i) respectively denote the
number of moles and partial pressure of the ith

CaCOs (s) -CaO (s) -CO2 (g) system

Suppose that solid calcium carbonate is placed
in an evacuated vessel and is allowed to dissoci-
ate and reach equilibrium. The species present
in the equilibrated system are CaCO, (s), CaO (s)
and CO, (g). As noted earlier, the atom matrix con-
structed of these three species has a rank of 2. The
only reaction equilibrium to be considered is

CaCO,(s) = CaO(s) + CO,(g)


No stoichiometric constraint exists because the
products CaO(s) and CO,(g) occur in different
phases (unlike SO, and 02 in the dissociation of
solid MgSO, mentioned earlier). Thus N = 3, c* =


2, r* = 1, p 3 and s = t = u = 0. Substitutions

f= (3-1-0) -3 + 2-0 = 1
c =2-0= 2

This is a univariant system which is completely de-
scribed if temperature or pressure is specified.

FeCrS4 (s) -HC1 (g) -Cl1 (g) system

This chemical transport system is prepared by
placing a mixture of these three species in an
evacuated vessel held at an appropriate tempera-
ture. At equilibrium the gas-phase is observed to
contain 18 species: FeCl., FeCL4, FeCl3, Fe2C16,
CrC12, CrCL3, CrClI, CrC1, S, S, S4, S6, 8 SC, 2,
H2, Cl2, HC1, and H2S respectively, and no con-
densed phases other than FeCrS,(s) occur. The
atom matrix constructed of these nineteen species
has a rank of 5. Thus N = 19 and c* = 5; there-
fore r* = 14. The maximum number of linearly
independent reactions that are required to describe
the system fully, thus, is seen to be 14. These are
as follows

FeCrS,(s) + 4 Cl2

FeCl2 + 1/2 C,
2 FeC12
2 FeCIl
CrC1 + 1 Cl1
CrCls + 12 C12
2 CrCl2
/2 S2
2 S2
3 S2
4 S2
S2 + C12
H2 + Cl2
H2 + 12 S2

= FeC12 + 2

= FeCIl
= Fe2Cl4
= Fe2C16
= CrCl,
= CrCl4
= Cr2C14

= S4
= S

= Ss
- S2C12
= 2 HCI
= HS

CrCI3 + 2 S2

It is of particular interest to note that there
are two stoichiometric constraints inherent in
this manner of preparation of the vapor transport
system. All of the Fe, Cr and S atoms in the gas-
phase (albeit present in the form of various
molecular species) originate with the solid
FeCrS,; also since no other condensed phase ap-
pears, the following obtains

Each of these relationships constitutes a stoichio-
metric constraint. There are no special constraints
or variables that have to be reckoned with. Thus,
we have
f= (19-14-2)-2+2-0=3
c= 5-2 =3

Three system properties have to be specified. These
may be selected as (i) temperature (ii) initial
chlorine pressure in the system, P (Cl,) and (iii)
Cl/H atom ratio of the gas-phase. The specifica-
tion of temperature yields 14 equilibrium constant
expressions, one for each of the reactions identi-
fied above. These 14 relations together with the
two stoichiometric constraint equations coupled
with the values of Po (Cl,) and Cl/H should en-
able the determination of the equilibrium partial
pressures of the 18 gaseous species that occur in
the system. An iterative method of calculation
suitable for complex systems is presented in a re-
cent publication [3].

Mn (s) -AICl (g) -MnCl, (1) -A1 (1) system

For this four-phase, four species system, the
atom matrix has a rank of three. The only inde-
pendent reaction equilibrium is

Mn(s) + 2 ACl, (g, Patm)

= MnCl2 (1) + -Al (1)


Suppose that the pressure of AlCl (g) is arbi-
trarily set at 1 atm. This would constitute a special
constraint. There are no stoichiometric constraints
or special variables. Therefore N = 4; r* = 1;
s = 0; p = 4; t = 1 and u = 0. Substitutions yield

c = c*-s = 3

The system, when subject to the single special
constraint stipulated above, becomes invariant.
This simply means that there is but one unique
temperature (Te) at which the four-phase system
is in a state of equilibrium for a P (A1Cl) of 1

Cr 2 P(CrCI2) + P(CrCl3) + P(CrCl4) + 2P(Cr2Cl4)
Fe 1 P(FeCl2) + P(FeCl2) + 2P(Fe2C14) + 2P(Fe2Cl6)

Cr 2 P((CrC + P(CrCI) + P(CrCl4) + 2P(Cr2CI4)
S 4 P(S) + 2P(S,) + 4P(S4) + 6P(S6) + 8P(Ss) + 2P(SC12) + P(H2S)


atm. The value of Te can be found as follows. For
the reaction equilibrium

AG = 0 = AGf (MnC12) ( --) AG0 (AIC1s)

Using the tabulated data [4] on the standard free
energies of formation (AGr'), we find

0 =- 39,162 + 41.601 Te
Te = 941.4 K

The equilibrium Mn (s) -AlCl\ (g) -MnClI (1)-Al (1)
is unique in that it occurs only at this temperature
when all the species are in their respective natural
standard states. Had P (AlCI) been specified as,
say, 0.95 atm instead of 1.0 atm, then we would
find that the corresponding value of Te becomes
935 K. Only one special constraint may be imposed
when Te = 935K: for example, we cannot arbi-
trarily set P (AlCI,) at, say, 0.95 atm and at the
same time fix the activity of aluminum (presum-
ably present as a liquid alloy) at, say, 0.8. This
would result in negative degrees of freedom which
has no physical significance.

Ga-In-As-H-Cl system

The mixed crystal (solid solution) GaxIn-xAs
is grown from vapor phase. The system is pre-
pared by introducing a gas mixture consisting of
GaCl(g), InCl(g), As,(g), HCl(g) and H,(g)
into the crystal growth system. At equilibrium,
there are present eight gaseous species (GaCls,
InCl, and As, in addition to the initial five) and
two condensed phase species GaAs(s) and
InAs(s). Since c* = 5, it follows that r* = 5.
These five independent equilibria are:

GaAs(s) + HC1 = GaCl + 1 As, + /2 H,
InAs(s) + HC1 = InCI + 14As, + /2 H,
GaCI + 2 HCI = GaCl, + H, (38)
InCl + 2 HC1 = InCl, + H, (39)
/2 As, = As2 (40)

There are no stoichiometric or special constraints.
In order to facilitate the equilibrium calculation,
however, sometimes two hypothetical species,
GaAs(g) and InAs(g), are introduced. The
number of moles of GaAs (g) and InAs (g) (hypo-
thetically) present in the equilibrated system is
simply equal to the number of moles of deposited
GaAs and InAs respectively. The hypothetical

species constitute special variables. Thus N = 10;
r* = 5; p = 2; s = t = 0; and u = 2. Substitu-
tion gives
f= (10-5-0)-2+2-0+2=7
c= 5-0 = 5
These seven degrees of freedom are satisfied by
specifying (1) temperature, (2) total pressure,
(3) Cl/H atom ratio, (4) n(Ga), (5) n(In),
(6) n (As), and (7) interaction parameter f for
the GaAs-InAs regular solution. In here n (Ga),
etc., denotes the number of g atoms of Ga, etc. in
the initial gas-phase albeit present in the form
of GaC1, etc. The atom balance equation for Ga is
n (Ga) = n(GaC1) =
n(GaC1) + n(GaCl,) + n*(GaAs)
where n* (GaAs) represents the contribution due
to the hypothetical species. Other atom balance
equations can be written similarly.

In attempting to make an equilibrium calcula-
tion in complex systems, a necessary and useful
prerequisite is to conduct phase rule analysis of
the system. Such an analysis helps clarify the es-
sential elements of the calculation procedure. The
extended form of the Gibbs phase rule presented
here is especially useful in analyzing multicom-
ponent heterogeneous systems. E

1. Hadley, G., Linear Algebra, Addison-Wesley Publish-
ing Co., Reading, Mass. (1973), pp. 148-52.
2. Gibbs, J. W., The Collected Works of J. Willard Gibbs-
Thermodynamics, Vol. 1, Yale University Press, New
Haven, Conn. (1957), pp. 53-353.
3. Rao, Y. K., Metall. Trans. B, 14B, 701 (1983).
4. Rao, Y. K., Stoichiometry and Thermodynamics of
Metallurgical Processes, Cambridge University Press,
New York, (in print), (1984).



AGfo (AlCl3)

AGo (MnCl,)


number of components
rank of atom matrix
degrees of freedom
minimum number of degrees of
standard free energy of formation
of AlCl (g)
standard free energy of formation
of MnCl, (1)
initial constituents
new species


k kinds of atoms or elements
n (i) number of moles of the ith species
n (i) initial number of moles of the ith
N species
p number of phases
r independent reaction equilibria
r* maximum number of independent
reaction equilibria
RHL H/C1 atom ratio
RNL N/C1 atom ratio
s stoichiometric constraints
t special or additional constraints
u special or additional variables
x (i) mole fraction of the ith species
Greek letters
Ei extent of reaction for the ith

REVIEW: Diffusion in Liquids
Continued from page 29.
correlation of experimental data, via kinetic theory
and, more extensively, such approximations as
hydrodynamic and free volume theories. A separate
section is provided for electrolytes. The utility of
these theories is discussed for binary and ternary
nonelectrolytes in Chapter 7 and for binary electro-
lytes and fused salts in Chapter 8.
This is a densely written book of high techni-
cal quality, and it is difficult to write a definitive
review without extensive study, a procedure not
feasible for this reviewer. However, I think it fair
to say that this is a useful and reliable treatise, but
that it will not attract large numbers of chemical
engineers as readers. Much of the material pre-
sented is available elsewhere in equivalent form,
and little attention has been paid to the problems
of those wishing to use the subject matter in
typical engineering applications. However, this
book should prove valuable to those engaged in
serious experimental or theoretical investigations
and who wish to be sure that the basis of their
work is sound. A few examples are given below
to back up these comments.
The phenomenological discussion of Chapters
2 and 3 is representative of both the strengths
and weaknesses of this book. The discussion of the
Onsager reciprocal relation clears up a number
of widely held misconceptions in a clear definitive
manner, but little is done to provide the reader
with convenient sets of diffusion equations, or of
means to test and interrelate the wide variety of
apparently different expressions found in the
diffusion literature. The authors confine them-

selves largely to the flux expressions used by a
relatively narrow group of physical chemists cited
in the acknowledgement. These have not for the
most part found widespread acceptance by chemi-
cal engineers, and it is not a simple matter to
relate them to those which are more common. The
means for making these inter-relations is pro-
vided in Chapter 3, but this reviewer did not find
the treatment a convenient one to use. However,
the definitions of mutual, self- and intra-diffusion
coefficients in Chapter 1 are quite clear, and very
useful as there has been much confusion about
these terms.
Chapter 5 is, in this reviewer's opinion, highly
useful, and a real strength of the book. The dis-
cussion of experimental techniques is detailed and
practical, and also generally sound in terms of
underlying theory. I do have a minor criticism
in the discussion of Taylor dispersion in that the
extensive literature on departures from Taylor's
asymptotic theory is not referenced. Such de-
partures can be important and may result from
end effects or a variety of flow disturbances. This
objection is, however, more than balanced by the
strength of the discussion of errors in the use of
light scattering. The authors have done much
here to clear up longstanding controversies as to
the significance of measurements made in concen-
trated solutions.
I found the organization of Chapters 6 through
8 awkward, but it may be that I did not take
enough time to accommodate to it. It is clear that
the authors have a prejudice which results in
more attention to even doubtful theory than to
useful empiricism. Thus they ignore many useful
empirical and semi-empirical correlations totally.
However, they do present a substantial amount of
data and discuss it critically in the light of avail-
able theory, and these discussions should prove
highly useful to many readers. They do seem more
concerned with the experimental proof of the On-
sager reciprocal relation than with the practical
description of multicomponent diffusion problems,
but in this they are constrained by the limited
amount of practically useful information available.
On balance I expect to find this monograph a
most welcome addition to my library, and a chal-
lenge to those like myself, with more applied tastes
than the authors, to meet the above objections. I
think this is the most authoritative source avail-
able in the area of diffusion, which is accessible to
an engineering audience. E


Continued from page 39.
to find others. The teacher acts as a resource and
an adviser while retaining some assessing and
monitoring roles. This strategy is generally used
for design projects, and can be used to extend the
more gifted students.

Successfully carrying out this major program
of modernization will require
A commitment by the departmental staff to the new
The willingness of departmental staff to make short-
term sacrifices
The diversion of financial resources to fund the
Discussion within the department during 1983
has resulted in enthusiastic support from the staff
and a commitment by the staff to the concept. As
part of the plan each staff member will be relieved
in turn of normal duties to be retrained in CAL
and video techniques and to prepare new resources.
The total financial resources required, including
cost for staff retraining, is estimated to be in excess
of half a million dollars.
While each element in the proposed mode of
operation is not novel, the implementation of the
integrated package on a departmental basis in
chemical engineering is both new and challeng-
ing. This is the beginning. E

1. Briggs, L. J., Handbook of Procedures for the Design
of Instruction, American Institute for Research, Pitts-
burgh (1970).
2. Himmelblau, D. M., Basic Principles and Calculations
in Chemical Engineering, Prentice-Hall, N.J., Fourth
Edition (1982).
3. Pask, G. and B. Lewis, Teaching Strategies: A
Systems Approach, The Open University Press,
Bletchley, Bucks (1972).
4. Rowntree, D., Educational Technology in Curriculum
Development, Harper & Row., London (1974).

Continued from page 21.
integrals in Eq. 14 in terms of area integrals ac-
cording to

There is a minor problem in the use of these
relations at the contact point between the surface
of the averaging volume and the p-a- interface.
As indicated in Fig. 4 the error is on the order of
PAs2 where P is the length of the contact line be-
tween the surface of the averaging volume and
the /-3- interface. Use of Eq. 15 in Eq. 12 along
with the estimate of the error

6V = O(PAs2)

leads to

d dV
ds cAdV

= lim

ciAAs -ng dAi + cAASX)

AIi(s,t) A1(s,t)

nB dAI + 0(cAPAs2)


Since As and X are independent of position, they
can be removed from the integrals and in the
limit as As--0 we obtain

i A dV = nCA dA

V (s,t) A (s,t)
Here we have used

Ae (s,t) = lim (Ai(s,t) + Aii(s,t)}

and expressing the derivative with respect to s
in the form

quite obviously leads to
quite obviously leads to

naCA dA (21)

, (t)

dVI = AsX- dAI

dVII = + AsX- dAll



since X is arbitrary. This is Eq. 7 of Slattery's
derivation [15] and in terms of the nomenclature
indicated in Eq. 3 we obtain



Y 1 nc dA
A (t)A
Ie M

while the vector form of this result is obviously
given by

' = nA dA (23)


The spatial averaging theorem can be obtained by
use of the divergence theorem

yc dV = fncA dA +

VB(t) Age(t)

9aCA dA


along with Eq. 22 to arrive at the result

= V + V I9CA dA

A B(t)

The analogous form for a vector is given by

= V- +

A (t)

We are now in a position to continue our
analysis of Eq. 9 using the general transport
theorem and the spatial averaging theorem to
interchange differentiation and integration.

The general transport equation provides the

in which we have used w'np, to represent the
normal component of the velocity of the f-o- inter-
face, and we have made use of the fact that the
normal component of velocity of the surface
Ap (t) is zero. Use of this result allows us to ex-
press Eq. 9 in the form

cA w." 0 dA + =


and the spatial averaging theorem given by Eq.
26 can be used to obtain

a + V CA(A )a dA =

A A(t ) (2 9 )

Since the phase average concentration is associ-
ated with a fixed point in space we have used the
partial time derivative in writing Eq. 29, and we
have used Eq. 2 to express NA in terms of the con-
centration and the species velocity. From Eq. 23
we see that V' represents the flux at
entrances and exits and under most circumstances
[21, Sec. 7.4] diffusion is negligible compared to
convection at entrances and exits and Eq. 29 can
be written as

a 1
at + + c )'nBo dA = A00(t) (30)

Because the intrinsic phase average concentration
is preferred, we can use the representation given
by Eq. 6 to write

C ( >80C 1 + V. E
+ cA(A )'a dA = (31)


d acA f
dt CA d= dV+ c wn dA
d (t ) t A (t)

V0(t) 0(t) A(t)

(27) At this point we follow the procedure used in
the time averaging of turbulent transport pro-
cesses and make use of Gray's [12] spatial de-
composition to write


CA =

V = + V

Under normal circumstances [5, Sec. 2] the aver-
age of the deviation is zero

B = = 0

and Eq. 31 takes the form

time rate
of change


mass transfer

a ( +V <> a a) 1
at (E 8
A (t)

= (0 (34)

dispersive homogeneous
transport reaction

If the flow is unsteady or turbulent this re-
sult must be time averaged before it is of any use.
The time averaging procedure has been discussed
elsewhere [20; 23, Sec. 5] and it is clear from that
development that the analysis of unsteady flows
is very difficult.
At this point we have been able to extend the
precise analysis of single-phase transport phe-
nomena to multiphase transport processes in a
rigorous manner. When the flow is steady and
laminar the domain of rigorous analysis can be
extended [4, 9, 14]; however, in most cases the
"process modeler" must emerge if a closure is to
be obtained. While intuition, experimental observa-
tion, and dimensional analysis will provide the
guidelines in this next phase, there is no excuse
for the construction of models based on intuitive
versions of Eq. 1 rather than the rigorous result
provided by Eq. 34. O


This paper was prepared while the author was
a Visiting Lecturer at the Universidad Nacional
del Sur and Planta Piloto de Ingenieria Quimica
in Bahia Blanca, Argentina. The financial support
of BID-CONICET is gratefully acknowledged.

1. Anderson, T. B. and R. Jackson, "A Fluid Mechanical
Description of Fluidized Beds." Ind. Eng. Fundam.
6,527 (1967).

2. Bachmat, Y., "Spatial Macroscopization of Processes
in Heterogeneous Systems." Isr. J. Tech. 10, 391
3. Bird, R. B., W. E. Stewart, and E. N. Lightfoot,
Transport Phenomena. Wiley, 1960.
4. Carbonell, R. G. and S. Whitaker, "Dispersion in
Pulsed Systems. II. Theoretical Developments for Pas-
sive Dispersion in Porous Media." Chem. Eng. Sci. 38,
1795 (1983).
5. Carbonell, R. G. and S. Whitaker, "Heat and Mass
Transport in Porous Media," Fundamentals of Trans-
port Phenomena in Porous Media, edited by J. Bear
and Y. Corapcioglu. Martinus Nijhoff, Brussels, 1984.
6. Cushman, J. H., "On Proofs of the Volume Averag-
ing Theorems for Multiphase Flow." Adv. Water
Resour. 5, 248 (1982).
7. Cushman, J. H., "Multiphase Transport Equations:
I. General Equation for Macroscopic Local Space-
Time Homogeneity." Trans. Theory and Stat. Physics
12, 35 (1983).
8. Drew, D. A., "Averaged Field Equations for Two-
Phase Media." Studies in Appl. Math. 50, 133 (1971).
9. Eidsath, A. B., R. G. Carbonell, S. Whitaker, and L. R.
Herrmann, "Dispersion in Pulsed Systems. III. Com-
parison Between Theory and Experiments for Packed
Beds." Chem. Eng. Sci. 38, 1803 (1983).
10. Fahien, R. W., Fundamentals of Transport Phe-
nomena. McGraw-Hill Book Co., New York, 1983.
11. Gray, W. G. and P. C. Y. Lee, "On the Theorems for
Local Volume Averaging of Multiphase Systems." Int.
J. Multiphase Flow 3, 333 (1977).
12. Gray, W. G., "A Derivation of the Equations for Multi-
phase Transport." Chem. Eng. Sci. 30, 229 (1975).
13. Howes, F. A. and S. Whitaker, "The Spatial Averaging
Theorem Revisited." Accepted for publication in
Chem. Eng. Sci.
14. Paine, M. A., R. G. Carbonell, and S. Whitaker, "Dis-
person and Adsorption in Pulsed Systems. I. Hetero-
geneous Reaction and Reversible Adsorption in
Capillary Tubes." Chem. Eng. Sci. 38, 1781 (1983).
15. Slattery, J. C., "Flow of Viscoelastic Fluids through
Porous Media." AIChE Journal 13, 1066 (1967).
16. Veverka, V., "Theorem for the Local Volume Average
of a Gradient Revised." Chem. Eng. Sci. 36, 833
17. Whitaker, S., Introduction to Fluid Mechanics. R. E.
Krieger Pub. Co. Inc., Melbourne, FL, 1981.
18. Whitaker, S., "Diffusion and Disperson in Porous
Media." AIChE Journal 13, 420 (1967).
19. Whitaker, S., "Advances in the Theory of Fluid
Motion in Porous Media." Ind. Engr. Chem. 61, 14
20. Whitaker, S., "The Transport Equations for Multi-
phase Systems." Chem. Eng. Sci. 28, 139 (1973).
21. Whitaker, S., Fundamental Principles of Heat Trans-
fer. R. E. Krieger Pub. Co. Inc., Melbourne, FL, 1982.
22. Whitaker, S., "Diffusion and Reaction in a Micro-
pore-Macropore Model of a Porous Medium." Lat.
Am. J. Chem. Eng. Appl. Chem. 13, 143 (1983).
23. Whitaker, S., "Transport Processes with Hetero-
geneous Reaction." Paper presented at the 25th Coni-
cet Anniversary Reactor Design Conference. Santa
Fe, Argentina, August 1983.



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lht,h..,.kalmlill t l.-and.........,..ofMpart,,...,toladminla t nt.tion,Ttdloon in tr< p i~r a nion.r,withlnotr Uln oon, t rainla (anyth i 111r plonttd hu IO be hal'll.y,pe,.,.nlal,andMn-.U>tninlmlzeor=;:.:~: i::;;i:.,~:::.~~:...,~ '11 :: \ ~=:~~-=~~ .. n:~ hu -l'dt. lnlt...U io ""' pn.,.,y a.-: tarl>u .. ttwophaNllo,rUldlht\n, tn,u.f,,..,,..1lonotolmu !:l:::i:-..:.:.iw::h~nd~"?.17~~:/:: orta. I n th t lalt.r, R kh hu bffn wl111C.A.,.........,ot JIH)'land.Slo.-oN>mpletlhio,l<=t,nte J ..-Gtalry, ll ela.,.uptttlnN1111put..-op plibolnro rlOtdt-hor,Sto,...isquitt"-ln\he l abonto,-y o nI.I.T.,lffl).l~hupro<1kalo,url .. ....,,.-h1<11otandollle,l,ah>:nrinttrinr with ,_na1. ~t~::.~:~ =!.~:! ~~:{;;. ~,;. ~~""::: afor....,,hal,...noftllo.....,.r1..-t,Allawtll oqoippe,llolltlatell"'luallraklllf1entionlntol'K'lionaJ111lyM,andontlaHtUr! ola1\rae ..-ilh 11ro, ..... f.. dlotilla\1011-"'n"""'IN>l and obort-cut -lq tttkniq-. T"' bf!a_......, .. ,~utu,Jo to~ d1oaml

proo ; te ... oon, bloe~,h on th< Ch .. peak 8.oJ r, ... di~:'k1: k~;::~: ~":i'1'!;:i:. ControlMSimu la lion,.,...,motio,rlnt..-..:tion withindu>tryinpra,;t;;.lawlicatio""ofoontrol. Amon~ th,c,nte' octi,iti<, ""'biennial hor-t >u., ""App l k o tion o!Adv a nttr,,eri. mental u n itnlJ>Ut r, 1 ,,r a m.ln add i liont o helmr a main tayinund,,...,.dtal e e<>,r ,. ln o \n,ctioo.iocludimrun ; t,,.,.lonl\>ontory. TomhMeul i kill ~hkh,at e 1 u excellen. Wi l burt1 C. S,hrotd.,'a (~1khi~ 1933) po.rt time pro1....,,.;.1 pooition i n ohemi< l t i no. tobu ; ld a mmoniap l a n,.,t lttfhi.otou,of :;;~:~~:~::i~~! ~ ;,;' : d~ oc ~:;I .;~;: lat N tro.o l .. ion to< hn..,.yincludln,,the S,h......i,Prott._n,tlon o lpolitico ndth e ,tattrri,mboollho p u r<:lluedfor .. l ntheintrodoctoryl reo hm,n ?o:~2~:~~~~~; ,::?::::~~:t:=:""t ~ Xuc l,o R n ~l n "'ri"-" l'ocn,. Kaz.y o K ~~~~~::\~~:,:;~=~~~;:: ~!~~--lt!;~; t "r n~I.Munno(Florldo.1964):G ny A.l'lumbl a ,1978);Ma,,;nI Rou,h ::~~t"'"' !000: J ooeph Sil,ermn (Columbio. E nrln,..,.in r ~1,,. i>k ]> ""' "''" Rirh.,d I. ::,1'.~~:..":.t~;i"::~~;.~oo{_> ~r:::;:.,J<~1:;.. JiH#M book reviews J~"TRO D UCT IO:S TO l'KOC&'SS 1' :so mc s. 2nd ~dltioo l/ j l' .-l.llo/lod,F A .W ~!ooao.d J K \l";/l,,'n J o hWil o > poflhl book .. .lhetlt le tr of n n:n ~~::;';1 .-"'" \d .-~P-::. ~'7.: ,:;,'~"n : ~.!" ~ra,!. ,':;',:~ ~~ ~ ta i l l>mm<:n ta ry aa dth ,nitlo,,di",..nt -, lon o nd theydidnotol l at>o n.t onodllin~.Soml,conc,pt., & roartrul!y a 1Hllho<0u

aMlpio.areba~,-.,u.a,,.....,.-.,-.. ... _ladld .. i_,...,andelori.,..IM ...... are .,.peo:1....i.....,.1a<111.iUILThel"Of...--are :::::!"~,:.: ri":' upotir hondlinJ,t.r .. llto,t<#tlon.and brtak"""" IYf.lo:-otp~tabi li\7""""'" ,_,.,i,,,a 1ton ofnoitalln,..,.,.....,leandtl>eo'""''ioaofan. ... 1op,1,otonrn-.10-lteo<...,.p0ndo -IOU..ftnt(l97tJtdt-.Cliaoi.,.J ,_rt,1,--.i.n .....-ot--f ... --0 ,--..1;, 1 (t..-ot.., io fo,o. Cl>o..-~id, dloolt wit~ lld"ffl l.mitod. Forin te,tlHtA,,..lerotIC: o pittlR..,.,,..,.y !~T~%;~i:E~~uii~=~I~ (SPVJ ond lnte"'"I rota of mum at a timo -t,e,,\be.,....,._tol....,tln,_lnte,.tu.d tbeholfJ'N--lioalo,-and..,,"1r. =..,;;i:~:~.= E ~: ,.,.,._p,-mo,Ul\catlou,ond""ul_t,. piono, rindai,rn !i-::-.:.i torniod t ;oonomle,..,,.) art not ,on, ~-,,.. 1 top1,.lntl1t-ondha l l,00ffloll &llalyoio aod ,..,kri1nc an t-tI In a.....,..,,. l-tlloy-11tuteo_rc_"""of=~~.':':'.';"..,"11o-.:ri..::. IGo<0,_,. tllo ~~-::i~~~~:~~::i.:.-:=:: o<-n.,,..l,od1ol p.-o/ltobility -n1tnldoo

riJJ'plviews and opinions I CHEA TING AN OUNCE OF PREVENTION ... or tl, e 1 r<1J!ic T,d e of th e D y ing Cnmdmo,hcr RI C HARD~FF. l.ll~)R 1-,m c,....i, .. stol Uolt-.rri t ~ llokigi,1"Cll7695 ~~:: ~=:::-,..:~~ .. :: .. -;:;:7:::. 1;.,.sr,,1.u.;n,.;,,.., .,.,.""11, ,. ... M..,"" l,_diof -la ... no /.....J ,.;,,,.Mo ~!= ';;~and ...... ~0'1,,::: )'W!>i<>-l"moot111"'1hele oub Jei,oron,thin10INYGUC. .... ,_ .. """"<.-.. ....... _, __ ..,_..,"""~ ... ._ .. c.,, ............ .._ .. _.., ... _...~ ... .u.1.- .. -c----.__ ...... ____ __ ------.. -------... ....... .. ,__,,_ .. _,_ i.-in lt.Thwilli-ot ....... l,wiQlo ci..,ly,\heliltel!hoodotclleatiurvorie,f...,,, '-.. .. ,1on to It .... -inJOJt ...... nttllontat ...... U,ltitp-.i,Nfoto1<,i1-.\he ""'"1durinr otOratlo,,oro lle>:.iblo ....,.I OO .,., tmi YGU l,n_, ond plde YGU.-.elt _,,.inrt., ,. w. ,,., .,.u,._,_,___, .~ .. ,1.g/ Jol ootobvio,aly.henotudento,.,_,andrtt owoywitkit,,.,.i-t.,....,11,l ,_fo,cleJIMnOto

-polulion, In ftloo (popular """"'' lratornlly ""'"'l>t,,.).and,t~en Loxti-l< ::!.i:"',:i::.~.=.:::.:.::.liti.,..1-..r<-. n,,..,,...,,,.,...._,;o.,,o,ontribotlolltolho -la\l,t ........ NlfflpuleTfilo.lnotnoetonwbo ,..,,_--.r1r.oototioou<111M..iiska4 .. oP _.ito....-,.,_dialts)--t,o,, _,.bucldlr.,f\ .. .., .. ..i..,11,an.-nto..-....i o,ft,...,,w pi mlpt pla to tl,e;rftlelo.d"'l"and~blyr,pn,d Umpuu,rpro,rrom.,,,wl othorotude111 1ao! otionft l elooltenlM lexe, INf01"-"ho~oow1bi1waya""ndan OPtr>tl,..oYII..,._ I. 11 .. d-/.,.S,.;li--,k!ti1,trid4'0PJ"icahle""ly!o ,!colo id,i> I n,qui,.IM'lrl :::~::!".:..:: ::~:z=k= lha\.....idltavtt\~Mpedthnaaoiadividi,..-u..m.11-.~ .. ... ..-111o1. -inriab(ybo..-00,1>,-the_,,..leott. :"!:..t"':"! ~h~h~I= ::t.;!.~:,'i: T H K > '-'K ~ I W, ....... ,. ......... .. .. _..,_ .... ,, ........ ,_ ........ ... ... ..... -.. ...... TH R KTll K !T,TM, _,. ,,_ -,.__,,,,_ .. ........... __ ..__......._m,, .. ... _. .............. ,_,. __ .,_ _____ .... ...,. TH EYOTKot' ~ flCa .. ,,o,..,~ ... .. .... -.-...... ___ _,, ... ,_ T H Kc,1.1.0,(0WARrHl!)Ynt!aE, ..... ,,. .. ... ......... .. ,_ ......... ...... .. ........... k .. .... ,, .. ........................... ,_,..., (1~1(:11 CHAY~ K 0'"1STU, n,,, i<' .. ... ... ____ .. __ .. .... ,.,,,_. .... -............ .,,.._, ,..., ____ ..,_ ...... ... __ ,. _____ .. .., ... _M, ...... -,_ ..... ...,, .. _,.._..,., ..


__ .,_,_., ... ...... .. ,_ ...... ,...... ..... .. ....... ,, .. ,_._ .... ~. /IOW ou ij ~~ I T. SOlf YOO OOST, _, ...... ..... .. ~_,, .... .., .... _.,,, ... ,,., .. ............ ... T N-~ 0:,PAC R ,OO~TH, _, ..... _,_ ----... .. ......................... .. ,, .. .... M~ron&ATIYG.Tl!HLf ,_, __ -...... ... .... .., ..... ... ..... .... -.---,...::.:,.~;.,~.:--~:-!Mt-: ,_otth-ltl&ldo _,il.-J.._..t.t ~ltsltl.:,"= !r-1ee1':.:.."'::1:,d~=~ """7,-..-.r.Aom11t .... rt--.- pO,ptrnltorto--.oboutl / llnd,.f,-tllt ~:::t :::.::: ~==.:.~:la<~ At~ .. n1

---.. ..... ~ -.. ... .. ...... .-. ..., ___ Gf,,_ ... N _, ...... ... .. ,,.e;r6*. 1~7.'"n';;:, =~ ... :!':;.";'h~(:~ fromthtodJootntotude o todr f 11llrroet-.,.wi-Juovl-. ""-'lcloooft.o,,1odotht,..,....., iooo!~'!:'Z!.i~:.~ ... ~~:'":':'.~ k!>Owlo"l>t!ltffmy1t.....,!&co n tokethtmo t eriol l h o o ,l,t n!h m>-<00 ..., noloo.,... ldUN 1l tooolvt p ,.,.._ ...,.., 1 ,...1i,,<1ono1u .. m u,hdato M)'ca,i ,,..,lnlotbel,.i.o.t-tenn--i.othtolPt ~o;:,':".,.i:';.~:"'-~ ::. =-==~r:t:~IE :.::-:,t:1~= !,7.,".::~ =b~--~'"' Tbt,.!,noq ... t i onl,u\ t ho l o i>00 l1eon ll n1< tl teotln 1 i1 .. h .. tin r .Jkn owopro f wllo-molodeli,l, t i n m.okinrllpoo~,_tlon, \ ~!.::"!:, r;:; !".Z.....'-:: :~":.t"::,':;~ 1 ~:!. 11 .. ':..~:::. "!t~:=-.i--:'!r:.-"..: rialoolr-"tht""iloi-tMJ'do.ot _.,.,...,........,ODdllM1oflffl,.Uwbat.. ::; ::.: :.:~:: ~~e1~i:.'~ ..... ~~~ ~ 11e: ; :~:;n:-:.:::-: ool s odot o ll ell< hp roblemool"'"\l n h iJ'o p. ;::,2::~:;:iE~~!:i!.E ~ :..ic::::.=:..~a~.::,';.:;.; nu11y,,..i..veu.e1..,,.....,...,.1;m1o -"-.for~lclitM-io!alho 20'00,,00.. R !olb'or.,._....ot,_ .. .....,rOlea'-t-boel&ffl0-. 1 ..,tafontlltou m tOII\ o f ol)(>Mil>lolOO l l< ,.oaroodmouPfo,, a R ln t hecw ... ,t~oho< .. hou,~IHl,r<>t !2 ond ll ROI A 1 .Ko,, e,. tr ,J! roiJ,hellOl'< t ho ifl< h ,.. t f Go00 r ,udllw.,ubtflo.. ith.iothtolloltod --. H.o .......... 1,,_.,_of,ho .... t polmo f lllshe,-tloll.T..,;d;,.-1,.. .......... o1 ........ ___ nit.oddoclon -....ilmtht_ol_donl_,,,tlolla tatrvtcltol...,.lo-pe,:l.(Tltioo p vr-loia porl iP'"riotel f U..i,..t,_,....k procti<> f d,opplnrthti.. 1teot.-,o0ot.....,!& t hr7 l,u tl lu."'ll1Jli111ito.Twoot ....... 1.1.-bo,n;-io~l1 ~=::: :!: ':. "":::: i:;i:;~

:m~:J;::;:h~:~:~fi2~1:~;i::~ \rill<,kop\ieal,..,aftthti-.Th two,tudtzoroooothoQui,, :;! ~~yt~n,=de~o~h:~,"'!1~:: .:=~ Jt IV.lot ,Mld lf a otudent'op,,.oer,how,evi0 l)Oiiid thio ~~::;k:~:tl:~,k":!.,:,~:totol'::J:i~ ?~:~~,~~~~~;Z:.;.~1;.~~i: <00,.., ndln,.,,,.,inl.on"'""''"'"""dinro, d.thi o rifh to h0uJPolicya11dinformtho o tudpmenl. Finally,malceourethatyou...tainropiof o i,y inOW rtifted to pTaclkoehomicolttomo. oth~;, '::: ':1tl.:'!:!~ ::, -;i: ty]'.leofbehoviorfrom him, and whon itoe

'i",[!fHJlHH, a i;.. ,ur,tu,i'I i H~n.,t,:s 1 1 HHlifHHh!li

@ff#I c lassroom A S I MPLE GEOMETRICAL DERI V AT I ON O F TH E SPAT I A L AV E RAG I NG THEOREM T ;::::::::::..":':;=,:-: offtuld-"""i<>r\phe. """'""o,oltoo\iorulnhkh1helnft..,..,.of t he OKOn~ pt, ... !o ,.p.-nled 0011 In.,,.... of o bo\lneN loNI,_ =~:!!1:-!!:r""c.': _.,_. ( 1(1, Sec. 1i..1 1. ud ... _,plal. lloo of -h--t ,,_,_. ,..___ p.. S... IU tialfonJ'lo!lollM....W ofpo,tloldill ..... tlolequatiou.. Wlo.&\ rollowllil Orl,..,_,..,llc,,,-nor,thepn><>rt pl,e"""'"" "f\en ,. ..... ,,o-tatoQ-ioo\hHrinr-od...,,..n,,..fa<>rt...,._ ilMOily-pil,hed.,,.,.,...,..,.11<,potial o,erqinJt_,.,,Thl oo pp,-h,. .. .,..; .. 1i, I. b1 Sloll<'I' [ l~ ] ,..llo ,tO(!I! lhe problo,o ol vl ""llo: llow in_ ,,, e, Ho. and b,the othor ( 1 8Jl>o-lhe...u.odtoderi,-.adllponlon oq11&t;,.._t

ll'h;t ~fl3]ha,..,...,m inodtMq-tiot .. r a ilod hy Ve,-.rl<& and ftnd them to be un;mWrlOnl for ,..,.ofpra<\l a ... ,..ult, but mr,ly :,~:~:: ;;:, ':~::~~ : ~~ 1 :g ,::::..,lMl Jn f~~. l lo-pll .... yat:\if f &.;:;71; altentioototho, ph .,..,nd""'th<hospin rontinuily,quationh -"'ftu i dondtho J hoobjom .. ofri,;,,,,..;,_ ... .......................... .. ,. ....... -. ........ ....... .. ... ... ..... .. ..... .. ..... .. ,,. ... ,! l< ote that hilo t ho indi, i dual ,-olum,., V (tfandV (t) m&ybefun)i ntro..,ntrotlono! OJ >ed ,. A i o t>t.-e-frml>

>nn1rat'on'on<>ttan t v a lue u .. ofU>t,..\edby Jl a u .. of lhl >. uoually prr., u,lot ..... ltho~ .. 'h'' 101 ~" ~:: ,:1e~~'; ; ~::~~~.;~:. ~:,:~ ~,.: ~i~,h io th< .,.,ume frfflion of -Ph:;;!:'t:"1hZ..i:-;~~'~:~:~~,t~~\:: i::::: U1 ~~i~"~.:~::,':::,::':~ 1h :;;=.:,;,u:.:;;~ Thoav,ragiogproctedin tornuoftheph ... a\'orage.aod t hu eint.,.,.. t, lnr,o,ral r,qui,., n., enlt;ins>olu""'to ,[;;, .. 1,) 1 ) """'inman)'""potn"or portid .., ofbolh~ inorderlOol""inunoothondr,p,-n"'ti, e, olue. [~. 19 ~ So,;h a n o, or q; in r "'""""' ;, illo,t .. t ed in.'i s .2 i \' e1,arlyidentin..:1,ond ;:!;.;,~~-~:;-:.::~~if;~.., i o OOUnded l,y ... (t) ',.( .. ... .. .. ...,. ..... .. o mtforlhew,_orou,dri1otioniti o ffi.,-. i llo,., a,ea .,.,,..,,ni volu....,"iththuntr<>ids>

C!e,.,ly1heint<.--tiooo/1hetoin"" willcan

Affl:i views and o p inions I TOWARD ENCOURAGING CREATI V ITY IN STUDENTS T ::!.~1.~;:,_~,:-..=~~ --" it ia on.,, for _u,.. ,.,,_, ...... ....._ polit;clauudadm1nit1111lonanoritl11

ol-ifo....-"ftllk..,...-pt.oofidnd .. ptr..,. whltdtbo..,.0ttor1><,~n)()lfm ...,,oold,wi th Sij~~~t~:-::::~r\;:2:,:~:;.~: pl,li-s,l,7. Athln:lol>dftnal...,mploi.opl'OVidod"1tl>o pl\yolei.ot SIN llolir ,.COMpiffl,Nowity 1i-ry1t-..,,,d"1-ifflhrto .. o tll,ehoale-olpkyaica.ThioU-r,, aloobo-,,'o .. \N~i-tlooiot -m-llanb.loo-ofaatonwhid, bol,.._tha,4uohtyloMt .. --bolto tuw-,.11 .. ,.,.ornatural~,1;p, ioMt .. iquoly__.1o,...,.ioi tu iQ,,tlyo ,...,..,ltlobolk,_..lhot.dopondinr""""'c,b. :,,7::.:..~~:.=-:1: 1: :,. r:7.,.:: ....,1o,1,t1,edple.AordioJtothtop. proxlmationowhio li of t h.It two


.. :!~~:~1~:::!~:'7:'::.: ~~.!_i~ ;~:".:1;.~,::.i""ti"~~ t) his books, Ei!~.,. /0,Bohr atudiod Kiukegur>elly ; todolh&t.oor,tudenU,hooldbtoome familiar v;ith ,..,... of thinkinR a nd with pro ~ur,oofinquirrhkh re dltrerel dofhum.o.n,ryh a -.C(lmfor .. riou od i ..,.....t hY ,.. only ~!i..::~~o:~:.,..~~~ :.~ i~t. :!:~; iaowpe rad i ation Similarly. re~uN-fertiliutioo and to ot,....tbotinonyareaofhuman0oLnbeput ;ntovrocctioe .i,i,enlhIOMO n ,.._


,po,,.,l:>lefotbeeurriculumt<><>l< lh,..rou,_ hentheywere>tudenu)and\>ecou .. ~e,,pro. r....,inthd,parUMntinoiauthat ki, pa,tkulor 5~:~~:7i~;~,==~: ,; ,',; : ;':: ;:d ~~:!"AA ~~~~i:.;:1-;:,;-.;1:~-~ .,.., ,.; nr. ci..,1,. not o ll tudenl.S ill btnefit rrom t>oold h.,-., ne,;0111,,,...,h1hat .. a>..,ntuden1- more or i... o t they do 1:>ut where th e >toden1,dthunu.,,,lpotntilispemit\e"tn'1-hyln,;u. lnr ll' o ,h"no1on li n gi,.,ri,g1<;1h Pol ~ ""hY PeterC P<> ell Mh a ni,o lE "ti ... ,inrO.parn.l a i.xtdeai r n,,Jforrtno l y,., un.lod intent to p.--n,"';he minimnm u .. fol koo lOlymomotO:r'""ri< t..,,,rth.(3)0n< r n,in loroolook"omootoomprohena_trulment ,..,n tothide mor< romp~ ~~~= ; ;~r:.:;:::..:~/"'ci"'"""''",.. ~


@fi:j l abo r atory C O MPUTE R-ASS I S TED L A B ORATORY S TATIO NS Wll ..LIA 1tl l S NYm'.R MI C HH :l.~. II ANYA ~ ll~h#IU;~r, IA-,.,PA 11837 n :.~ :=:: ~":"'.;.=~~ Mh ..... thoo 118 dt:srtt i f..,, fN" -. e<-ofbudp1,_.,,.18i..011<1tln'" _..-;,,,_,;_,;""--td.,Olf,_ IMINoO'o.AnartocleinC-.,..i/;o.,_,_. =f=tl""K!l"ll""'

~;;~~.::1~~~p::::. ~~:~::i::-:: ::I~ x:,: 1 ~ol'::~\:~ :r: >to,th<>tur po~o,fol & to an, l yio.ot"""1ts tollucknell ',timk h>ri n,; rom poUr u o i na th<, mim1modtm In a&lo ,aodtooilh<,rottat< od i ,pJayor<>,.lho = ..,,,.,1,1,-laoo,J-.. Tho,talioo,houldl,elinkedto ,m.o infr&meromputerb yoO i rhpeodrnod,m lor lon r1< rmdat ast or,fl". '1li,lkl nlr>i>, tion ,hoold pPOVldo ,i,uol a talu a ~port upon ~;.:fi~"#i~.ff~iftP~ T h<, ,,instrU

FIGUll,.H.,.;,!"rCh o m ':~ u:! i:; ~ :~':on-:"~~"'.:.~=~:;!~:.:.~y:~~.-::;; ; .,..,,,.,t, n l reoho~ n ;nr bi.hndPi~ 6


,:.rrl LJ ...... .. ,. .. .. ...... CitON book reviews IJll't' US I0 ..1 S l M!UII I;! hH.v.r ,u11 .. ...tK.11.11 ,.,;,, 11,u,..,..r,UilQJ).Ul"",_., $ ;,.oo. N .,;,~~, t:. s.urcr-, ir .. ,..,..,,., 111 -.i. Till,bool,,o..ilfSnally<0oc,oi_..,,,.,;,;o., d"fy r ,..ll'a"Dllhoi<,t,,,>aU,.tflowlnUqu.L,." lolol-to,rltho-ialiatabo,londat-oft..........,_1-,..,,.rtl .. with tl,eduoiral ~1-.r.,tloa. n,, ~1;ot....iur11o111or-t,,-o .......... .,...,'81..;11bri ....... ;., .... 1-t.a.Q hlchpio>'compo1tya,,. NOlly,.,.,.lvaledtoexpoodlhoiridnJobtyondtho l&bon.l<>qtl.,.ondpiovaluablo11<1HobJNif at_,._lka,_1M,..,.. .. .,....n.-. .. to1n1tt ,.,.u,.,1pp1oc ... .. -.,..,,.,pm ,,_,,.,, __ ..,."''"11y .... 1i.i,1o,u .. ,...,,k1ooK1.., ~.':::::.~ i7_::~!,. -:;::~~::!!; _._ ... lbi~lrand-ofopentioailhout .. _"':dpllMldflr,...__ll,~tll.Mof'fllylordloponlon(whlodopoUculorl)' im....,.n\for mo,:romolulooo..,ho,_,lnLbu\odo,eq";..,.nde .. "-"i"-"ofthe .-,.; .. .,.,..._ .. u,. ot ........ ---r..---.tpu ... ot....., .,..... ::~":-= :::: ot hlo ,_ Choptor 6 Chop!Olldovotodlothellm,rttOllono,


(eifti laboratory A SEQUE NTI AL D ES IGN L ABORATORY E X PERIMENT FOR SEPARATING P ART I C L ES BY FLUIDI ZA TION PRINCIPLE S DOSAl, 0 0.WY E Yillo,_..u,.;...,..;,, l'illo,....,l'Alto85 o ~~=~-=:=::~:..:= or&...tllot.Yoeunt,.. poo r lyt ,... t duct'"ul,.....nta.Tho ponl<1Ndlf10,ln6olwtya..Jol.,,oothat l,lldiu1-ortlutri&ti,ont0olol>.-rion :.N: wh1 U..t po.'1~1ar j.i, &.-1ow0<1.lmriothc .. ,ly _.... toOri otio<>a. Otller lat> .... po .. 1"'1 \-Ito I>)' ftnff(llxporimentall1.FMdiu.. ho,, tMl' .,,. ll>tn bJ -.,...,1 '""'"" to-oappn,pria"'luid.-;1ytha1...,ld .,.,.,.\l>olip\portltlao""lwillolhoftaidnd


IN"'IM-bolliN.Dooip.tU.. .... n ... oo1oc11o,,ofu..prilM-f"'"'-ltrialovai~ ablol11Clltlab(aclooip-~110""'thon "'rriedo.t.s.rv-lpe11pochtlon =~lll~~l~ltolloo, prinbltm ooh'lnr Cakulatlonofto rmi1tal 1pt,edloolnvol .. un k,.,....._ Al,. .... 1 u\l,oftuld d .. I<> Ille .. ,uroof11,t,-nlclol.Tl>t\,rmlnol,poodoo11M ,-rtkloolaolrto)' whlCit, ,an bo <>kulatodll ) ~~! ::: ~~::) v. l!, ~ l ,:tl _o -; : ;srsr=) --tr 1 ,u,1.a,-u.. ....... ...... ., .. ..t .. o,&l .. 1.0.-U,o,-.,ofll1 o po.>1kloo-ld notbeQUOnlll'lodb7 .-.l lk-nnwrbolhklndoolpo.rtkloo. F..-.thi odlo rr&n1on>11"'o,l&'"alr.....,;1y<"bo--.L ladditkw,.U.lo..._.,.,,.,..,_..,1,a,willbt,,...,,,...., ... ,tu.. --n,t-loir.-;tr DooipeftlMI __ ..,.....,,., ... __..,......, __ ___ tlMI ,-rtltlodwntrwandtllefad p,_ .. d.-.p. n., p, o u .-. drop t h '"l(l, \he ftuidi=l be"'""tlnrthelol'lnrthert'< (r-tU

r rouprnt0>ndlobvoopl..,orkedonthoden><. nonpoTO< s p.o.rtid.,..Theyu..,ia,imilorttthnique forden,ityme.uul'ffJIOntbU\w;thwaterMlhe orkinrnuid.Thei,denoilyw .. l.3 l r 1 .light. ~'.t;::\~l~~l:G~~~"E. otionin N mp leota konfromth e b, .. dp.o.rtinumt..rsreintheSto..., Lo..,,.ion l 2.3 )1 .th.\ion~:":;~;::;,:~::~.~: 1~ 1 ;h; I~ den" :.:.:::;:.::~~ ~.:,:~~ .':' .~ : i:~::: \lolnmedi,p l a\ruetobly a bithiah. ,.... lollo"lnK irrouJ>< <0mple\Plionofoilond""'1pa,,,...uTedexperi. mentolly.Jnthe<0rlymeuu,..m

u,eqol...i1<1atton....,.,.1t_nfor t,m,lul """ nu. caa be ,.mod "t.,,. o cn,plt,lnllnlof:nlioaolUf-..... 1u dt,y lolcCabe and Smn~ fl) .,._ di ... _loottequaltotlMin,..-ralofdl.n..,. 1u11&.i.o,,t<1thotthelirt,.t po,tl ... --t 2.16mlo.--ht6 .,,o rterminol ,po,od ,"'hl lt the mo,.......,Portid .. n-bout22m1<1tff. Tl"Ol.ityurin,tho..-1...i.,-otthe-t.roix oytho~tal 11x '"'""" Tho .,..,,11 dai~n ooo~pt ~u lh&l ol, rilul<01umnofartainhoirt,.t andd l ametor """ntrit _,. d......-U,.,,.rt,.po\ ,t,,.,..ttriotln. T"" rrooi .. "'"'--" at-, tho lab loollln1 for oult oblt"'"i-nt .lC,....tlWlyaplaatlteblowff. llwao dttidodto-ralebott. 1 2Tm!~ inlo fortMbk,,er.ootl\o :~:l~.h~tr.~:i; :~ :~ ~=~h:,i.:1~".: lhroUlaplatoandon ori!lc,o.m>non>e1rottupto =~~~:-~=:.:~i:::.7~='7.:

:::.=.:: ~I\~ a lol"K'O plu t i< ttuh bq ith ho! .. n.. .. ,;..,.l

r.util book review s t'11"1TE E l,El l E1'(T $ :llA T IIF.'>IATICAL A~l'ECl'S.Vol.lV H<1 l,wNlb y ~;:; ,; i,~::r1.o\~; :;. ~ 1 .. Th e finiteeloemontmethodl.o_,_ in r i n. <,_.inrlypo p ularasamethodforoh'ingd i ll',.. : i ::1,,:";';~:!~" :::-~.~r:t7."r~rmC:: a bou t itO\"ffi lfth,ir pmfouor,obtalnod thofon,ft n iteeltm/,n\methorlhonnlt<,eJ,montop proxiimlion,<>flh prol:,lem,and t heor,mson, pro,.,dundeiwhkh \h o y o pply Fin ol lyHAmp le o pplicotioru, o r,~,onusuo l lylothoP<,i ... nOing'-lh< ....,,..,h .. oomoo x poouretofontuotd lhoo~ .... 111toot o fu n tionalon ol y lis bocl41roond.Thw,ll,iobookwill =E::;~~~ ~~~=:~,:~t @:fiil l etters "l'1C0f!>

t-Gi$I curriculum A RESOURCE BASED APPROACH TO ChE E DUCATION R B .SF.WF.LL.r.Ll,EJo:.I..S.LEt.:1'Hl v,.;_,,.,Q,ott,w,,oo1 !',;,~Qlol.~Ol7 I ~:~.::n:,.C::!.:;:1 ... ~h=!:;1~:0...,,~~! contrilKIUonp....., .. u,., .. ,...,tpl'OO..,,,..n ;_: ~111 uo _,..,.,. _.., p,otkoad criti<,,lty....i .. ,-Ito. To ,.,-f, ... ko _,_, ____ ,.. __ ., _..__,_ ... ~-..... -"' ___ ,_..., ... ._ _____ ... .. __ -..... .. ... .. ... -... ______ ....._ ... ..... _____ ... ,__ --------.... ________ .___ __ .,,.., ____ ,.. __ --.... ----"'


~~-4 r""1~----=--C'A ---ir:::::::::4, ~~ -----l':::_.,, ~ --;: hooldboth.,,...ghlyv,,un. KIIUTION, ~!KIUICHSEO lOUCTION To~thotru, '"'"""' plonn i n~ dia.t

Bt~-iinrr pilHiH'l HlfPilUHtjH1'lff 'i i, i i.J 1 ~1 ~,:r 1 ii 'F~!U (i"'s. { rt~! Hi', 1 if Hi ~.f; ll i' .: ~t ; sl -~I ~c ,, hi ii, n,,! l s,11 '1?iWr ., i,.,,~H~Jn 1 ,.,!:,HII' .l''f !'-hr! 'ri1!g,~f'"!,r: -ijl~~i:l4i~t"!lla~ ~ ~ti i"l!li;il:h: iilh::"~}f1~~f; ~ut~uH~ th,otf~t~h.eUtiii~H : ,'ta l-~ri' ,, ,.,. .'-'1,11 ,p,u-, 1t~1r!i:;;,1 t~H;t~l.i ;!jir!,}gtlt~ lii"f~J;r1=r;,,;: f.,;r3!i=~!, e~ 1J~g,1~ ~P="'l:eii;p! li;HH;Hn! tHHiMH HmmhHH1f~t[i f ,iLrni..t.t ;trudru ,r~rim:;Hh:hM ~'~!! ... i!H; !h--, "!"'! 'Hu ,l "! ,, ., f!I! l);Hl ':''1 ,i;;: hi .. ft l!r: i!l H,Hll ,[1; 1 1 11 1 .. i, : i.1 r,-. i, =1 j~: t ~rif-i 'f 'I i [ f~ i 1; } f! I !.rf Iii r !!~ti; lih; 1: ; l ii!! n-'Hil!l, !;.p ""i;nfJ'l!@.i. i!:~j tti~1'~tsJ .. 1!"f : 1"1-ift ht"'~ r -~ =1~r iH~h;~4!f .. 1~;2.trnP !; ;.;;-[[ii .-(2.a:ttp-J;h,,ii!~ir !l lnhf "'!if!.,, ;1, ,!j; aui:,.i i1EH~i tlf 1111 1 n;i1 i;!1~1Jit!liit~a;; 1 :}~ti i;i iliirift~fllr"'lii i~.~ 1 p~ 'H"'W;;; ,! i~l 1 ,H 1,H[[i~tP tnil1~1L ; ;l J:,;oianl .. ,aftlil at il! ,rt t\ .r, it' ti !H ,11 ttl 'ff Jj i 1


c.,...,..,\; m s.Th,G<,elopmentolim,fo,-th, ,ore"""_, i, foHo~i~ tho tndition,I Oppr<>oeT ol r,neralaimsfocthorraduat.o: c, .. .. ... .. -. .,..,_ ., .... ,t ttl .. .,., -. ,..._,. ,. ,._, .. ... .. .... .. ... ..... ., ...... u ..... .. .. ............. Wik, .. ,., ... ,., r., .. .. ,. ... .. ... ........ .. ... ...... ...... ... .. ..... .... .... ..... .. .. .... b.. .. .. <......... k. .............. ... ... .. .... Ht = ,) .. """' ...... .. ... .. ._ .... ... ..... ,... ._ .. ... .. ... .. ,, .. ....... .. .. .._. .. ,-, ,.,w ...... ., .... ,.. Gh".. .. ........ I ,_ .... ...... .. ... ................... .. .. ... .. ............ ., ,, ......... .. ..... .. ........ ...... ... ., .... ... .. .... ............ ..... ... .. ,..._ .. .. ... .. ......... ... ,, .. ........ (;. r. ...... .. .... .. ..... rv __ .. .... .. .. .. .. .. ...... ..... ... .. ... ,,_..., .. ,. .. .... ..... .. ( ,. .... ,, .... .. ----kt, ,t .. ., ., ,. ........ ,. .... ,, ....... .. ..... .... ......... ,_ .. .. ... .. ._ ......... .. .. .. ... .. ~............... .. .. .. ,. S ub jttt Obj e< ll, .,._Threioa l& rir,lit,raturo on objttti,,.. and on their p,..p,, ,.._tl .,.,. typ i ~ed by tnt.oau,h .. Ro wn t, ,. (4 ].,.Jl.lrl 1 .. [ L].Theyare ::::-:: !;:-'...1.~ ~~=:i ~~~;:: n,t~o,k d i o,,., m o, Jo,rie diog,amo, ete. Himm el blou(? J hudonthi e,yn iulyondthl o tOd )"Ject. aoo,ie m i<:o tolfwillb< !,::t i ~:-Y:.::::~hi;,;:,a;~~tj:.~~~:. ubi&inthrir a reaof,xperti1lfot:otion o w lll o vo;d th e "'rlp nd np p..,t,lem, whit ... to; ,. of,ruidodd i ooo,-.,ry a ndofoon,erA1 1 ., .,.,.h.i;........., .. t1,o ""'""' .. doe,..19H ,, plonho, o vol .,i to,h,..,.tl,o,.odo ol .... ,_ ,_ ,_. .. d, .........i.....i~ po..., ""-"" Mtio"'I IH.rni n r .. denned by l'o J, and l..owio ,. Rot h t hNO a l rat,g i .. ronoidtrtho>tudtntto beopl"OOl""-lh e, tudtnto u ,ri N ohub-..,.l&wh i ehthey explo,.. u ,inr_,randprot, J .,,,,.,upo]ilby thetea.inathi ot "'!OD o ;.~~~i~. ;!:~.~~~~;;,! "\ :..~~ =~ Thorom.,rutional i..rninr ,t,..le,,:y h ., t ho ~:'fi E.~~~E ~:~~;21~:f i o >,.,red a ndi o frto"-"'"PPlil,-urO a nd


LiH#I classroom E X TE N DED F ORM O F THE GIBBS PHASE R U LE ,. ~ ~-.. -~ .. ~,,,-___ .. ,_,._ ,. .. -~ .. ,._ .. _.,_ ... .. --*-"'""' ___ .. __ __. ... -.. ---_.,. ___ .. --"' .. .... ,........_., ... __ .. -... -~Th,,,..u l \hcc ton'lm&lrixi,,....Udtooo ;;,';:'-;;,!"""llli1in r1ta ndo,,i pnx,du...., [ I ) Ther>nkofthehelonmatrix ~,WO,i- to be 2. !:';.'.":.i : ~~p.,.,..tobotho,aokof\hopo

Th n"mb

~=-~::=:.:-...:.:~: ...,bt-toted..., ....... ......i11>rlho o1,t.o-otext<11tofrtiolom ,.,lo In ""rtiStnoctivt S..-a,-.lff,iapnp0rbyplotlnon o,l)ltto'1-tofSH.Cl()iaoa..-&e11&ted __ ,.,.. __ ... 1on1aei:1,....i ... Port'"of!Multto--lnto_,. prod..eta.Tbooi>itoP-llhtoyotomln :::-~:~ 1 ::.!.~~ !~;t 1 t1~7o1~ 1 .:}:= ......... th .... 1i .... rt,-i........-,.-1-. =-"":.-andU........ pondiar-t.oof NH,Cl(o) NH ,+ HCI : ,, CS) ~t~ : :irn:::;6'.' 11 ::: ,m Tl!.numbt,of...-of-hoi>itotonbt writt+2n(N,)-4,, Cl-niJICl)+2n(CI,)-<, ;r:.;.;:::.:.::..:~ioo~:beriltent,e. .. s Suboht..tiona_..... ~--~-: n(IICII +!n( H ,)-a( SH ,) ln{S,) 3n(Nll.)+2ll-3n(IIC1)+1n(CI,) Divi1ioohylhttol&lnumbe,ofmoleoof1_.. ooe&I to l< nbo,.,.,lllyaorml,edbyoni,..peOllof ;~\'.;-;~:E;EE~ 1 [il~~~==: ::==b,lhtoppli<1nin1,-f \l' e ,nay""'""";<1 .,, ,,n,tionofthofo,.. =~ ~~~1: 1 1~;.s ~=,.'~~ ~.~,~~,: ofNll,Cl(o) / Nll (rllnon<'lacoaltd-l on d ot"'lnilibriomthere ra-tllCl.s,.11,. nd =ly.=7t! ::~~o~:~~':"=l~ ""'oqualto l.11_.....lhen,-ai

,_., __ ._.., ____ -----.... ---"'>'-- rolatlono hlp betooen th o atom ra\l.,. SI,,.. \ho inillalml,1u.-.10,oml)OOtdor arbi truy "'""U. otthIMofS H ,pt,'MOltOl 1'H ,(;l(a l 51,... tl>o l oo, r ne,r ,i-.,. ....,.,.,..i fro111 t-two""""""..i., ... ,an..,;i. SH,C1-:,i,tH,C1 :-: H -q:-:,:lqH ~.-R:,/L-1 +q ~ 1 Rlll .t + 3q re RNl. and Rlll. & l"O & tomra!ioalnlh\fo,,,0quallon alnolo""ly !~7t"1a1::~:..:,;,s::,~;,;,;;.;.~ 1n1y1........-,.nw...,,.;oin1,...beoMaintetooll,owthat lootol<:hiomCll_..,,._,. _, -2 Tho,,..,_ SH,Cl(a) H Cll1), SK ,Cl(o) S,(ll. SH,CHI H ,111, u,d SH .Cito) Cl,Cll ...,.betreotodloa&lmlW-.....,..,._ 1 0-i.ot ::=~.~:=3~~~~:"' = t..t ... >r>aklet-am,...,111&1;,....,Poredb1 pla,,in1 J1 .SO,(o)loanovoeuatod,-landl1 allo-eotto0qolllbroto.The.-;.p, ,.so,.so.o, .s. s, .s ,.s .. s"s .. s,. :~!, 9 ;,;:,~~~:' 1 ~~ :~1:~} '! O ::. :i m~ ~ ~~i~i::::...~-=.::.~ ,-.ntodlntloyotoffl :;::::,;:.:ttalntoth o fol\o'(!I0 ,)+2!IOl+S~i ,1 (0. I Add,t-1,-N-tl,< "-$.r'l lu,d al $o,bel;t,,tNIIIOrleW This,o .. lt io>n-tliMP,1metrleotN_....loeuda10ni10u., :;;,.~,.,_lredto

@fi#j c l assroo m S IMUL A TION OF S I MP LE CONTROLLED P ROC ESSES W IT H DEAD TI ME Kl:lTHll WAT$0S.JUUUSP WO:<(l ol>d PllAD!:JWB .Di;:!I HPA:aunlk __ Kl"40lln T ;:-:~ 1 :,'\-;";!"',::.:~::-;-; t h4111<11hatolo,..oumbo,-of..-.,lp~~~~~;:r~~:;:;:::; de,-..1,-duote P-Olllodlobooe(l ... thed e l\htr for &el ])Olnt

T ho--l b uodon,.,_ ,.. ;,.,h,.ri,o,looodloop._.., ,. .1. Nmp,... .. ...,"" Pl"" ...... !l, .. o/ ~m;:,;~-,:':,::;:;"'" FIGUK(l. S..,...,, ......,,.olM,q.;..t.n .. ,log ,onnot nd ..,....,. .. ... ,., .,.,_, wheroa,b.e,d,e,farowie, .. locted00110l>nt> ~~=!i:":i1~f; :"~~~:!~;;,~ : ~.~;..-: Th< transform hued oomp,,,tl The"ndtr.,-aduolu,...,~ill prob ablyootboablotoha n d l e .. tron fmm o. llo,., allthatthetul,wlbyE.l'.Co ll i nK [ow aSta 1Un!'"l1 y Th,1oxt<-0.,.,..1hotraditlonaltepl,, o ofotol(3) ehiomt1ry,unit-Ol) < m;, a 11eohoolon, Th ronotaoto in ~,i. (3) &ro fonction of tho p ,_ .. ,.mete,.. (K ~ .. or K ~ ,. ). ;:':;': 1 ;; ~t~~~~-~~;.;:!,,~: ~ "~ ~I::: ::.,~l i !~in:=.loor::. :r'.:po~ .. t~ ,;;ripe,: """''anbo,imi"'rlye,ol" 'ed II]. Adi.oA

GIBBS PliASE RULE c.. eo ...i i. -,.... .u ph .. oY,.,,,.onlJ".For\htmororomplu.,.... tem>ln,ol1inJl<\"e"'lph-.tMmor,del,.I~ u~ :.=::-:t~.~;=~~ ~-:::~ In ,nyportilopt. po~)occ,.,,ins;nthatph..,leo,thentaximwm nom,,.,.ofli,...,lylnd.ntp....,ul"6oYln'lpOOition (i <,.molnner .. donootoic hioH ,rmor,tM,i, a, in.,:le-ph.., ys tom.Suboti tu\00 1 W<

2,r'-l,o-3 o nd --u 0 $ubot.itutio,,s "" Thisis a uniariaoty,temhichi,completlyd~ ocrib<olemiop~ro,dhy pJa-th,nFeCr S,(,)0ur.Tho ~:: ".':~t:t:.~7.~ ~I :~-=d:~'='~,:::: ro.-., 14.Thomuimum numboroflin,arly ~~=:~~= .. ;:;:;r;:_;::~~ ... 1~:: ::.:=~:n:::.~.~.t::.::i-: tlliamanntitu_tff a otoiehio::-, ~:~.: ... that ha1 lo"" ,...konod ~"ith, Thu,, Threeayotemproperli,.ho,etobe plft"'1 Th ... m o,b,,eh,ctl..,,(i)tn toc,thari a nt Th ,.-mplyntUn o thotthor, s OO\oneun qu< \empe ... tu .. (T ) a lwhiTa-:rTI~) + 2P!S,ci ) P(H,S)


&\.III.Tho&kltofT.<&11obofoond .. U...-t--llibri.WO..C,,1-c; ).lG,"(Al(.1,) UalthtU1holl&UddoU114]onU..ota"'-tdf,..,. ..i,. of lo,rnabon (.:>G, I. ftnd -S 9.162+U.601T, T.l41.4K Thoilibri,. M -A ICl,(rH I io .. lq,ltlalha lh.....,,..oaiyatU, lo,-po,,,tu,. w""aHlho_,...,.. ; .u...;,.....,.u,-.natur&I ll& ..... ..:111&,__llodP(AICl,)-pari"""u. -.O.t6&1IOIM1Ndofl.Oat111.U.,,,.-ew .. ld ftlOd u,,,, tho -.,..,dinr .,.h,. of T. 13o!K.0.11onoP"'l ....... mntma,bolMpoood ,..~T,fflK:fo,oxamplo .-eu""'ri>i tl"&,ilyod l '(AICl,l at,uy.0 .' al m ondo tt l>o 0&nH1 tlmtftxLhe &< foityotalumlnum 1p, al:,lyp,_,,t .. & li4u;dolloY1 .. .. ,o .ll-.Thl would,..ullnMl' & lido:a',_Oft-whlerryatol-\llaystem.A\tuillbrium, ""' p- .;,t, .,._... ,poelea (G aCI., lnCl ,an dA ,l add.tio,,totheinlll&lft,el o d two conJonM.fpothetkol ,.,... ; ,. C..Ao() "d ln.U( 1 ). ono i nt rod...ed, The numl>orof-o!Ga.U(t)and ln.U! 1 )(1>.fpo thetlcoll1) I the oquil,bnted ayII ai111plft11<olhomo-ofmolooof.._;\b! G,t,A,ao,d l oAo,..poct;veb'.Tbohn,ott>otlcal aporioatGUtllute..,..ialY&rial>leo.ThXlO: ~: p ?: o t 0: and 2. Sobotlt tioarit-(10 5.~ 16 -2/_z,,-OZ-7 T h..-.n ,.,,.,_ ot f.--lom or< .. ioftod by '"""ibl (1) temponlur<. 121 otal p ,.,..u,. (3) Cl / ll a tom ,..\lo. (4) n"(G&) (~) n (lof. (6)n (A o ). andnf .... .... ionparam.fl>(ltllotk alapci..Ot1...,.01<1mbol&nI oquatlonocan be writtffl ai mllarly lna\temptin ,rtomokt Hihriom< akula '""' in complu ayat......, _,..,. antl&h"..,_.i",-..Tho u........itonnof1-Gibbopi,aw,.lo-lf

kindsoftornsor,lement. r.~~~~i~~;:, %.;::~r ,.::ri~ .,..,, .. numb,o-,ofph.~::~~~,';",lu=~~'; ~J!:::~~nt l"Nction0qullihri 11 / Cl,tomratio ft!f;,~t=.~:i~traint. =1tETi}~J~::IFi:Eit oxtto otionl,,,.-o,i,ltoollquallty,onditi,dillkulttowritoadnn;,;,.., ;:.~;-.. :V"'1e"!~; I~';;::,. ; ~'Z'.:':~ i'::~ \oNythatthilo u .. fulondrel;ablet,...ti .. ,bul :~~~:I~""',.:::::.~:~ ::~:::::,~~Im~ oentedi,availableel .. whe reln0qulvole ntform a ndllttleltent;,mho,boenpo.idtotheproblem, of\loo&twilhingto.,..theubj:lm>tterin :n :::~~:~,-:::::;,~hi:::~::: :-;.,:,,~ u~~:~/.;.,~i::mpl ,,.. gh-en bo lov, Thopheoomenologi
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RESOUICf-lASED EDUCATlON ~-" tollndotloen.11,o,_._.,,. ... ,_rttODd an kilo mainin and """'itori-Tkiattrat..,-U..,....111....i f..-lbt!linninr. 0 1, ...... 1,J .. N/,._.,.,.,,/.,,.,,,_....., ., ___ _.,,._,.,._ .... ... ... 1. H-"-".. a..-r_ ..._..._11.._,u.ho"" It .. _.,_._ ._...,.__e,._ .. ......_F ____ ,A -A--0,,.~-tr"--"r.2) --"---r,.._., __ _,,.,.,..,.-orm SPATIA l AVERAGING THEOREM c...,;,. .... -, ... 21 =:lo,.ln ~ :.q. H io llturl-otthl1rarJ.nti,io&;,.7of!!!otlt,-y'o d

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Our name has been synonymou s with engine e ring education for over 150 years Here are ei g ht more reasons why. ECONOMIC ANALYS I S AND INVESTMENT DEC I S I ONS ChiU. l koku .f1. ,, llSJ'h11,.i;,SrarcUni,.,,si1r { 0-47 1 -8 14 55-5) Apri!l985 JlJpp. PRINCIP L ES AND PRACTICE OF AUTOMATIC PROCESS CONTROL Ca rl os A. S mich. Uni ~ rsit) of Sourh fl.>ti<"1 Amiando B Co ,ripi o, L,u/.,i,ma S1a 1, Uni,w,ir1 ( 0 ...+71-88146-8) Janua ry l98 5 @pp. NATUll.A L GAS l'ROO UCTION ENG I N EERING ~:!:.!~ "'" ...... ,, ,..,.. ,;...., .,. M,a ......... ,,.,.,;1-J -4 1 198-1 11;,... nJNDAMENTAI.S Of M O MENTIJM II EAT. A N D M ASS TRANSFE R J,J f ,1;,;,,n E:1 :~~:;;~~ ; ~ 1: ~ s.;; _, ,.. .. !D-41 1 -IIH97,JI 1111H tll,... ~ ~~ l tf6t~ ~ ~rro'i 1 )S ~~!;~~; E ; L ---,,.,.,1 ,1111;6 1 -;J ,_ 110,... I N TROO UCTI ON TO ~:i;;~ E Nli K GY s..iuc;.., M --i ........ !0-41 1 .00111'11 I""' b/11 ... A G U IOE TOC ll liM I C A L ENGINE ERI NG l'R OCESS g~:~~l~i~ ~ ;~ \ll CS ,V,, ./1, -..Jw, ot'-411 .. -si;;..n '""' ... m/ey ll1f ENG I NEER I NG P UB LI S H ER T i........i...4Jo.__,.........,._ ;..,..,_ ...... 1.,it.,, 1 ,..-.0.,., ~'.':" .. ':'~ .... ~