DR.JOSEPH JOFFE,CH.E.
DEPT NEWARK COLL
ENGG 323 HIGH ST
NEWARK,NJ 07102
SUMMER 1968
CHEMICAL PROCESS PRINCIPLES TODAY
C9a1 /omf" :
PIONEERING EDUCATOR
CREATOR OF TEACHERS * INSPIRE OF RESEARCHERS
%'T.  ,
S"It is more important
to carryon research
Than itisto pay
S' dividends The speaker was
Lammot du Pont. The year was gloomy 1932, and he was
president of Du Pont. A proposal had been made to pare
the research budgets in order to protect the dividend.
As it turned out, the company was strong enough to
pay for both, and it hasn't missed paying for either in the
past sixty years. But there was no doubt which way Lammot
du Pont would have decided back in 1932. And today, we
, invest more than $100 million a year in the quest for new
knowledge and better products.
It is precisely this attitude towards research and
development that attracts so many graduates every year.
And that makes Du Pont such an exciting and rewarding
place to work.
There is no formal training period. Our men go into
responsible jobs from the first day.
They work in small groups where individual contribu
tions are promptly recognized and rewarded. Promotions
come from within the company.
They do significant work of positive benefit to society.
And they work with the best men in their fields in a crackling
technical environment that provides every facility needed.
If our attitude towards research and work agrees with
yours, why not suggest that your students sign up for a talk
with a Du Pont recruiter? Or that they write our College
Relations Manager, Wilmington, Delaware 19898, for
additional information on opportunities in their fields.
CU P0r
�?
I
~~
_<�*'
Chemical Engineering Education
VOLUME 2 NUMBER 3
EDITORIAL AND BUSINESS ADDRESS
Department of Chemical Engineering
University of Florida
Gainesville, Florida 32601
Departments
Editor:
Ray Fahiein
Associate Editor:
Mack Tyner
Business Manager:
R. B. Bennett
Publications Board and Regional
Advertising Representatives:
WEST: William H. Corcoran
Chairman of Publication Board
Department of Chemical Engineering
California Institute of Technology
Pasadena, California 91109
SOUTH: Charles Littlejohn
Department of Chemical Engineering
Clemson University
Clemson, South Carolina 29631
EAST: Robert Matteson
College Relations
Sun Oil Company
Philadelphia, Pennsylvania 19100
E. P. Bartkus
Secretary's Department
E. I. du Pont de Nemours
Wilmington, Delaware 19898
NORTH: J. J. Martin
Department of Chemical Engineering
University of Michigan
Ann Arbor, Michigan 48104
J. A. Bergantz
Department of Chemical Engineering
University of Buffalo
Buffalo, N. Y. 14200
CENTRAL: James Weber
Department of Chemical Engineering
University of Nebraska
Lincoln, Nebraska 68508
99 Editorial
98 Letters from Readers
104 Departments of Chemical Engineering
University of Washington, R. W. Moulton
100 The Educator
Professor Olaf Hougen
139 Views and Opinions
Thermodynamics: Death and Transfigura
tion, James L. Throne
Where are the Engineers?, T. B. Metcalfe
129 The Classroom
Programmed Instruction in Thermody
namics, Charles E. Wales
126 The Laboratory
ChE Kinetics Laboratory, Kenneth B.
Bischoff
135 Book Reviews
137 Problems for Teachers
Feature Articles
109 Irreversible Thermodynamics, C. M. Sliep
cevich and H. T. Hashemi
113 Approaches to Statistical Thermodynamics,
M. V. Sussman
120 The New Stoichiometry, E. M. Rosen and
E. J. Henley
107 DIVISION ACTIVITIES
Scriven Delivers Annual Lecture
CHEMICAL ENGINEERING EDUCATION is published quarterly by the Chemical
Engineering Division, American Society for Engineering Education. The publication
is edited at the Chemical Engineering Department, University of Florida. Application
to mail at secondclass postage rates is pending at Gainesville, Florida, and at
additional mailing offices. Correspondence regarding editorial matter, circulation and
changes of address should be addressed to the Editor at Gainesville, Florida 32601.
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., 137 E. Wisconsin Ave., DeLand, Florida 32720. Subscription
rates on request.
SUMMER, 1968
SUMMER 1968
I '
New from RONALD
Mack Tyner and Frank P. May,
both University of Florida
An introduction to linear control theory for college
students and practicing engineers. Emphasis is on the
universality of the control problem in process engineer
ing through mathematical equations that apply equally
to components from all technologies. Linearization of
nonlinear forms and its limitations are discussed early
in the book. Both the root locus method and the fre
quency response method are stressed as means of control
system analysis, and Nyquist diagrams, Bode plots, and
Nichols charts, which serve as useful analytical tech
niques, are demonstrated in many of the illustrative
examples. Attention is directed to the use of both digital
and analog computers. An Instructor's Supplement is
available. 1968. 472 pages. $14.00
Publishers since 1900
The Ronald Press Company
79 Madison Avenue * New York. N.Y. 10016
from the READERS
Editor:
Please refer to the article on the common thermody
namics course by Manning and Canjar in your winter
issue, page 11.
Why should the chemical engineering staff at Carnegie
have to put up with (a) a compromise, (b) conferences to
make the compromise work?
I advise the staff to scream loudly and try to get out
of the bed of Procrustes.
Ernest W. Thiele
University of Notre Dame
Editor:
The ASEE might render a real service to our country
if it could get pages 78 and 79 Spring CEE into the hands
of every senator and congressman in the country, with
a forceful letter of transmittal calling attention to the
analogy of General Hershey and Adolph Hitler as implied
in "The Rise and Fall of the Third Reich" and alluded to
in the last paragraph on page 78.
John E. Kiker, Jr.
University of Florida
Acknowledgments
The following have donated funds for the sup
port of CHEMICAL ENGINEERING EDUCA
TION:
Atlantic Richfield Company
C. F. Braun and Company
Dow Chemical Company
Mallinckrodt Chemical Works
Monsanto Company
Olin Mathieson Chemical Corporation
The Procter and Gamble Company
3M Company
Standard Oil (Indiana) Foundation
The Stauffer Chemical Company
CHEMICAL ENGINEERING EDUCATION
IPRCS
from the EDITOR
Since we wanted our first issues of CHEMI
CAL ENGINEERING EDUCATION to have as
broad an appeal as possible, we included articles
in a number of areas of modern chemical engi
neering. But in this issue, we are using a dif
ferent approach: we are emphasizing the areas
of thermodynamics, kinetics, and stoichiometry
the subjects that were joined together many years
ago in a threevolume work called "Chemical Pro
cess Principles." As our "ChE Educator" we are
featuring one of the brilliant authors of that
work, Professor Hougen, and, as our "ChE De
partment" his Alma Mater, the University of
Washington.
Olaf Hougen might well be called the inspira
tional and intellectual father of modern chemical
engineering: he is the inspire of many promi
nent chemical engineers who were his students;
he developed the areas of chemical engineering
thermodynamics and kinetics; and he played an
important role in the development of transport
phenomena when he brought Professor Bird back
to Wisconsin and charged him with the responsi
bility of placing the engineering computation of
heat, mass, and momentum transfer on a sound
theoretical and scientific basis.*
In this day of continued debate on the merits
of the socalled "chemical engineering science"
approach, there are lessons to be learned from
the example of this great man. The first and
most important lesson is that we cannot expect to
know what is at the end of the research path
before we get there; i.e., no one could know a
priori what applications would arise from the first
course in mass transport which Professor Bird
began to teach back in 1954; nor could Professors
Hougen and Watson initially know the extent to
which the theoretical subject of chemical kinetics
could be extended and applied to the flow, batch,
and fluidized reactors of chemical engineering
practice; nor could the profession know many de
cades ago that chemical plants would be designed
on the basis of the thermodynamic properties of
substances that were predicted by the theoretical
methods developed by these same two men. Al
though talk about the "practicality" of thermody
*Professor Bird recognized the inspiration and incen
tive placed before him by Professor Hougen in the pre
face of his text on "Transport Phenomena" with the
coded acronym: "This book is dedicated to Olaf Hougen."
namics persisted throughout the 1950's, today
not even the Neanderthals of the profession ques
tion the importance of thermodynamic informa
tion on enthalpies, free energies, heats of reaction
and PVT data to modern industry. The lesson
we must again learn is that chemical engineers
and particularly young teachers and graduate stu
dentsmust be provided an opportunity to delve
into those areas of science that are unexplored
even if applications are not clearly visible.
(An important area of this type today is the en
tire field of bioengineering and biomedical engi
neering). It is certainly destructive to stifle the
curiosity and dull the initiative of our young
scholars by harassing them with demands that
they show the immediate application of their
work. These men need instead the same kind of
encouragement Professor Hougen provided Pro
fessor Bird and others.
But another lesson that can be learned from
Professor Hougen's career is one that must be
learned by many of these same young scholars;
namely, that the work of the engineering scholar
should ultimately be placedby himself or by
othersin a form that is usable to the practicing
engineer. For the real utility of the work of
Hougen and Watson lies in the fact that these
authors prepared numerous charts that could
be easily used by the engineer in practice
(e.g. to find the final conditions in a Joule
Thompson expansion or to predict enthalpy or
PVT changes in a process.) Without such a step,
the important work of the scholar may long go
unheeded by engineers in industry who do not
have the time or academic background to use it.
The AIChE Research Committee is currently
studying the problem of the industryacademic
gap. President Max Peters has often spoken of
it and it was forthrightly discussed in the last
issue of CEE by Bob Lenz. Perhaps one answer
lies in our thinking again about the work of Olaf
Hougen in not only developing the Chemical Pro
cess Principles but also in further making them
applicable to real engineering problems. CHEMI
CAL ENGINEERING EDUCATION in this issue
is proud to present articles on the "Chemical Pro
cess Principles Today" and to acknowledge the
debts of the profession to a pioneering educator
and a very warm and sensitive human being.
R. W. F.
SUMMER, 1968
A GREAT TEACHER
OLAF A. HOUGEN
Olaf Andreas Hougen, Emeritus Professor of
Chemical Engineering at the University of Wis
consin, has pursued a distinguished career in the
field of chemical engineering education. He has
been one of the leaders in bringing the profession
from a state of empirical practice to a state
where it is firmly based upon sound basic prin
ciples of chemistry, physics, and mathematics.
He was born in Manitowoc, Wisconsin, on
October 4, 1893, the son of a prominent pastor,
who was a pioneer in the development of the
Norwegian Evangelical Lutheran Church of
America. When Olaf was four years old, his fa
ther was assigned a pastorate in Decorah, Iowa,
and it was there that Olaf received his elemen
tary grade school education. While the material
resources of the Hougen family were limited
one of Olaf's daily chores was to take the family's
cow to pasture and backit was a family rich in
intellectual and social activities, with constant
encouragement to the children to achieve high
educational attainments. Proximity to Luther
College and the fact that he had several attrac
tive sisters made the Hougen home in Decorah
the center of much lively social activity. The
family later moved to the State of Washington,
where Olaf graduated from Tacoma High School.
He then decided to enroll at the University of
Washington in the Department of Chemical En
gineering, which was headed by Dr. H. K. Benson,
one of the early leaders in the development of
chemical engineering as a separate educational
discipline. At the University of Washington,
Olaf established a distinguished career, both aca
demically and in extracurricular activities. He
received his BS degree in 1915, cum laude, and
was a member of Tau Beta Pi, Phi Beta Kappa,
and other honorary societies.
After graduation, he spent one year with
the American Smelting and Refining Company,
at their Tacoma plant. Then, with the encourage
ment of Dr. Benson, Olaf decided to take up
graduate work in chemical engineering. He chose
the University of Wisconsin because of the na
tionally recognized work of C. F. Burgess
(founder of the Chemical Engineering Depart
ment and of the various Burgess companies, in
cluding the Burgess Battery Company), O. L.
Kowalke (prominent in gas manufacture re
search; Chairman of the Chemical Engineering
Department for 25 years), and 0. P. Watts
(leader in the field of applied electrochemistry).
After two years at Wisconsin, first as a Graduate
Fellow and then as a full time Instructor, he
served in World War I, 19181919, in the Chemi
cal Warfare Service, assigned to chemical engi
neering work at the Saltville, Virginia, plant.
Following his discharge from the armed forces,
he spent one year with the Carborundum Com
pany, in their research laboratories at Niagara
Falls, New York, where his work was largely
focused upon the development of refractory ma
terials.
The post war upsurge in student enrollment
that was felt throughout the country resulted in
an invitation being extended to Olaf to resume
his Wisconsin connection. He accepted, and re
turned to Madison in the fall of 1920, as an As
sistant Professor. Since that time until his re
tirement in 1964, he has been associated continu
ously with the University of Wisconsin, except
for several leaves of absence. He rose through
the various academic ranks, and served three
terms as Chairman, totaling to 8 years. His first
graduate degree, Chemical Engineer, was earned
in 1918; his PhD was received in 1925, number
4 in a list that now includes over 200 names.
When Olaf Hougen started his career as a
teacher, chemical engineering courses were large
ly qualitative in character; the pioneering texts
of Walker, Lewis and MacAdams and of Badger
and McCabe had not yet been published. Through
CHEMICAL ENGINEERING EDUCATION
S educator
This article was contributed
by an anonymous associate
of Professor Hougen.
The Academic'Tamily Tree"of a Great Teacher
S0.A.NHOUGEN
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The above academic family tree indicates those persons who have held university
professorships by white numbers on a black background. Over the years
Professor Hougen has been advisor for 44 PhD's of which nearly half are now
in educational work.
SUMMER, 1968
I SIMKOVICH
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10 YEN
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SHAMR/N
Despite his many honors, Olaf remains a modest person, with a
warm and outgoing personality; with a host of friends not
only in University circles, but in the Madison community
as well.
out his career at Wisconsin, Olaf was a leading
force in bringing about a constant modernization
and upgrading of the undergraduate curriculum,
including the establishment of unit operations
theory and laboratory courses, chemical engi
neering thermodynamics, and kinetics and re
actor design. It was through his influence that
Bird, Stewart, and Lightfoot wrote their text,
Transport Phenomena, which has had such a
widespread impact in chemical engineering edu
cation in recent years.
When Olaf started his teaching career at
Wisconsin, graduate enrollment in chemical engi
neering was low, being generally limited to one
or two graduate fellows and to the young mem
bers of the teaching staff working for their de
grees. While some growth took place, it was
greatly accelerated when Olaf, in recognition of
his substantial research contributions with limi
ted support, received a grant in 1941 of $100,000
from the University Research Committee, using
funds given by the Wisconsin Alumni Research
Foundation. This grant enabled him to start a
program of graduate research that not only re
sulted in a sharp increase in the number of gradu
ate students, but also enabled him to initiate a
program of staff additions. He was largely re
sponsible for bringing in K. M. Watson (who
later resigned), C. C. Watson, W. R. Marshall, E.
N. Lightfoot, W. E. Stewart, and R. B. Bird, all
of whom contributed greatly to making Wiscon
sin's Department of Chemical Engineering one
of the leading ones in this country.
When Olaf Hougen joined the Wisconsin staff,
his unusual talents as a classroom teacher became
apparent at once. While his courses were de
manding, his enthusiasm, his clarity of exposi
tion, his excellent organization of subject matter,
and his fresh approach to solving chemical engi
neering problems won him immediate acceptance
by the students as being one of the outstanding
teachers in the College of Engineering. Olaf has
always treated his students with courtesy and
respect, and has encouraged them to do original
analytical thinking in solving difficult problems.
Olaf Hougen early recognized that the ideal
teacher strikes an effective balance between class
room teaching and research, and he constantly
strove to match this ideal, with the high degree
of success that his associates fully appreciate.
Over the years, he has trained 44 PhD's, with
somewhat less than half now being in educational
work. The widely disseminated influence that
Olaf has had in graduate education in illustrated
by his academic "Family Tree," shown in the ac
companying figure, which was prepared by R. B.
Bird and presented to Olaf at a recognition dinner
given in his honor on October 8, 1966. On this
chart, the white numbers on a black background
indicate those persons who have at sometime held
university professorships. Olaf's publications
cover a wide diversity of subjects in the field
of chemical engineering, and total to over ninety.
Olaf Hougen's influence in the field of chemical
engineering education has been felt not only
through his classroom teaching and his direction
of graduate research, but also by the publication
of a series of widely used text books. Industrial
Chemical Calculations, published in 1931 with K.
M. Watson as coauthor, was later followed by the
three volume series, Chemical Process Princi
ples (Material and Energy Balances; Thermody
namics; Kinetics), again with K. M. Watson as
coauthor. These texts have been highly success
ful, and have been translated into Italian, Japan
ese, and Spanish.
Many honors and awards have come to Olaf
Hougen because of his distinguished career in
engineering education and research. He has de
livered many invited lectures at other universi
ties, and before industrial groups. His major
awards are as follows.
Awards Based on Contributions in Engineering
Education
1. The Warren K. Lewis Award of the American
Institute of Chemical Engineers, 1964. Second
recipient of the award.
2. The Lamme Award of the American Society for
Engineering Education, 1961. This is considered
the major award of the ASEE.
3. Appointment to the Burgess Research Professor
ship at the University of Wisconsin, 19551961.
4. Benjamin Smith Reynolds Award for Excellence in
Teaching Future Engineers, 1955. An award of
$1,000 given annually to an outstanding Wisconsin
Faculty member. First recipient of the award.
CHEMICAL ENGINEERING EDUCATION
n" ' 
Ir f ..* *  i.I'
Professor R. B. Bird
presented the academic
"family tree" to
Professor Hougen at a
dinner in his honor.
Awards From Professional Societies
1. American Chemical Society Award in Industrial
and Engineering Chemistry, sponsored by the
Esso Research and Engineering Company, 1961.
2. Founders Award, American Institute of Chemical
Engineers, 1958.
3. Institute Lecturer, American Institute of Chemical
Engineers, 1950. The second lecturer to receive
this honor.
4. William H. Walker Award of the American Insti
tute of Chemical Engineers, 1944.
International Recognition and Awards
1. Scientific Attach6, U. S. State Department. As
signed to American Embassy, Stockholm and cov
ering Denmark, Finland, Iceland, Norway, and
Sweden 196163.
2. Honorary Doctor of Science Degree from the Nor
wegian Institute of Technology, Trondheim, Nor
way, at 50th Anniversary Celebration, 1960.
3. Honorary member, Indian Institute of Chemical
Engineers, 1958.
4. Fulbright Professorship
To Norwegian Institute of Technology, 1951
To Kyoto University, Japan, 195758.
5. Invited to give keynote address before the Deut
sche Bunsen Gesellschaft, Duisberg, West Ger
many, 1953.
Despite his many honors, Olaf remains a
modest person, with a warm and outgoing per
sonality; with a host of friends not only in Uni
versity circles, but in the Madison community as
well.
Olaf Hougen was married in 1919 to Olga M.
Berg, and one daughter, Esther, was born to
them. Esther is married to F. G. Taylor, and has
3 children, in whom the Hougen grandparents
take great pleasure. One of Olaf's brothers, Joel
O. Hougen, is presently the Alcoa Professor of
Chemical Engineering at the University of Texas.
A nephew, Wendell T. Berg, is a chemical engi
neer with Union Oil Company. The nationally
known CBS commentator, Eric Sevareid, is one
of his nephews.
Because of his Norwegian ancestry, Olaf
has taken a prominent role in NorwegianAmeri
can activities, as well as developing and main
taining strong ties with Norway. He is a member
of Sons of Norway and of Ygdrasil Literary So
ciety. Because of his activities in 194045 as Wis
consin Treasurer for American Relief for Nor
way, he received a citation from King Haakon of
Norway. As a result of his father's influence,
religion has been a strong and continuous force
in his life. He has participated extensively in
the activities of Luther Memorial Church, a large
church located in the University area. Olaf is
a long standing member of the Optimist Club, and
has served as an officer. Golfing is his chief out
door recreation, and keeps him in excellent physi
cal condition.
Though Olaf retired in 1964, he is still actively
interested in his department and in the chemical
engineering profession. He frequently is at his
office, and the members of the staff have the bene
fit of his counsel and advice. He truly is one of
the revered elder statesmen of the chemical engi
neering profession.
SUMMER, 1968
1
Department
UNIVERSITY OF WASHINGTON
R. W. MOULTON, Head
History (19001968)
In 1895 the University of Washington moved
from downtown Seattle to its present location
about 4 miles northeast of the city center. Denny
Hall was the first structure built and in its base
ment there were facilities for what was known
then as the Chemistry Department. Chemical
Engineering at the University of Washington had
its roots in the Chemistry Department. In 1904,
Dr. Henry K. Benson joined the faculty of the
University and while his educational background
was in chemistry his interests were motivated
strongly toward industrial chemistry.
Dr. Benson was interested in the application
of chemistry to agriculture and he was a leader
in the chemurgy movement in the Pacific North
west. He was extremely conscious of the pulp and
paper industry locally and throughout the world.
He did much research during his lifetime in fields
related to the production of pulp from wood and
other forest products. In 1919, Dr. Benson was
appointed executive officer of the Department of
Chemistry and Chemical Engineering as it was
known at that time. He served in that capacity
until 1947.
In 1911, an organization called the Chemical
Engineering Club was formed at the University
of Washington. At that time leaders from chemi
cal industry in the Pacific Northwest together
with appropriate faculty members at the Univer
sity of Washington established the first chemical
engineering curriculum. This curriculum was
somewhat weighted toward pulp and paper and
also coal and gas technology. This curriculum
was the precursor of the chemical engineering
program as it is known today.
In 1922, Professor Warren L. Beuschlein
joined the faculty of the department. Professor
Beuschlein had received his Bachelor of Science
in Chemical Engineering degree from the Uni
versity of Washington and his Master of Science
degree in Chemical Engineering from the Cali
fornia Institute of Technology. Professor Beu
schlein became a dominant figure in the thinking
of the faculty of the department during his tenure
on the campus. He died suddenly in September
1944. Professor Beuschlein's research interests
were quite broad. He made important contribu
tions in the areas of the manufacture of charcoal
from wood waste, the high pressure hydrogena
tion of coal, the fixation of nitrogen from air,
and in the manufacture of pulp from forest
products.
The first doctorate degree in Chemical Engi
neering on record was that awarded to Dr. Cal
vert D. Wright in 1931. Dr. Wright joined the
faculty at Pennsylvania State University and
was active in research dealing with the utiliza
tion of coal during his tenure there. During the
20's the department graduated a considerable
number of individuals, some of whom obtained
significant national prominence in their profes
sional careers. Among these are Mr. Samuel G.
Baker, Dr. Olaf A. Hougen, Mr. Victor Mills, and
Dr. Waldo Semon. Mr. Baker had important re
sponsibilities with the DuPont Company before
his retirement. Dr. Hougen became a leading
educator and spent most of his professional life
at the University of Wisconsin. Mr. Mills was
employed at the Procter and Gamble Company
for most of his professional life and made sig
nificant contributions to their new product de
velopment. Dr. Waldo Semon was associated
with the Goodrich Rubber Company and was their
research director before retirement.
Accreditation of chemical engineering de
partments was initiated originally by the Ameri
can Institute of Chemical Engineers in 1925. The
University of Washington's department of Chemi
cal Engineering became the first department ac
credited in the Pacific Northwest and this action
took place in 1926. In the middle 30's accredi
tation was first carried out by AIChE for the
new organization, the Engineers Council for Pro
fessional Development.
In 1930, Dr. Kenneth A. Kobe, a new PhD in
Chemical Engineering from the University of
Minnesota joined the faculty. Dr. Kobe was a
very energetic, enthusiastic faculty member. Du
CHEMICAL ENGINEERING EDUCATION
Many prominent
chemical engineers,
including Olaf Hougen
received their
education at the
University of Washington
in Seattle.
ring his eleven years on the faculty he published
well over 100 significant papers dealing with his
area of research and related works. Dr. Kobe
resigned from the department in 1941 to accept
a position on the faculty of the Department of
Chemical Engineering at the University of Texas.
Dr. Frank B. West joined the department in
1939. He left later during the war years. The
author became affiliated with the department in
1941, as did Dr. Joseph L. McCarthy. Both Dr.
McCarthy and the author are still active mem
bers of the Chemical Engineering faculty.
The postwar years have produced extensive
changes in the department. There has been a
dramatic increase in the number of faculty mem
bers, the size of the undergraduate classes, the
size of the graduate program, and the amount and
kind of facilities devoted to the department. These
changes have created the department as it exists
today.
Chemical Engineering Today
The faculty of the Department of Chemical
Engineering now number fourteen individuals.
Four of these men have joint appointments; two
with Nuclear Engineering, and two with Forest
Resources. The College of Forest Resources has
developed within the last few years a Bachelor
of Science degree program in Pulp and Paper
Technology. Because of the long and deep in
terest of the Department of Chemical Engineer
ing in the field of pulp and paper these two joint
appointments were established and serve to main
tain close and good working relationships in this
area.
The Department of Chemical Engineering
played a significant role in the formation of a
Nuclear Engineering Department at the Uni
versity of Washington. The first courses in nu
clear engineering on this campus were given by
the Department of Chemical Engineering. An
early interest in the facilities at Richland, Wash
ington dating back to about 1950 initiated some
of this enthusiasm for the nuclear industry. Nu
clear Engineering evolved into a group effort of
five engineering departments and was eventually
established as a separate department wholly at
the graduate level. Dr. A. L. Babb, a member of
the Chemical Engineering faculty, serves as its
chairman. The joint appointments in Nuclear
Engineering serve to emphasize the close tie of
chemical engineering to nuclear engineering.
In 1953 the Department of Chemical Engi
neering was established as a separate department.
Prior to 1953 there had been what was then called
the Department of Chemistry and Chemical Engi
neering under one chairman who reported to the
Dean of Arts and Sciences for Chemistry and the
Dean of Engineering for Chemical Engineering.
While this was a reasonably good arrangement it
was decided in 1953 to formally separate the two
departments. After separation the two depart
ments occupied the same facilities and for all
practical purposes continued in the same manner
as before. The Department of Chemical Engi
neering owes much of its tradition and strength
to the Department of Chemistry which has always
been a strong department at the University of
Washington.
After literally decades of effort in planning
and study a new building for the Department of
Chemical Engineering was authorized and com
pleted in September 1966, in time for the 196667
school year. This new building increased the
gross square feet allocated to the department
from 30,000 square feet to 72,000 square feet.
SUMMER, 1968
The first courses in Nuclear Engineering were given
by the Department of Chemical Engineering ...
Dr. Babb's involvement in the development of the
artificial kidney has received international recognition.
Not only was there an increase in space but the
space was now functionally suited for the needs
of the department. Each faculty member now has
his own office, and his own research areas. There
are also many types of specialized research areas
built into the building for the needs of the depart
ment. The philosophy followed in the design of
the building was to provide for a maximum de
gree of flexibility. The building committee and
the faculty as a whole felt that it was unwise to
be highly precise about how space would be used
five and ten years in the future.
The undergraduate program in the depart
ment has undergone a major revision in the last
few years. The changes that have been made in
the curriculum provide for more options in plan
ning the students' programs. There is a core of
required courses for the department (which is
not common to all engineering departments). On
top of this quota of required courses both in
chemical engineering and related fields the stu
dents have the option of choosing technical elec
tives amounting to 15 quarter credits and electives
in the area of humanistic and social sciences
amounting to 30 quarter credits. By judicious
choosing of electives the student can plan his
undergraduate program to be a foundation for
graduate work or alternatively he can plan for
direct employment in industry following gradu
ation. Following this latter course he can spec
ialize to some extent depending upon his interests.
If he so chooses, he can take some courses in the
field of pulp and paper technology, or he can en
hance his background in fluid mechanics, heat
transfer, or other selected chemical engineering
areas.
The graduate program of the department is
the one that has changed most significantly in the
last twenty years. At the end of World War II
there were from four to six graduate students.
At the present time there are of the order of sixty
graduate students in attendance. Current re
search activities of the faculty encompass the
areas of reaction kinetics, transport phenomena,
fluid mechanics, heat transfer, mass transfer, bio
engineering, interfacial phenomena, polymers,
cellulose and lignin, thermodynamics and phase
equilibria, process dynamics and control, and ap
plied mathematics. None of the faculty members
exactly duplicate each other's interests, although
there is some overlapping. The fourteen faculty
members received their doctorate degrees almost
entirely from different schools. Schools repre
sented are the University of Illinois, the Univer
sity of California, Yale University, the Univer
sity of Minnesota, Massachusetts Institute of
Technology, Princeton University, the University
of Wisconsin, McGill University, the University of
Washington, the State University College of
Forestry at New York, and the University of
Michigan. It is obvious from the spectrum of
research interests and the backgrounds of the
faculty that there is a considerable breadth built
into the faculty of the department.
Future Trends
It is risky to predict the future with any
degree of definiteness. Within the College of
Engineering and within the Department of Chem
ical Engineering there is considerable interest
today in various interdisciplinary areas. The
most prominent of these at the present time is
the cooperative programs being developed with
the medical school. Fortunately, the University
of Washington has on the same campus a very
good medical school. This school has been de
veloped since World War II. Many cooperative
programs are already established. A prominent
example of one of these is Dr. Babb's involve
ment with Dr. Scribner in the development of
the artificial kidney. This work has received na
tional and international recognition. Other re
search areas are being jointly prosecuted at the
present time and it is certain that this work will
expand in the future.
The area of marine sciences is another inter
disciplinary area that is receiving a high degree
of support on the campus at this time. The Uni
versity has an outstanding department of ocean
ography and has recently received federal fund
ing through a seagrant award. A new division
of marine science has been established with vari
ous segments of engineering being a part of this
program.
Other areas of cooperation will certainly de
velop. About the only thing that can be stated
with some conviction is that chemical engineering
will be different in the future than it is today.
CHEMICAL ENGINEERING EDUCATION
4Qa CHEMICAL ENGINEERING DIVISION ACTIVITIES
Scriven Delivers
Annual Lecture
The 1968 ASEE Chemical Engineering Divi
sion Lecturer is Dr. L. E. Scriven of the Univer
sity of Minnesota. The purpose of this award
lecture is to recognize and encourage outstanding
achievement in an important field of fundamental
chemical engineering theory or practice. The 3M
Company provides the financial support for this
annual lecture award.
Bestowed annually upon a distinguished engi
neering educator who delivers the Annual Lecture
of the Chemical Engineering Division, the award
consists of $1,000 and an engraved certificate.
These were presented to this year's Lecturer, Dr.
L. E. Scriven, at the Annual Chemical Engi
neering Division Banquet held June 19, 1968 at
the University of California, Los Angeles, Cali
fornia. Dr. Scriven spoke on "Flow and Trans
fer at Fluid Interfaces." A paper based upon his
lecture will be published in an early issue of
CHEMICAL ENGINEERING EDUCATION.
PREVIOUS LECTURERS
1963, A. B. Metzner, University of Delaware,
"NonNewtonian fluids."
1964, C. R. Wilke, University of California,
"Mass transfer in turbulent flow."
1965, Leon Lapidus, Princeton University, "As
pects of modern control theory and applica
tion."
1966, Octave Levenspiel, Illinois Institute of Tech
nology, "Changing Attitudes to Reactor De
sign."
1967, Andreas Acrivos, Stanford University,
Matched Asympototic Expansions."
BIOGRAPHIC SKETCH
L. E. Scriven was born in 1931 in Battle Creek,
Michigan. He graduated from the University of Cali
fornia, Berkeley with honors in 1952, where he won the
University Gold Medal for academic achievement and was
elected to Tau Beta Pi and Phi Beta Kappa. He went on
to do graduate work in chemical engineering at the Uni
versity of Delaware and received the MChE and the PhD
degrees in 1954 and 1956 respectively. While there he
was elected to Phi Eta Kappa and held NSF and Shell
predoctoral fellowships.
After three years as a Research Engineer with the
Shell Development Company, Emeryville, California, Dr.
Scriven joined the faculty of the University of Minnesota
where he is now Professor of Chemical Engineering. In
1963 he was Guest Investigator at the Rockefeller Insti
tute and in 1967 Visiting Professor at the University of
Pennsylvania. In 1960 he was corecipient (with C. V.
Sternling) of the Colburn Award of the American In
stitute of Chemical Engineers for the outstanding paper
published by the Institute. His teaching abilities were
recognized in 1966 by the Distinguished Teaching Award
of the University of Minnesota Institute of Technology.
In research and scholarly activities his interests have
centered about fluid mechanics, some associated mathe
matical methods and the application of engineering to
biology. He has published highly significant papers on
continuum theory of transport and transformation pro
cesses, interface physics, interface transfer and dynamic
instability and pattern. Dr. Scriven is Advisory Editor
for the PrenticeHall Series in the Chemical and Physical
Engineering Sciences and is widely known for his editor
ship of Theory of Energy and Mass Transfer by A. V.
Lykov and Y. A. Mikhaylov, translated in 1961 from the
Russian by W. Begell. Many industrial firms have called
upon him as a consultant or lecturer.
SUMMER, 1968
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108 CHEMICAL ENGINEERING EDUCATION
IRREVERSIBLE THERMODYNAMICS*
C. M. SLIEPCEVICH and H. T. HASHEMI
University of Oklahoma
Norman, Oklahoma 73069
The macroscopic approach to irre
versible thermodynamics originally pro
posed by Sliepcevich and Finn in 1963 is
amplified to demonstrate that, of the four
possible alternatives for obtaining the re
ciprocal relations, fluxes and forces for
systems under the simultaneous influence
of two potential differences, one alterna
tive is identical to the results obtained by
Onsager.
IN A PREVIOUS PAPER by Sliepcevich and
Finn9 a macroscopic approach for deriving the
linear laws, which relate the fluxes to the forces
for irreversible processes under the simultaneous
influence of two potential differences, was pro
posed. Subsequent to this publication a number
of readers raised questions regarding the validity
of this derivation and whether the fluxes and
forces so derived had any physical significance.
More recently Andrews1 has published a negation
of the macroscopic derivation as extended by
Sliepcevich and Hashemi"1; however his para
phrasing of the macroscopic approach does not
appear to be tenable.
In an attempt to amplify the macroscopic
derivation, a simple example of a onedimension
al, onecomponent system under the influence of
two potential differences will be used. Multi
component systems will not be considered since in
these cases the definition of heat is at best am
biguous2, 5 and therefore, it is meaningless to re
late the fluxes to physically significant quantities.
Furthermore, systems under the influence of
viscous dissipation forces or external fields (e.g.,
magnetic) pose some unresolved problems on
their inclusion in the energy balance equations.
An analysis of the complications introduced by
the presence of electrical and magnetic fields has
been presented by Martin.6
*Presented at the Annual Meeting of ASEE, June
1922, 1967.
N GENERAL, the literature of irreversible
thermodynamics raises some profound questions
as to its range of practical usefulness; an excel
lent review has been published by Wei.2 In order
to circumvent definitional dilemmas associated
with more complex systemswhich would serve
no purpose other than to detract from the prin
cipal focus of this paperattention will be given
only to a simple process familiar to chemical en
gineers. Until agreement can be reached on the
validity of the derivation for the simplified sys
tem treated herein, it would be folly to attempt
to cover the more complex cases.
The system to be analyzed in this paper is a
onedimensional, onecomponent system in which
the properties such as temperature T, pressure
P, and chemical potential p. are assumed to be
uniform throughout. Likewise, the properties of
this same component which composes the sur
roundings are assumed to be uniform throughout
and are denoted by the subscript i, viz. Ti, Pi,
p.i, which in general are different from the pro
perties of the system. Obviously, then, disconti
nuities in the properties exist at the boundaries,
and for this reason it has been called a discon
tinuous system.4 Neglecting kinetic and potential
energy effects (without loss in generality) the
following equations apply when a quantity of
mass 8Mi, having a specific enthalpy, hi, and a
quantity of heat 8Q, are transferred simultaneous
ly and irreversibly across the boundary of the
system at Ti such that no work is done.
Energy balance: hi Mi + 6 (uM) = 8Q (a)
Entropy balance: 8 (sM) = 8( ) +
iSMi + 8 (b)
Mass balance: 8M = 8Mi (c)
Gibbs equation: 8u = T8s  P8v (d)
SUMMER, 1968
Defining equation: / = h Ts = u +
Pv  Ts (e)
where u, s, v are the specific internal energy, en
tropy and volume, respectively, . is the chemical
potential, and Iw is the lost work as defined in
81w
Equation (b) so that T= S, = total entropy
production. Combining these equations yields
81w = [8 ( + si8M] (Ti  T) +
M(i ) (f)
Replacing the potential differences by A's, noting
that APT = siAT + As and converting to the
differential form Equation (f) becomes
dlw = (AT) d + (APT) dM (1)*
Ti
Equation 1 is valid to the extent that Equations
(a) through (e) hold, and no other restrictions
are required. Although Equation 1 was derived
for the discontinuous system the same form of
the equation holds for steady state systems. How
ever, in the latter case it is customary to replace
the A's in Equation 1 by the gradients, namely
grad T and grad Ip.
Another aspect of Equation 1, which is com
monly overlooked, is that it is perfectly valid
subject to the aforementioned restrictionsir
respective of whether dlw is path dependent or
path independent. In general, dlw for closed
systems is regarded as path dependent because
heat Q and work W are path dependent. How
ever, if either Q or W is zero, then the nonzero
quantity becomes path independent, as required
by the first law energy balance, and in this case
dlw becomes path independent. For open systems
in which a transfer of mass occurs across the
boundaries as well as a transfer of heat and
work, then it is conceivable that the energy term
associated with mass transfer is path dependent
if the properties of the mass being transferred
vary with the amount of mass transported. How
ever, for discontinuous or steady state systems,
the properties are invariant at the boundary so
*Since _' s, then it follows that si (Ti  T) +
(/pi /) () Pi,T  ( P.,T + (i Pi,T  P,T
P= i' P,T P,T AT
that the energy term associated with mass trans
fer is path independent. Therefore for the case
of either discontinuous or steady state, open sys
tems in which no work is done, dlw is an exact
differential.**
In reality it is not essential to the objectives
of this paper to argue further regarding the ne
cessity and sufficiency of the conditions for which
dlw can be treated as path independent or an
exact differential. As will be seen in the follow
ing development, the subsequent restrictions to
systems under the influence of very small po
tential differences or gradients (or fluxes) is
equivalent to considering only those processes for
which dlw is an exact differential; in other words
the linear laws and the bilinear form of the en
tropy production or lost work equation are tanta
mount to the assumption that dlw is an exact
differential. Therefore, it is permissible to ex
press Equation 1 as
dlw = (AT) d (APT) dM
Ti
Ca lw
Ti
SQ
d T
M
( alw dM
+ QMT
Ti
Once the conditions of exactness implied by Equa
tion 2 are recognized, the remainder of the macro
scopic derivation of the reciprocal relations is
almost trivial.
FLUXES AS INDEPENDENT VARIABLES
EQUATION 1 CAN BE expressed in rate form:
1w = (AT) + M(AT) (3)
Ti
where the dot above the symbol denotes the time
(8) derivative.
From Equation 3 and wellestablished thermo
dynamic concepts, four postulates can be in
ferred:9
I. lw = lw , . Since both T
and M are continuous functions of AT and A[T,
**It is interesting to note that the form of Equation
1 is similar to the decrease in availability or maximum
work which is an exact differential.8 Likewise, dlw is path
independent for a process between two prescribed states
in which no work is transferred. In other words the lost
work, 1w, can be no greater, nor less, than the maximum
work that could have been transferred if each step of
the process was carried out reversibly.
CHEMICAL ENGINEERING EDUCATION
Iw can be expressed as a function of two inde
pendent variables, namely ( , M , (AT,
Ti /
AMT), ( , A/T) or (M, AT).
II. lw (0,0) = 0. If Q and M are each equal
Ti
to zero, so is Iw.
alw alw
III. (0,0) = 0 and (0,0) = 0.
Q 3M
& Q
Ti
Since 1w is always positive and is a continuous,
even function, with continuous derivatives,
Tw , _ Iw  and w (M) = lw(M).
Ti Ti)
a lw a2lw
IV. . The equivalence
a Q ZM aMa Q
Ji Ti
of the cross partial follows immediately from the
first postulate.
Referring to Equation 3 and recalling that ac
cording to Fourier's law, Q  AT, and according
to Fick's law, M I A/AT, it is postulated that 1w is
a homogeneous function of the second degree in
Q and M (or in AT and A/LT) at least to a first
Ti
approximation for small fluxes or forces. Thus
Equation 3 can be expressed in general functional
form for the case in which 1w is time indepen
dent, such as for discontinuous or steady state
systems,10
lw = w , M (4)
T
It is to be noted that Equation 4 implies that
dlw is an exact differential in  and M.
Ti
Applying Euler's theorem for homogeneous
functions of the second degree to Equation 4:
alw Q
1/ Ti 4
Ti M
/2 ( )
Ti
Recalling the definition of the time derivative
d(z) /do = z so that dz = zd0, Equation 5 be
comes, after multiplying through by dO
alw
Ti
dlw = 1/
d
Ti
M
�+ / w ( dM
\M / �
Q
T,
Since dlw is exact, the coefficients of the dif
ferentials of Q and M in Equations 2 and 6
Ti
can be equated. Thus,
alw
AT=  Q
M
A[w ah
T,
alw
=1/2 7^
2( T) (
TT, M
aM)w
� ( 9 _
The righthand partial differentials of Equations
7 and 8 can be expanded in a MacLaurin series
neglecting terms higher than second order.
AT 1/ M
T1 M
1 ( 2lw
Ta 0,0
a2lW
Ti 0,0
AT = Li, + L21 M
Ti
 2a lQ
Ti
( It
Ti
+ 7A \ 8 o
+ 1/2a2 1
8M20,0
(9a)
(9b)
Q
Ti
0, 0
(10a)
SUMMER, 1968
AT = L21 _  + L2, M4
Ti
(10b)
where the L's are substituted for the second order,
partial differential, constant coefficients. Note
particularly that since the second order cross par
tials are equal, then L12 2 La1. Equations 9b and
10b can be solved for Q and M without des
Ti
trying the symmetry (equivalence of cross par
tials) to obtain
S= L11 AT + L12 ArLT (11)
Ti
M =L LA. AT + L, AIT (12)
where the L's denote the terms containing the L's.
It can be shown easily that La,, L21, since
Lt = L21.
The forces as defined by Equations 7 and 8
and the fluxes as given by Equations 11 and 12
are identical to those of Onsager.3 7
SELECTION OF OTHER INDEPENDENT VARIABLES
A S NOTED in Postulate I above, 1w could just
as well have been expressed in terms of other
independent variables. For example, instead of
Equation 4, one could have started with
lw = 1w(AT, A/,T) (13)
By utilizing the same procedures as above, it can
be shown that Equations 11 and 12 will result.
In this case the fluxes and forces are defined as
Flux = Q= ( 1/2 w) . and Force= AT (14)
\i AT M
Flux = M = 1/2 aw and Force = Ar (15)
Ti
In the paper by Sliepcevich and Finn9 the fluxes
and forces were defined in the above manner. It
can also be shown that these definitions are equiv
alent to those of Onsager.***
Similarly, Equations 16 and 17 could have
been used as starting points.
***In reality, the definitions of the fluxes and forces
as given by Equations 14 and 15 are more consistent with
the treatment of the Onsager coordinates in the bilinear
form of the entropy equation as intensive, rather than ex
tensive, variables.
Ti )
(16)
(17)
or 1w = lw(AT, M)
to obtain Equations 11 and 12.
Of the four possibilities, Equations 4, 13, 16
and 17, Equation 17 would represent the most
logical choice since AT and M are the quantities
that can be measured directly.
CONCLUSION
IT IS SUBMITTED that the foregoing macro
scopic approach constitutes a valid derivation
of the Onsager reciprocal relations without re
course to the theorem of microscopic reversibility.
Recent experimental evidence has caused some
physicists to question the validity of the time re
versal invariance principle on which the theorem
of microscopic reversibility is based. Notwith
standing, the assumptions and postulates for the
macroscopic derivation presented herein are
Dr. C. M. Sliepcevich is George Lynn Cross Research
Professor at the University of Oklahoma. He was edu
cated at the University of Michigan (PhD '48) and has
taught at the University of Oklahoma since 1955. He has
received many awards for outstanding contributions to
research and teaching in engineering and in 1967 won the
University of Michigan Sequicentennial Award for dis
tinguished alumni.
Dr. Sliepcevich's interests include thermodynamics, re
action kinetics and catalysis, high pressure design, energy
scattering, process dynamics, cryogenics, and flame dy
namics. (Photo on left).
Dr. H. T. Hashemi is a consulting engineer and vice
president of University Engineers, Inc., Norman, Okla
homa. He was educated at Abadan Technical Institute,
Tulsa University, and University of Oklahoma (PhD '65).
His interests include the fields of cryogenic processing
and storage, hydrodynamics, thermodynamics, secondary
recovery of petroleum, and soil mechanics. (Photo on
right).
CHEMICAL ENGINEERING EDUCATION
1W = 1'�
equally tenable to those involved in the micro
scopic derivation since both are consistent with
empirical observations on related physical phe
nomena.
The principal result of the Onsager develop
ment is that the reciprocal relations, derived by
application of the theorem of microscopic re
versibility, permit a direct comparison of fluxes
and forces with physically, identifiable quanti
ties. On the other hand, the macroscopic deriva
tion presented herein achieves the same result by
virtue of the fact that dlw and dlw can be treated
as exact differentials for the conditions under
which the equations of irreversible thermody
namics hold and to the extent that the funda
mental laws of classical macroscopic thermody
namics are valid. In other words, since the lost
work is already known a priori to be path inde
pendent (when no work is done at any stage of
the process) no new information is gained by re
sorting to the theorem of microscopic reversi
bility.
ACKNOWLEDGMENT
The criticisms of F. Andrews and F. Mixon
were invaluable. This work was supported in
part by the Air Force Office of Scientific Re
search, Grant AFAFOSR56365.
REFERENCES
1. Andrews, F. C., Ind. and Eng. Chem. Fund. 6, 48,
1967.
2. Bearman, R. J. and Crawford, J. G., J. Chem. Phys.
28, 136, 1958.
3. Coleman, B. D. and Truesdell, C., J. Chem. Phys.
33, 28, 1960.
4. deGroot, S. R. and Mazur, P., Non Equilibrium
Thermodynamics, Chapter XV, Interscience Publishers,
Inc., New York, 1962.
5. Kirkwood, J. G. and Crawford, B., Jr., J. Phys.
Chem. 56, 1048, 1952.
6. Martin, J. J. "The Symmetrical Fundamental Prop
erty Relations of Thermodynamics," Presented at the
San Francisco meeting of the American Institute of
Chemical Engineers, May 1965.
7. Onsager, L., Phys. Rev. 37, 405, 1931; 38, 2265, 1931.
8. Sliepcevich, C. M. and Finn, D. in Chemical Engi
neers' Handbook, 4th ed., pp. 442, 444, and 469, McGraw
Hill Book Co., Inc., New York, 1963.
9. Sliepcevich, C. M. and Finn, D., Ind. Eng. Chem.
Fund, 2, 249, 1963.
10. Sliepcevich, C. M., Finn, D., Hashemi, H., and
Heymann, M., Ind. Eng. Chem. Fund. 3, 276, 1964.
11. Sliepcevich, C. M. and Hashemi, H. T. "Recipro
cal Relations in Irreversible Processes." Presented at the
Philadelphia meeting of the American Institute of Chemi
cal Engineers, December 1965.
12. Wei, James, Ind. and Eng. Chem. 58, 55, 1966.
APPROACHES TO
STATISTICAL
THERMODYNAMICS*
M. V. SUSSMAN
Tufts University
Medford, Mass.
Statistical thermodynamics connects classical
thermodynamics which describes the energetic
interactions of macroscopic systems with the
properties of the microscopic or molecular con
stituents of a system. The connection expands
the application of thermodynamics to extreme
temperature, solid state, thermoelectric, and
other phenomena. It permits derivation of equa
tions of state, and calculation of thermodynamic
properties from spectroscopic data. It provides
insights to many thermodynamic properties, par
ticularly the entropy. Like many other worth
while goals, statistical thermodynamics may be
approached in a number of ways. The various
approaches each have their strong proponents and
detractors and the selection of an approach is
often a subjective decision reflecting the user's
mathematical sophistication, epistemological phi
losophy and teacher's prejudice.
My purpose here is to outline the more com
mon approaches to statistical thermodynamics,
necessarily in qualitative terms and with more
emphasis on the similarities than the differences.
My point of view is summarized by the mountain
scape sketched in Fig. 1. In the brief time avail
able I will run you over the various trails, passes
and pathways which have been used to connect
microscopic to macroscopic thermodynamic ba
havior.
*Presented at the Annual Meeting of ASEE, June
1922, 1967.
SUMMER, 1968
Statement of Basic Problem
All approaches to the problem start from the
following common ground.
1. Recognition that every macroscopic system has
a fantastically detailed microscopic structure, and that
the existence of this micro structure makes possible
an astronomically large number of different arrange
ments of the microscopic elements (quantum states)
which are completely consistent with the macroscopic
system's properties.
2. A realization that there is no way of knowing
which arrangement or state actually represents the
system and therefore, all (or a most representative
portion of) the possible microstates must be con
sidered in determining the system's properties.
The basic problem of statistical thermody
namics is therefore the assignment of a weight
(a probability) to each possible microstate which
reflects its contribution to the properties of the
macroscopic system.
It is in the rationalization of the averaging
technique, that is, in the derivation of the func
tion (called a "distribution" function) assigning
weight or probability to each micro state, that
a variety of approaches are used. All approaches
arrive at essentially the same result: For a
closed constantvolume system in equilibrium
with a heat bath the probability of the i'th micro
state is equal to
1
Pi  exp / Ei (1)
where E, is the energy of state i and P and Z are
constants of the equilibrium system.
The sum of all the probabilities = 1, and
therefore
1
2 Pi = 1 = i exp  /E,
Z =  , exp  /E, (2)
Z is called the "partition function," or "sum
over states."
/3 is shown to be 1/kT.
The expected energy of the macroscopic system
is equal to:
CHEMICAL ENGINEERING EDUCATION
(E) = Z(3)
and the entropy of the system is equal to
S =  kIPi In P, (4)
(or S = k In W) (5)
From here the expressions of classical thermo
dynamics are obtained by straightforward, unso
phisticated mathematical techniques.
Ensemble of States
Let us now explore the Fig. 1 mountain be
ginning at its basethe concept of an ensemble
of all possible microscopic states of a macroscopic
system. In quantum mechanics, the Schr6dinger
equation specifies the possible discrete macro
scopic or quantum states of a system. The totali
ty of these states is the quantum mechanical
representation of the ensemble. An alternate and
older view of the ensemble is provided by classical
mechanics where a many dimensional hyperspace
is used to chart the total spectrum of mechanical
states of all the microscopic constituents of the
system that are consistent with the macroscopic
knowledge about the system. This hyperspace is
called the "phase space" of the system.
Having set up the ensemble of all possible
states in either quantum mechanical or classical
mechanical terms, it becomes necessary to con
nect the ensemble to the macroscopic system of
interest. The connection is made in the ways indi
cated in Fig. 1.
QuasiErgodic Hypothesis
The average properties of an ensemble are re
lated to the properties of a given macroscopic
system by making an assumption about the actual
mechanical behavior of the macroscopic system,
viz:
A property measurement (for example pres
sure) made on a macroscopic system is a time
average property measurement rather than an in
stantaneous property measurement. The measure
ment time is long on a microscopic scale and with
in the measurement time interval the system
visits (or comes arbitrarily close to) all points in
the phase space of the ensemble. It therefore fol
lows that a time average property of a macro
system is the same as an ensemble average prop
erty.
condition '"
n2= I
En.= 4
Znei . 3+2=5
S= =4
w 3111 =4
condition "B"
n,=i
n2
no= 2
 n.=4
Y n.E4 = 5
W = 4! 12
b 2! I I!
E=3
3
E=3
3
Figure 2.Most likely "condition." Condition "B" is more
likely than condition "A" because Wb > Wa.
The validity of the ergodic hypothesis is ques
tionable particularly because systems can be
imagined where the hypothesis does not hold; for
example, an ideal gas in a rigid parallel wall con
tainer whose particles are so arranged as to move
perpendicular to the parallel faces of the con
tainer, and in such a manner that no collision oc
curs between the particles. This system would not
visit all regions of phase space, that is go through
all configurations of its particles' positions and
velocities consistent with the total energy of the
system.
Equal APriori Probabilities
Another method of connecting the ensemble
to the macrosystem of interest is to assign equal
statistical weight or probability to all equal micro
states of the ensemble. This is a reasonable as
sumption because knowing only the energy of the
system, we have no basis for choosing one micro
state over any other microstate having the same
energy. The system has an equal likelihood of
being in all such microstates. Therefore, its
average property is the average over all the
equally likely states.
A corollary of this approach is that the prob
ability of a microstate is a function of the energy
of that state only, that is,
SUMMER, 1968
P 2
i 'a
ZP = 7P
'a lb
Figure 3.Moment of a distribution.
Pi = f (Energy of state i) (7)
The third way of connecting an ensemble to
the system of interest indicated in Fig. 1 is the
information theory approach which implicitly
agrees with the equal probability assumption, al
though it does not make the assumption explicitly.
More will be said about this later.
True Ensemble Average
We now turn to the trails ascending from our
base camp to the "distribution function" (Fig.
1).
Given that ensemble average properties are
the same as the macroscopic properties of a sys
tem, the system property (M) is found by inte
grating over phase space
M f p(p,q,t) M(p,q) dpdq (8)
where p and q are the generalized coordinates of
phase space; t is time and p is a density function
which gives the probability of finding a state
point in any unit volume of phase space. A
mathematical theorem due to Liouville is then
used to show that the density function is inde
pendent of time
dp/dt = 0
if p is a constant or a function of the energy of
the entire system. (When this condition prevails
the ensemble is said to be in statistical equi
librium). A suitable function is p = exp 
(X + PE) which leads to the conclusion that the
probability of a state is proportional to exponen
tial (PEstate).
This is the route taken by the professional
statistical mechanician. It requires considerable
mathematical sophistication. It is thorough, ele
gant, rigorous, and generally unsuitable for pre
senting the useful concepts of statistical thermo
dynamics to undergraduates.
Most likely "Condition"
An alternate route to the "distribution func
tion" I have called the "most likely condition." It
is supposed to be a short cut since it attempts to
evaluate the average property of an esemble, not
by covering all states in the ensemble, but only
the most likely states, as represented by the most
likely "condition." The "condition" of a system
is the set of occupancy numbers (ni) which
designate the number of microscopic particles in
each of the energy levels accessible to a system's
particles. For example, Fig. 2 shows a system
which has only four particles. The "acondition"
of that system is given by the set of occupancy
numbers (n) ; ni = 3; n, = 1. The sum of the
ni is equal to the total number of particles in
the system, in this case 4; and the energy of
the system is equal to
E = ni Ei = (3 x 1) + (1x 2) = 5 energy
units
Now, three 1energy unit particles and one 2en
ergy unit particle can be permuted in 4!/3!1! =
4 ways. (The general rule for the number of per
mutations of N total objects where N is equal to
nni; is W N!/Trni!) Condition "b", given by
n, = 1, n, = 1, no = 2, allows for 12 accomoda
tions or permutations. Therefore, if we were
betting on condition "a" or "b" we would put
our money on "b" as the more likely "condition."
Quite clearly, the most likely "condition" of
any system is that set of ni's (consistent with the
system's energy) which produces the maximum
number of permutations. It can be shown that
as the number of particles becomes very large
the likelihood of any condition other than the
most likely condition becomes very small. There
fore, the ensemble as a whole can be described
with reasonable accuracy in terms of its most
likely "condition" and the set of ni's that cor
respond to that most likely condition is simply
found by maximizing the number of permuta
tions W or In W taking into account the fact that
Xni = N and Y ni Ei = Et. This technique if fol
lowed carefully, and if certain pitfalls are
avoided, eventually leads to an expression for the
partition function of a multiparticle system in
CHEMICAL ENGINEERING EDUCATION
terms of the allowed energy levels of its consti
tuent particles. The pitfalls and somewhat odd
rationalizations* used to arrive at this final result
offset the shortcut promised by averaging over
the most likely condition rather than over the en
tire ensemble. In this approach S = kln W.
Mathematical Necessity
Using the equal apriori probability assump
tion, the probability of a state is a function only
of its energy (see eq. 7). If we have two systems
at equilibrium with a thermostatic bath whose
size is such that fluctuations of the energy of one
system will have no effect on the energy of the
bath or the energy of the other system, then we
can state
Pi =f(Ei) (7)
Pj = f (E,) (9)
where Ei represents an allowed energy state of the
first system and Ej represents an allowed energy
state of the second system. Now, considering both
systems together, the probability of the first sys
tem being at Ei and the second system at Ej must
be
Piandj = f(Ei + E) =Pi P (10)
therefore f(Ei+ Ej) = f(Ei) f (E,) (11)
The only function satisfying (11) is an expo
nential
1
Therefore Pi = f(Ei) = exp PEi (1)
and we are again at the top of the mountain. A
mathematical consequence of (1) and the classi
cal definition of entropy is that S, can be shown
to be equal to S = klPi In Pi (13)
This is the approach taken by Denbigh,2 An
drews,1 and others. It is straightforward enough
to be taught to undergraduates, requiring only
acceptance of the fact of the existence of a multi
tude of quantum states and the assumption of the
equal probability of equal energy quantum states.
A maximization computation is avoided.
Information Theory Approach
The Information Theory approach, while us
ing exactly the same mathematical forms estab
lished in the older statistical thermodynamic
literature, has a somewhat different philosophical
or logical orientation. It states that statistical
*Particles are assumed to be distinguishable. Also,
Stirlings approximation, In n! = n In n  n, is used.
thermodynamics is not a physical theory whose
validity depends either on the truth of additional
basic assumptions, such as ergodic behavior or
equal probability, or on experimental verification.
It is instead a form of statistical inference; a
technique for making the best estimates on the
basis of incomplete information. If experiment
al verification is not obtained this is not a short
coming of the statistical thermodynamics, but of
the information supplied.
The relationship S = kPPi In Pi (13)
occupies the primal position in this approach. The
equation is the basic equation of Shannon's
"Mathematical Theory of Information" and is
identified with thermodynamic entropy. Maxi
mizing (13) subject to the constraints that
Pi = 1, (The system must be in some state)
and ZPiEi = E; (The system has energy (E))
leads immediately to
1
Pi =  exp P8Ei
Z
It is the contention of the information theo
rists that maximizing P In P subject to con
straints produces the least biased distribution of
probabilities; a distribution which is maximally
noncommital with regard to missing informa
tion.
An identical technique using a different ra
tionale was suggested by Pauli who showed that
the distribution functions are obtained by mini
mizing the Boltzmann H function
H = PPi In Pi
subject to constraints. The latter technique is
discussed in detail by Tolman.3 Taking $ P In P
to an extremum is not a new idea. The "informa
tion theorists" however give it new importance by
insisting that it is the most fundamental ap
proach to statistical mechanics, because evaluat
ing the Pi is a problem in guessing (i.e., statistics)
and not physics, and therefore there need be no
further concern with Ergodicity or Equiproba
bility and their justification.
From an undergraduate teaching point of
view, the information theory approach is almost
as simple as the previously mentioned mathemati
cal necessity approach. The student is asked to
accept, without proof, the axiom that maximizing
S subject to the known properties of a system
produces a minimally biased set of Pi's. The
mathematics of maximization are reasonably
straightforward. The trouble with the axiom is
that it does not relate to much in the undergradu
SUMMER, 1968
ate's experience whereas other thermodynamic
and mathematical axioms usually have some in
tuitive acceptability.
Smoothing Function
A way of making the axiom more acceptable
is to demonstrate qualitatively that maximiz
ing Pi In Pi or minimizing +PPi In P is a
smoothing operation which tends to minimize the
"moment" (lower the center of gravity) of a plot
of Pi vs. i.
As qualitative example, assume that we have
a system which is capable of existing in a great
number of possible states, and we are asked to
arbitrarily assign probabilities to each of these
states. The states can be ordered in a sequence,
and indexed by an integral subscript i. Assume
that all we know about this system is that it
must be in some state Pi. In Fig. 3, line b is an
arbitrarily assigned distribution for this system
which is constrained only by the fact that the
sum of the ordinates equals unity, that is IPi = 1.
This is not an unbiased distribution because I
have put maxima and minima in this distribution,
that is, I have given some states more weight
than others, without information that would jus
tify so doing. The relative smoothness of the
arbitrary curve in Fig. 3, can be represented by
the mathematical index
EPi2 (14)
which evaluates the "moment" of the distribution
about the horizontal axis. The "moment" in
creases as the magnitude of the singularities or
extrema in the system increase, and conversely,
decreases as the center of gravity of the distribu
tion drops, that is, as the curve becomes more
uniformly smooth. In fact, it is a straightfor
ward exercise in calculus of variation to show
that the minimum "moment" corresponds to line
"a," a constant value of Pi which is certainly the
smoothest possible curve. If, in the smoothness
index, (Eq. 14) we replace one Pi with a mono
tonic function of Pi, that is ln Pi, we should ex
pect similar behavior. In other words, the effect
of maximizing Pi In Pi is to smooth out our
distribution. The advantage of the logarithmic
function is that it allows expressing S as a func
tion of the probability of the microstates, and it
prevents Pi from taking on negative values.
Allow me to end with a speculative aside.
Maximizing entropy smooths a distribution. This
suggests to me that it might be possible to re
state the principle in terms of geodesics. I say
this because I would assume that a maximally
smooth curve should have a minimum arc length.
I have tried using a criterion of "minimum
arc length' to find a distribution function, har
boring secret hopes that the criterion would lead
to Pi In Pi and even more general expressions
for new entropies. I regret that I've not been suc
cessful. The geodesic idea (that an unbiased dis
tribution has minimum arc length) nevertheless
continues to intrigue me and I would welcome
thoughts of others on how to work it into a
selection formalism.
References
1. Andrews, F. C., "Equilibrium Statistical Mechan
ics," John Wiley & Sons, Inc., 1963.
2. Denbigh, K., "The Principles of Chemical Equi
librium," Cambridge University Press, 1961.
3. Tolman, R. C., "The Principles of Statistical Me
chanics," Oxford University Press, 1942.
Dr. M. V. Sussman is Professor of Chemical Engi
neering and Department Chairman at Tufts University
and is presently on leave with NSF in New Delhi working
on an Indian Engineering Education program. In August
he will be an NIH Fellow at the Weizmann Institute
studying biological thermodynamics and mechanochemis
try. Dr. Sussman has degrees from City College of New
York (BChE) and Columbia University (MS and PhD).
Thermodynamics is a compulsive hobby with him and some
of the ideas expressed in this article will appear in a
book to be published by Wiley.
Join THE AMERICAN SOCIETY FOR
ENGINEERING EDUCATION
and Receive
CHEMICAL ENGINEERING EDUCATION
W. Leighton Collins, Executive Secretary
The American Society for Engineering Education
2100 Pennsylvania Avenue, North West
Washington, D. C. 20037
Dear Mr. Collins,
Please send me an ASEE application blank
I would like to join the Chemical Engineering
Division.
Name ..
A d dress .. ...... ...............
                               
CHEMICAL ENGINEERING EDUCATION
The world of Union Oil
salutes the world
of chemical engineering
We at Union Oil are particularly indebted to the colleges
and universities which educate chemical engineers.
Because their graduates are the scientists who contribute
immeasurably to the position Union enjoys today:
The twentysixth largest manufacturing company in
the United States, with operations throughout
the world.
Union today explores for and produces oil and natural gas
in such distant places as the Persian Gulf and Alaska's
Cook Inlet. We market petroleum products and petro
chemicals throughout the free world.
Our research scientists are constantly discovering new
ways to do things better. In fact, we have been granted
more than 2,700 U.S. patents.
We and our many subsidiaries are engaged in such
diverse projects as developing new refining processes,
developing new fertilizers to increase the food yield, and
the conservation of air and water.
Today, Union Oil's growth is dynamic.
Tomorrow will be even more stimulating.
Thanks largely to people who join us from leading
institutions of learning.
If you enjoy working in an atmosphere of imagination and
challenge, why not look into the world of Union Oil?
Growth...with innovation. Union Oil Company of California.
unitn
SUMMER, 1968
The New Stoichiometry*
EDWARD M. ROSEN COMPUTER AIDED CHEMICAL PROCESS
Monsanto Company DESIGN SYSTEM
St. Louis, Missouri I
PROCESS PHYSICAL MATERIAL &
ERNEST J. HENLEY LANGUAGE PROPERTIES MODELS ENERGY BAL. COSTING
University of Houston
Houston, Texas Fig. 1.Elements in computer aided chemical process
Houston, Texas design systems.
In May of this year we sent a questionnaire
to all AIChE accredited schools to determine the
subject matter now included in stoichiometry or
the equivalent first course in chemical engineer
ing. The replies to this questionnaire indicate
quite clearly that 1) the overwhelming majority
of the courses are still in the mold cast by Hougen
and Watson in the 1940's, and 2) there is a cer
tain amount of experimentation, dealing mostly
with the introduction of computer techniques into
the curriculum.
This introduction of computing techniques
into material and energy balance courses must
ultimately give rise to what we call 'the new
stoichiometry.' The new stoichiometry, in turn,
will form the foundation for the computer aided
design and simulation courses which we expect
will find a place in all chemical engineering cur
riculums within a decade. It seems appropriate
to examine first, therefore, the elements of a
computer aided design system.
Table I is a partial listing of computer aided
chemical design systems. Of the industry pro
grams, the CHEOPS is considered by many to be
the grandfather because of the wide publicity it
received in the early 1960's. The CHEVRON
program, which is oriented towards hydrocar
bons, has been made operational at the Univer
sity of California, Berkeley. The PEDLAN pro
gram is one of the first to be written in a problem
oriented language and requires a Fortran pre
compiler.
The CHIPS, KELLOGG, PECOS, and UOS
programs are available through service com
panies, as is PACER, which was originally de
veloped at Purdue and Dartmouth. The CHESS
program is in operation at the University of
*Presented at the Annual Meeting of ASEE, June 17
20, 1968.
Houston, and its capability is now being greatly
extended with help of a Themis grant, ONR
Contract N001468A0151. SLED, under devel
opment at Michigan, is analogous to PEDLAN in
Table I. Computer Aided Chemical Process Design
Systems*
Industry
CHEOPSChemical Engineering Optimization Sys
tem, Shell Oil
CHEVRONGeneral Heat and Material Balancing
Program, CHEVRON Research Company
PEDLANProcess Engineering Design Language, Mo
bil Oil Company
Service Companies
CHIPSChemical Engineering Information Processing
System, IBM Service Bureau
KELLOGG Flexible FlowsheetM. W. Kellogg
PECOSBechtel Company
UOSUnit Operations Simulator, Bonner and Moore
(Fluor Company)
Education Institutions
CHESSChemical Engineering System Simulator
University of Houston
MAEBEMaterial and Energy Balance Execution,
University of Tennessee
PACERProcess and Case Evaluator Routine,
Dartmouth
SLEDSimplified Language for Engineering Design,
University of Michigan
SPEEDUPSimulation Program for the Economic
Evaluation and Design of Unsteady State Processes,
Imperial College
that it utilizes a problem oriented language.
MAEBE is a first generation material and energy
balance program, and SPEEDUP is not fully im
plemented.
If a stochiometry course is to serve as a pre
cursor to a computer aided design course, we must
analyze the design system in terms of its com
*A complete tabulation and discussion of computer
aided design systems is given by Evans, Stewart, and
Sprague, CEP, Vol. 64, No. 4, 1968.
CHEMICAL ENGINEERING JOURNAL
L
LEVEL 5: MASTER EXEC. CONTROL
LEVEL 4: SPECIAL SUBEXEC. PROGS.
LEVEL 3: UNIT OP'NS
LE VEL 2:
THERMO CALCS.
1� LEVEL 1:
PHYSICAL
S,$ PROPERTIES
Fig. 2.Building blocks in a preliminary design and capital cost system for
fractionating columns.
ponent parts to see what fundamental principles
are involved. Figure I shows the five component
parts:
1. The process language which converts the language
of the engineer to that of the computer
2. The physical property package which generates the
necessary information regarding transport, PvT,
and thermodynamic properties
3. The mathematical representation of the building
blocks (transfer functions, if you will)
4. The material and energy balance 'executive program'
which links the building blocks
5. Costing programs, which may include some sort of
optimization program.
In Figure 2 we see a more detailed breakdown
of the blocks in Figure 1 as they are used in the
design of a fractionation column. On the lowest
level we have the physical property tables or
equations. These are really a part of a system
which includes subroutines to produce enthalpy
values, equilibrium constants, etc.
Next there is a second level of thermodynamic
calculations which use the lower level physical
property programs. Dew point, bubble point, and
flash programs are the examples cited.
On the third tier we have the transfer func
tions for the building blocks; the mathematical
representation of the classic unit operations. The
level four function ties together the block of pro
grams comprising the fractionation system, and
overseeing the whole conglomeration of subpro
grams which comprise the bottom four levels we
have an executive control program which takes
into consideration all input and output format and
everything else that goes into a well formulated
system.
If one of the objectives of the 'new stoichio
metry' is to train a student to create and use
computer aided design systems, it is necessary to
define the topics which must be included. In
Figure 3 we define the five building blocks for
the new stoichiometry.
We have (1) thermodynamics and (2) classi
cal stochiometry; these two blocks together form
the manual method block in the 'HougenWatson
mold.' The other three elements, (3) linear alge
bra, (4) solution of equations, and (5) algorithm
development, together with (1) and (2) are the
required building blocks for machine method cal
culations. The remainder of this paper details the
material in building blocks (3), (4), and (5).
The examples used are from our forthcoming
book "Material and Energy Balance Computa
tion," John Wiley (June 1968).
SUMMER, 1968
Fig. 3.Elements of the new stoichiometry.
Linear algebra, in the words of Rutherford
Aris, "is the proper language of stoichiometry."
Indeed, linear algebra is the only type of algebra
digital computers can do; they cannot handle non
linear problems. Consider, for example, Gibb's
Rule of Stoichiometry, Figure 4. It states that
the maximum number of linearly independent
chemical reactions in a set of reactions is equal
to the number of chemical species known (from
experiment) to be present, minus the rank of the
atom matrix. The atom matrix for a five com
ponent mixture consisting of CO, H2, CHSOH,
CO2, andHO is shown in Figure 5, where the
rows are the species and the columns the atoms.
The determination of the rank of this matrix is
an exercise in linear algebra. A classic technique
for determining the rank of a matrix is the Gram
Schmidt method where we attempt to construct a
set of m orthogonal vectors, Y1, Y,, .. . Y, from
X1, X,, . . . X.. If the length of a Y vector is
zero, then orthogonalization is impossible, and
the X vector is parallel to one of the others. The
procedure is shown in Figure 6: the rank of the
atom matrix in Figure 5 is three. Thus, accord
ing to the Gibb's Rule of Stoichiometry, there
are are two independent reactions.
Taking the two reactions shown in Figure 7
as the independent reactions, we construct the
reaction matrix in Figure 7. The rows are the
species; the columns the stoichiometric coeffi
cients for reactions (1) and (2). The matrix
formulations of the material balance lead logi
cally and simply to the elegant statement for the
MAX. NUMBER OF \ NUMBER RANK OF THE)
LINEARLY INDEPEN = OF  ATOM
DENT REACTIONS \SPECIES MATRIX
4 = N 
Fig. 4.Gibbs rule of stoichiometry.
conservation of atoms shown in Figure 8. The
product of the transpose of the reaction matrix
times the atom matrix must be zero. We hope
that this example is a convincing demonstration
of Aris' axiom.
Next we consider the nature and function of
block four, the solution of nonlinear equations.
In the isothermal flash vaporization shown in
Figure 9, fH(a) and fR(a) are two valid and
identical solutions of the material balances. In
these equations a = L/V and Ki  yi /xi. Since zi,
the feed composition is known, and K is known,
ATOMS
SPECIE C 0 H
CO 1 1 0
H2 0 0 2
CH OH 1 1 4
CO2 1 2 0
H 20 0 1 2
Fig. 5.Atom matrix for a five component system,
example 1.
GIVEN: XI, X2, ... XM
Y1 = X1
1 1
Y X Y1X
2 2 Y'* Y 1
I
Y X YM 1 X
SM MI YM_
Y  "
Mi ...
 (Y : Y
Fig. 6.The GramSchmidt procedure for example 1.
Rank, R = 3.
CHEMICAL ENGINEERING EDUCATION
REACTION
SPECIE 1 2
CO 1 1
H2 2 1
CH3OH 1
CO2 1
HO 1
2 0
M= 5 3= 2
CO + 2H2 =CH3OH (1)
CO2 + H2 = H20 + CO (2)
Fig. 7.Reaction matrix for two linearly independent
reactions.
these are simply nonlinear equations in one un
known, a. They can be solved readily by any
number of onedimensional, nonlinear root find
ing techniques.
In Figure 10 we have a plot of both fB(a)
and fII((a) vs. a. The root, at f.(a) = f.(a), has
been successfully found and is, as it should be,
identical for both equations. There are, however,
major differences in the shape of the curves, and
we see that the f,1 (a) function gives us two roots,
REACTION MATRIX ATOM MATRIX
1 2 1 0 0 1 1 0
0 0 2 =0
1 1 0 1 1 1 1 4
1 2 0
%0 1 2!
Fig. 8.The conservation of atoms.
one of which is spurious. Clearly, if we are to
avoid such pitfalls we can not blindly set up and
solve material and energy balances and feed the
resulting equations to a computer.
In this 'onedimensional' example we had only
one nonlinear equation to deal with. Let us now
examine the multidimensional set of equations
F z
Fzi = Vy. + Lx.
BY REARRANGEMENT:
N N
SV z.K.
i= 1i 1 + a(K
i R
N N N
Sx. L y =
i=l i=l i=l
V Yi
L x
I
 . = fH( )
d1)  1. fR(a)
zi(1  Ki)
1 + a(Ki 1) fR)
1
Fig. 9.Isothermal flash equations, example 2.
which will arise from the flowsheet for the cata
lyting dehydrogenation of propane, Figure 11.
We note immediately that there are two recycle
streams, S12 and S2, which preclude a straight
through solution to the material and energy bal
ances.
f
H
Or
fR
BUBBLE
POINT
 ' ()
1. DEW
POINT
/ =_V
Fig. 10.Plot of functions fH (a) and f, (a) for
example 2.
One method of handling problems of this type
is by 'tearing' the flowsheet and estimating a
composition. If, for instance, we tear stream
S13 (between the stripper and absorber) and
guess at the composition for S7, we are able to
calculate all of the remaining process streams, S1
 S13, in the sequence S8, S12, S10, S11, S2, S3,
SUMMER, 1968
S4, S5, S9, S6, S13. If we have guessed the com
position S7 correctly, then S13 will equal S7. If
not, we have to reestimate S7 and try again.
This physical situation is given a mathemati
cal formulation in Figure 12. We estimate the
stream vector X, calculate the process vector
0(X) and if 0(X) equals X we are finished. If
not we pass through a convergence block which,
hopefully, will give us a new X which is a better
approximation to O(X). Since the X stands for
all unknown parameters of temperature, pressure,
compositions, and properties, it is apparent that
the solution of problems of this type are primarily
exercises in the solution of large sets of non
linear equations in many unknowns.
ABSORBER
FRESH
PROPANE
FEED
Sl S3 n S4 7 S5
The methods of the new stoichiometry provide
the tools for the development of useful algorithms,
which is building block five for the machine meth
ods. By useful algorithms we mean a well defined
set of statements that lead to the solution of a
problem. In order to obtain the output of any
building block as a function of the input to the
block, and hence to set up our design system, we
must have algorithms. Let us now see how we
would use our knowledge of thermodynamics and
nonlinear equation solving techniques to develop
PRODUCT
COLUMN
16
STRIPPER
13 S7 S10
., f PRODUCT
Fig. 11.Flowsheet for catalytic dehydrogenation of
propane to propylene, example 3.
The next block in our 'new stochiometry' is
a notsonew subject, thermodynamics. The rigor
ous formulation of material and energy balances
requires a deeper background in thermodynamics
than is now attempted in the majority of material
and energy balance courses. For example, if a
chemical reaction takes place thermodynamics
tells us that at equilibrium the stoichiometric co
efficient times the chemical potential equals zero
(Figure 13).
In terms of the reaction extent, e, the number
of moles of component i present at any time is
ni = nio + ale, where nio is the initial number
of moles. The final equation from which we cal
culate the composition of the reaction mix given
free energy data and the initial number of moles
is a nonlinear function in one unknown,
0(e) = 0. To obtain this equation we needed
thermodynamics.
ESTIMATED
STREAM
CALCULATED
STREAM
0(x)
FRESH PRODUCTS
FEEDS AND WASTE
S0 ) 0(X)  X = 0; X 10
Fig. 12.The convergence block as an equation solver.
an algorithm to calculate the composition of a
mixture in physical and chemical equilibrium.
CHEMICAL ENGINEERING EDUCATION
CONDITION OF EQUILIBRIUM AT T AND P IS
N
Z a.i. = 0
i=l
FOR IDEAL CONDITIONS
i. = Pi + RT In P.
1I 1
N
RT 2. In P
RT 1i i
1= 1
N
i=
i=l
0
(iXi
FOR: n. = n. + a. e
1 10 1
SOLVE: 0 (e) = 0
Fig. 13.Use of thermodynamics, example 4.
In Figure 14 we have a simple system in which
we have a flash vaporization plus a series of M
chemical reactions (j = 1 to j = M). There are
N components (i = 1 to i = N). The component
balances as well as the overall balance are shown
in Figure 14 and our final equation is shown in
Figure 15 in terms of Ki which, as before, is
yi/xi.
V yi
F z
I
If the temperature and pressure and the feed
composition zi are fixed, f(a) is one equation in
two unknowns, a and e. To solve the equation
we propose the algorithm shown in Figure 15.
We (1) estimate the e reaction extents, (2) solve
for a, (3) calculate the material balances, (4)
check to see if the equilibrium constant has been
satisfied. If it is not, we make a new estimate of
e and start again. The new estimate is usually
made using a Wegstein or similar convergence
forcing routine.
What we have tried to demonstrate in this
paper are (1) the techniques now being used by
industry in the formulation of computer aided
design and simulation systems and (2) how these
may be incorporated into existing stochiometry
courses to produce the 'new stoichiometry.'
BY REARRANGEMENT
M
z + F (I  Ki)
/ N M
1 a +  1ij
i=1 j=1
e) + K.a
1. ESTIMATE el, e2 ... eM
2. SOLVE FOR a
3. CALCULATE x. AND y. FROM RESULTS OF STEP 2
4. EVALUATE
RT  n K. = j 0(y)
J
j = 1, 2, ...M
Fig. 15.Suggested algorithm.
COMPONENT BALANCE
M
Fz. = Vy+ Lx.  a ej
j=l
OVERALL BALANCE
N M
F=V+LZ Z c.. ej
i=1 j=l
Fig. 14.Model of process.
Professor Henley is Associate Dean and Professor of
Chemical Engineering at the Cullen College of Engineer
ing, University of Houston. He received his BS from the
University of Delaware and an MS and Dr. Eng. Sci.
from Columbia University. He served on the faculty at
Columbia from 1953 to 1958, was associated with Stevens
Institute of Technology from 1958 to 1964, and from 1964
to 1966 was ChiefofParty of the AID mission at the
University of Brazil. He is the author of over 50 re
search papers, and five books, and is the editor of the
Advances in Nuclear Science and Engineering. He has
done extensive consulting for government and industry
and is a member of the Board of Directors of three pub
liclyheld corporations.
SUMMER, 1968
l laboratory
Ki 4ticb *
KENNETH B. BISCHOFF
The University of Texast
Austin, Texas
The background of the current extent
of chemical engineering kinetics laboratory
work is briefly discussed along with some
observations on laboratory operation. The
statistical results of a survey on this topic
are presented and indicate that although
many departments have laboratory work,
there are a number that do not. As an aid
to the introduction of more experiments,
a list of successfully used reactions is
given. Finally, a detailed example of an
experiment used at the University of Texas
is discussed.
It is realized that some type of formal chemi
cal engineering kinetics course is a vital part of
chemical engineering education. Utilizing the
aspects of applied chemistry through reactor de
sign is a unique feature which differentiates
chemical engineers from other engineers.
In the 1940's Hougen and Watson began to
systematically treat chemical reactor design,
which resulted in their wellknown textbook.
Even then, it was felt that this was essentially
graduate level material. It was not until the late
1950's that many chemical engineering depart
ments had undergraduate courses dealing with
reactor design. During the last decade this seems
to have changed in that now most departments
have some sort of undergraduate lecture course
in this area. Although the trend had started, the
Dynamic Objectives Report1 of AIChE, with its
recommendation that more emphasis be placed
upon the chemical content of the curriculum, un
doubtedly also had an effect.
In recent years with the introduction of
courses on transport phenomena, process dy
namics and control optimization, along with ki
*Presented at the annual meeting of ASEE, June 19
22, 1967.
tPresent address: Department of Chemical Engineer
ing, University of Maryland, College Park, Md.
Dr. Bischoff was educated at the Illinois Institute of
Technology. He has written many articles in the fields of
chemical reaction engineering and bioengineering and has
recently written a textbook (with D. M. Himmelblau) on
"Process Analysis and Simulation."
netics into the curriculum, the time available for
extensive laboratories has been steading decreas
ing.
The major aims of this paper will be to first
discuss what is currently done in the chemical
engineering departments of the U.S. and Canada
concerning chemical engineering kinetics labora
tories and to list some examples of chemical re
actions which could be used by other departments
to introduce kinetics experiments into their cur
riculum. The final part of the paper will describe
in detail an experiment used with success at the
University of Texas.
Survey of Chemical Engineering Kinetics
Laboratory Work
A survey of the North American departments
was conducted to obtain data on the extent of
chemical engineering kinetics laboratories. Re
TABLE I
Extent of Kinetics Laboratory Work*
Number of
Topic Departments
Separate chemical engineering kinetics 8
laboratory course and/or taught in con
junction with chemical engineering
kinetics lecture course.
Experiments in other chemical engi 41
neering laboratory courses.
No chemical engineering kinetics 28
experiments.
* Note: 76/145 replies were received.
CHEMICAL ENGINEERING EDUCATION
TABLE II.
Type of Chemical Reaction
Number of
Departments
Type
Homogeneous 38
Heterogeneous, noncatalytic 6
Catalytic 20
Reaction engineering/design study 16
plies were received from 76 of 145 surveys mailed.
The results are shown in Table I from which it
is seen that very few departments have either a
separate kinetics laboratory course or have one
taught in conjunction with the chemical engineer
ing kinetics lecture courses. These two categories
from the survey have been lumped together, since
there is not a clear distinction between them.
Most of the present work is designed as a part of
other existing laboratory cources. In other words,
the term "unit operations laboratory" quite often
seems to be something of a misnomer since things
other than this topic are studied. Thus, about
half of the replies indicated that they had some
work dealing with kinetics and, in fact, several
departments had more than one experiment of
this type.
Perhaps the most interesting figure in Table
I is the fact that 28 departments indicated that
they had essentially no work at all. This seeming
ly large lack does need some qualifications, since
most students do get some exposure to kinetics in
physical chemistry. However, it does seem that
chemical engineering kinetics laboratory experi
ence is lacking in a substantial fraction of chemi
cal engineering departments. Several depart
ments are presently in the process of adding ki
netics experiments, but many are not.
Table II indicates various types of reactions
that have been used for the laboratories. It can
be seen that the major emphasis has been with
homogeneous reactions, probably because they are
the easiest to perform and obtain consistent re
sults. Heterogeneous catalytic reactions are also
fairly extensively used, probably because of their
great practical interest. Very few noncatalytic
heterogeneous reactions were reported. The final
category of reaction engineering design study
seems to have a relatively small amount of work,
but this may be somewhat ambiguous. Many of
the homogeneous and heterogeneous reactions are
run for "engineering" purposes and could pos
TABLE III.
Examples of Reactions Used for Kinetics Experiments
Homogeneous
1. Ethyl acetate saponification
2. Acetic anhydride hydrolysis
3. Methyl acetate hydrolysis
4. Ethyl acetate hydrolysis
5. Acetone bromination
6. Isopropanol oxidation to acetone
7. Acetic acid + ethanol esterification
8. Benzaldehyde oxidation to benzoic acid
9. Permanganate reduction with dissolved hydrogen
10. Crystal violet hydrolysis
11. Methyl acetate saponification
12. Phthalic anhydride + butanol esterification
(pilot plant scale)
13. Ethylene glycol + periodate
14. Hydrogen peroxide + iodide (iodine clock
reaction)
15. Ethylenepropylene polymerization
16. Formaldehyde + methanol esterification
17. N.Ndimethylaniline + ethyl iodide (by DTA)
Heterogeneous, noncatalytic
1. Coke oxidation on cracking catalyst
2. Corrosion kinetics
3. Cyclohexane hydrogenation
4. Cu++H+ ion exchange
5. Cottonseed oil hydrogenation
6. Pyrolysis of plastics
Catalytic
1. Ammonia decomposition, iron oxide
2. Cumene cracking, silicaalumina
3. Ammonia oxidation, platinum gauze
4. Toluene hydrogenation, Raney nickel
5. Isopropanol (liq.) dehydrogenation, nickel
6. Propylene oxidation, copper oxide
7. Acetaldehyde decomposition, copper gauze
8. Benzene alkylation, acid catalyst
9. Propylene disproportionation to ethylene +
2butene, cobalt oxidemolybdenaalumina
10. Sulfur dioxide oxidation
11. nPropanol dehydrogenation
12. Cumene hydrogenation
13. Styrene hydrogenation
14. 1Hexanol dehydration
15. Catalytic cracking
16. Permanganate reduction with dissolved hydro
gen, Ag+
sibly be included here also. Many of the depart
ments out of the 16 indicated that an important
part of this topic was the use of analog or digital
computers to simulate chemical reactor operation.
Also, the various reactions were run in a variety
of reactors such as tubular, stirred tank, as well
as batch.
Table III presents a list of the actual chemi
cal reactions used, which might serve as an aid
to those who are trying to find proven reactions
for their own laboratories. The saponification of
ethyl acetate is the most popular reaction in use,
SUMMER, 1968
probably because of its good kinetic characteris
tics, the ease of measuring the results, and the
experiment devised by Kendall.2
Detailed Example
An example of a chemical engineering re
action kinetics experiment that has worked well
in our laboratories at the University of Texas is
ethyl acetate saponification in a tubular reactor.
Kendall2 has given a very complete discussion of
the system he developed to study the effects of
different flow patterns in the reactor. Our system
has many features in common with his but the
emphasis is somewhat different. A major aspect
of our system is to measure and interpret the ef
fects of nonplug flow in the liquid phase tubular
reactor and to interpret these results quantita
tively in terms of mathematical models.
The fact that the ethyl acetate saponification
is a very "clean" second order reaction with no
side reactions is given to the student as basic
data. The reaction is run in a Tygon tube of 0.615
cm diameter and 810 cm (35 feet) long, looped
through baffles in a section of glass pipe which
serves as a constant temperature water bath.
Gravity feed lines from bottles of ethly acetate
and sodium hydroxide are run through the con
stant temperature water feed tank to attain
reaction temperature and joined in a Y section at
the reactor tube entrance. Analysis of product
samples is by a simple titration method similar to
that described by Kendall. Electrical conductivity
methods were tried but did not work any better
and were somewhat more complicated than sim
ple titration.
In order to have high conversions of 5090%o
the reactor is run at a temperature of 100�F,
where the rate constant is 0.22 liter/gm mole
second, and with the feed concentrations of both
reactants Co = 0.2 gm mole/liter. Since nonplug
flow is most pronounced under laminar condi
tions, the flow rates range between Reynolds
numbers of 100 to 3000. A comparison of the
experimental data with theoretical predictions
from the axial dispersion model (see Levenspiel3)
is required, using the established correlations of
the axial dispersion coefficients.
Results of some of the recent student data
are shown in Figure 1. At the turbulent end of
the range, the plug flow equations give good
agreement with the experimental data. At the
lower flow rates, although there is quite a bit of
1.0
z
IO 0 PLUG FLOW
o 0
o o
DISPERSION MODEL
.5 ' obo oo
50 1000 2000
REYNOLDS NUMBER
Figure 1.Student data for ethyl acetate saponification
in a tubular reactor.
scatter, it is seen that the plug flow predictions
are not very good and the data approach the axial
dispersion model line. The data actually fall most
ly between the two predictions, but this may be
caused by the looped Tygon tube which would
lead to less effective axial dispersion than that
predicted by the correlations for straight tubes.
In any event, the experiment not only gives an
example of tubular plug flow reactor results but
also illustrates quantitatively the effects of non
plug flow.
Conclusions
The survey of chemical engineering kinetics
experiments indicated that many departments do
have some work in this area, but there are a large
number that do not. Very few departments have
separate kinetics laboratory or one taught in
conjunction with a lecture course.
In addition to the statistical information, the
survey produced a rather large selection of chemi
cal reactions that apparently have been success
fully used. These have been tabulated to help in
structors find experiments that might develop
their own laboratories. Finally, an example of
an experiment used at the University of Texas
was discussed in some detail and the types of
results than can be obtained in a student labora
tory were indicated.
REFERENCES
1. "Dynamic Objectives for Chemical Engineering,"
Chem. Eng. Prog. 57, (10), 69, 1961.
2. Kendall, H. B., in "Small Scale Equipment for
Chemical Engineering Laboratories," ed. R. N. Maddox,
Chem. Eng. Prog. Symp. Ser. No. 70, 63, 315, 1967.
3. Levenspiel, O., "Chemical Reaction Engineering,"
John Wiley and Sons, Inc., New York, 1962.
CHEMICAL ENGINEERING EDUCATION
classroom
Te'moaeSyifaics
View Programmed Instruction*
Wright State University
Dayton, Ohio 45431
The potential of programmed instruc
tion as an educational device is demonstra
ted by its present use in the classroom, in
dustrial training programs, the continuing
education program of the medical profes
.sion, and by the recent interest of several
large corporations who have entered the
education business with systems based on
programmed instruction. This paper de
scribes a set of thermodynamics programs
developed at Purdue University and ex
amines their potential from the viewpoint
of the student who used them, the teacher,
and the psychologist. Various aspects of
the design of these programs are examined
including linear versus branched style,
step size, concrete illustrations of abstract
concepts and perceptual organizers. The
programs and the textbook are compared
in terms of their ability to transmit in
formation to the student. The program is
described as psychologically superior be
cause it shapes behavior from the simple to
the complex and guides the student so he
avoids misconceptions which must be un
learned. Finally, the value of the programs
in freeing class time for more valuable ac
tivities is described.
If you asked Harvard psychologist B. F.
Skinner' what programmed instruction can do for
education he would reply, "What is now taught by
teacher, textbook, lecture, or film can be taught
in half the time ... by a teaching machine" using
programmed instruction. Before you dismiss
Skinner's claim you should carefully consider the
fact that RCA, IBM, GE, Westinghouse and
several other large corporations have recently
*Presented at the Annual Meeting of ASEE, June
1922, 1967.
staked a claim in the education business with sys
tems that involve programmed instruction ma
terials. In addition, many industrial firms al
ready use programmed instruction to teach basic
skills to their employees. And the medical pro
fession is using programmed instruction in a pro
gram of continuing education. While Skinner's
claim of a 50% gain may be a little unrealistic,
it should be clear that programmed instruction
has definite potential as an educational device. In
the discussion that follows I will examine this po
tential from three view points: that of the educa
tional psychologist who applies the theories of
psychology to the classroom; my own viewpoint
as a teacher who has written, experimented with
and used programs in my teaching over a period
of five years; and the viewpoint of the student
who has studied from my programs.
WHAT IS PROGRAMMED INSTRUCTION?
The concept of programmed instruction was
introduced by Skinner in 1954. Since that time
three methods of presentation and two different
styles have been developed. The three methods
are:
1. Computer assisted instruction: the student
operates a typewriter linked to the com
puter which contains the programmed ma
terial.
2. Teaching machines, any device which me
chanically controls the presentation of the
program to the student.
3. Programmed texts, which place the mater
ial in the hands of the student.
Each method has its advantages, but the pro
grammed text is basic to the other two. There
fore, this discussion will be limited to that meth
od.
SUMMER, 1968
The Student
The Teacher
The Psychologist
CHARLES E. WALES
The two program styles are called linear and
branched. Table I shows an example of a simple
linear program, a series of questions and answers.
To use this program the student covers the an
swer with a sheet of paper, reads the question
and thinks or writes his answer. He then un
covers the program answer and checks his work.
Table II shows a branched program. In this case
the student reads the question, selects one of the
given answers, and then checks his choice against
the answer given in the program. When he se
lects the correct answer he proceeds to the next
question.
Table I. Simple Linear Program.
Consider the open system, steady state process
shown below, mixing operation with salt and water.
TABLE II. Physical Material Balance Calculations
Two or more process units may be included in the
system chosen for a material balance calculation. For
example, Figure 8 shows two driers used in series
to remove water from salt. In this problem it is pos
sible to write material balances not only for each unit
but also for the pair of units combined
Figure 8
SH20 20
A  E 98% salt
18% H20 10% H20
82% salt 90Z salt
Section 1
Q. 1220 lbs/hr of wet salt (A) are supplied to the two
stage drier system shown in Figure 8. Assume steady
state operation. How many unknown flow rates are
there in this system:
Your A.
5 unknowns
5Q. How many flow rate unknows are there?
5A. Three flow rate unknowns: A, B, C.
6Q. How many composition unknowns?
6A. Six composition unknowns, two in each stream. The
total number of flow rate and composition unknowns
is 9.
7Q. What is the total number of material balance equa
tions that can be written?
7A. Three material balance equations can be written:
salt balance
water balance
stream balance
8Q. How many of these material balance equations are
independent?
8A. Two material balance equations are independent.
Program Versus Text
If you have had no previous personal contact
with programs your first question will probably
be, why a program instead of a text? The answer
to this question is provided by the psychologist
Ausubel2 who identifies the most crucial condition
affecting the acquisition and transfer of knowl
Section 2
A. 6 equations. No. You counted material balances around
unit 1 and unit 2. What about balances around both
units ?
Go to section 7.
Section 3
A. 4 independent equations. Correct. All the other equa
tions are dependent, they can be derived by adding or
subtracting the four independent equations.
Is it possible to solve a salt and a stream balance
around unit one, a stream balance around unit two,
and a stream balance around both units?
Your A.
Yes
No
See section 6
Section 4
A. 5 unknowns. Check the problem again, you probably
counted the flow rate of stream A as an unknown.
The flow rate of this stream is given and should be
used as the "basis" for your calculations.
Section 5
A. 9 equations. Correct. You can write a stream, salt,
and water balance around each unit and around both
units combined.
Now, how many of these equations are independent?
Your A.
4 equations
6
See section 3
8
CHEMICAL ENGINEERING EDUCATION
See section 4
7
9
Table II. (Continued)
Section 6
A. Your answer is yes. The correct answer is no. It is
impossible to get an answer if you use three equations
of the same kind (i.e., stream balances). Try it if
you have doubts.
Go to section 3.
Section 7
A. 4 unknowns. Correct. The unknowns are stream flow
rates B, C, D, and E. Streams B and D are pure
water so there are no composition unknowns in this
problem.
Next, what is the total number of equations that re
late these 4 unknown variables?
Your A.
4 equations
See section 10
Section 8
A. 6 independent equations. No. You have correctly
reasoned that not all three equations in one set (i.e.,
unit one) may be used. But it is also impossible to use
all three equations of one kind( i.e., salt balances).
Go to section 5.
Section 9
A. 8 unknowns. No. You have counted 4 composition
unknowns for the water streams which are pure water.
Go to section 1.
Section 10
A. 4 equations. No. You didn't read the question care
fully. What is the total number of equations you can
write for this system that involve the stream flow
rate unknowns?
Go to section 7.
edge as the internal logic and the organization
of the material. The usual text is logically sound
but psychologically incongruous because it segre
gates material by topic, does not clarify the re
lationship between topics, and presents material
at a uniform level of abstraction instead of build
ing from the simple to complex. As a result the
student treats meaningful material as if it were
rote in character. He memorizes formulas, learns
type problems, performs mechanical manipula
tions and both learning and retention are reduced.
By contrast, Ausbel identifies the program as
a psychologically correct device because it is con
structed around the basic organizing concepts of
the discipline and ideas are arranged sequentially
to build the hierarchial structure that matches the
way in which psychologists believe knowledge
is organized and stored in the human nervous
system. The method used to construct a program
illustrates Ausubel's point. First, the basic con
cepts of the course must be identified and or
ganized into a logical pattern. Second, a detailed
set of performance objectives such as those shown
in Table III are prepared for each concept. Then
the teacher begins the final step, the writing of
the questions and answers that will lead the stu
dent from the objectives he learned in the prev
ious program to the objectives of the new pro
gram. It is the combination of all these steps that
gives the program its great strength.
Table III. First Law of ThermodynamicsSummary*
A. State Properties (Q 13)
1. Define a state property: a property that depends
only on a point's location, not on the path used to
get there.
2. Name 5 state properties: P,T,V,U,H.
B. Path Properties (Q 412)
1. Define a path property: A property that depends
on the path used. Q and W are path properties.
2. Use a PV diagram to prove that W depends on the
path used.
C. First Law of Thermodynamics for a Closed System
(Q 1332)
1. State the first law of thermodynamics for a closed
system:
Q  W, = U2  U, = AU
2. Define internal energy
a. Q  W = AU for any closed system, any ma
terial.
b. AU = C,(T,  T1) for any ideal gas process
and for an isometric process for any material
which has a constant C,.
c. Units, BTU/lb mole or BTU/lb
d. Zero point, arbitrary
3. Apply the First Law to a Closed System
Ideal Gas Real Material
a. Closed Isothermal Process
Q  W, = U,  U Q  W, = U,  U,
= C,(T,  T,)
Q  W = 0 U = (P,T)
Q=W,
b. Closed Adiabatic Process
Q  W, = AU = CAT Q  W, = AU
W, = C,AT, for Q = 0.
R
+W,
+ ,
1 (TI  T2)
U = 0 (P,T)
+ PV  P2V2
Y1
*Part of the Performance Objectives for the program
on the first law.
SUMMER, 1968
By its Socratic form the program provides the
student with many of the best features of fine
tutorial instruction. The program shapes the stu
dent's understanding by establishing simple be
haviors which are gradually combined and modi
fied until they lead to the final performance ob
jectives which include both abstract concepts and
concrete applications.
Programs were the primary vehicle for trans
mitting information in the thermodynamics
course I taught at Purdue last semester. The stu
dents also had the regular text and they were told
which sections of the text they should study. At
the end of the semester they were given a ques
tionnaire which asked, "If you had to choose
between good programs or a good text as the
basis for study in a class, which would prefer?
Some of their anonymous replies were:
"The program, you can understand it rather
than memorize it."
"In a program a person can usually tell which
points he did not understand, whereas in a text
he may not understand the whole material."
"The program, it forces you to stop and
think and not just read, I tend to read over things
in a text."
As you can see, the students identified many
of the factors predicted by the psychologists. In
all, twentyfive students preferred the program
while three preferred the text. One of those who
picked the text gave the following reason. "I
would probably choose a good text because that
is more familiar, but I never read a text that left
me with as clear an understanding of the subject
as the programs did." Because the material in
the programs is not exactly the same as that in
the text I asked the students the additional ques
tion, Would you have preferred to have the ma
terial in the programs written in text form with
out the questions and answers?" Twentysix re
plied no; two were undecided.
Linear or Branched Programs
As he creates the program, the teacher must
make many decisions. First he must choose the
style of the program, either linear or branched.
The linear style was chosen for my thermody
namics material because it provides the most di
rect control of the shaping process. In addition,
the linear program makes the student a more ac
tive learner. To answer each question he must
reformulate the material in terms of his own vo
cabulary, background and structure of ideas. Ac
Table IV. First Law of ThermodynamicsSelf Quiz*
7. The flow work terms do not appear in the equation
Q  Wo = AH, the first law of thermodynamics for
an open system. Does one of the terms in this equa
tion include the flow work energy? If so which one?
a. Q
b. W,
c. AH
d. none of the above
7a. The term Q accounts for the energy transferred to or
from the system as heat. Flow work is not included
in this term. Return to question No. 7.
7b. The term W. accounts for the energy transferred to
or from the system as shaft work. Flow work occurs
when a stream crosses the boundary of a system.
Some of the flow work energy may be converted to
shaft work in a given process but the two types of
work energy are not directly related. Reread the pro
gram from just after A31 to Q33, then return to
question No. 7.
7c. This answer is correct. The flow work is accounted
for by the enthalpy H = U + PV. The terms U and
PV are added because U represents the energy car
ried by a stream that enters (or leaves) and PV
represents the flow work done at the boundary when
that stream enters (or leaves) the system.
7d. This answer is not correct. In an open system, flow
work occurs whenever a stream enters or leaves the
system. One of the terms in the first law must ac
count for this energy. Reread the program from just
after A31 to Q33, then return to question No. 7.
*Sample SelfQuiz question for the program on the
first law.
cording to the psychologists these acts are cru
cial to the learning process. In a sense the linear
program is an experience in guided discovery.
The student participates in the development of
the first law and in the application of the law to
different reversible and irreversible processes.
The students find this participation stimulating.
In response to the question, "What is the great
est strength of the programs? they replied: "Hav
ing the student answer the questions to work out
the principles for himself." "I got into the act of
actually developing equations."
In a branched program the student does not
construct answers to the questions. Instead, he
demonstrates that he has learned something by
choosing the correct answer from a set of given
answers. This behavior is most appropriate for a
testing situation and that is exactly how the
branched program has been used here. Table IV
CHEMICAL ENGINEERING EDUCATION
is part of the branched program used as the Self
Quiz at the end of the program on the first law.
A branched program requires that each question
have one correct answer and two or three rea
sonable alternates or distractors. Since each
incorrect answer must provide some feedback in
formation to the student, more effort is required
to construct a branched program. In some types
of material there are no logical alternates and
the branched program cannot be used. However,
when these alternates exist, the branched pro
gram can be very effective in teaching the stu
dent to discriminate between similar ideas.
Step Size
The second decision the teacher must make is
one of step size. Skinner's original concept of a
linear program involved a short, one or two sen
tence question properly cued or prompted to in
sure the correct answer would be forthcoming.
Recently, several, psychologists have questioned
the wisdom of the small step. For example,
Resnick3 has said "good students become bored
with too many small steps and come to resent the
time spent on such programs." Ausubel also sup
ports this conclusion with the thought that small
steps often artificially and unnecessarily "frag
ment ideas so that their interrelationships are ob
scured and their logical structure destroyed." By
a trial and error process I came to the same con
clusion, the small step does not suit the ability of
the engineering student. Using feedback from
my students I finally evolved the program style
shown in Table V. These programs involve rela
tively large steps, meaningful, unprompted ques
tions combined with uninterrupted sections of
explanatory material. This style integrates the
best features of a textbook, the lecture that fills
in the gaps left by the text, and the recitation or
discussion that supplements both.
Guiding the Student
Some of you may question the idea of care
fully guiding the student through derivations,
proofs and sample problems. In fact you may pre
fer the incomplete ideas presented in textbooks
because you want the student to provide the neces
sary clarification for himself. I agree that the
student should learn to think for himself but I
would argue that this struggle should not take
place when the student is learning basic concepts.
This reasoning is supported by Ausubel who says,
"Excessively difficult material makes for an un
Table V.Sample Page from the first law programs
Since we can always use a path such as (1a2)
between any two points, this equation can be used to
evaluate AH for any ideal gas process. This is an im
portant characteristic of a state property, any path be
tween two points can be used to evaluate the change
in a state property.
37Q. An ideal gas is compressed adiabatically in an open
system process, can the work for this process be
evaluated with the following equation?
W= AH CdT C ,T C(T,, T)
37A. Yes, the AH of an ideal gas always equals
C,(To  Ti).
38Q. If a real material is compressed adiabatically in an
open system process, can the work for this process
be evaluated with the equation
Wo =AH = COdT
38A. No. The equation Wo = AH is valid for any ma
terial, but AH = CdT is valid only for an iso
barbic process for all real materials.
The enthalpy of an ideal gas is a function of only the
temperature. The definition AH = Cp(To  Ti) proves
that when T. = Ti, AH = 0. Pressure has no effect on
the enthalpy of an ideal gas. We can reach the same con
clusion by noting that both U and the (PV) product (note
PV = RT) are functions of only the temperature. Since
H  U + PV  U+RT the enthalpy of an ideal gas
must also be a function of only the temperature.
2. Isothermal Process
39Q. Write the first law for an open system, combine it
with the definition of AH for an ideal gas and prove
that Q  Wo for an isothermal process involving
an ideal gas.
39A. Q  Wo = Ho  Hi = C,,(To  T,)
Since T. = Ti
Q  W, = 0
Q =W,
desirably large number of initial errors and mis
conceptions that have to be unlearned." This in
terferes with further learning, it lowers the stu
dent's self confidence and motivation, and pro
motes task avoidance. It is not that the student
doesn't want to learn on his own, but rather that
he lacks the necessary selfcritical ability. The
student usually finds it easy enough to manipulate
words so as to create an appearance of knowledge
and thereby to delude himself and others that he
really understands. Does that sound like some
SUMMER, 1968
of your students? By contrast, consider the fol
lowing reactions of my students to the programs:
"They don't let you get a misconception."
"We could go back over a question to clarify
points."
"Being able to correct ideas before going on
to new material."
"You can't go on unless what came before is
understood."
Other Factors
We have considered several of the factors the
psychologist considers crucial to effective learn
ing. They are: organization around the broadest
principles, systematic sequential organization
which shapes the students behavior, and an ac
tive learner who reformulates ideas in his own
words. There are two additional factors to be
considered.
First the psychologists say that new, abstract
subject matter should include concreteempiri
cal illustrations and analogies to clarify mean
ings. For this reason, my programs include both
theory and example problems. The student's re
action to this combination is very positive. Their
response to the question, "What is the greatest
strength of the programs?," was:
"Working with the material as it is intro
duced."
"Seeing how each concept can be related to
a problem right after the concept is presented."
The second factor to be considered is what the
psychologist would call an integrative perceptual
organizer, a device which helps the student relate
similar concepts and discriminate between over
lapping ideas. In my thermodynamics programs
this organization is accomplished by relating each
concept and calculation to an appropriate phase
diagram. As each subject is introduced it is re
lated to a process line on a projection of the three
dimensional surface for an ideal gas. For ex
ample, the concept of reversible shaft work is re
lated to the area under a process curve drawn on
a PV diagram. The concept of reversible heat
transfer is related to the area under a process
curve drawn on a TS diagram. When real ma
terials are introduced the appropriate threedi
mensional models and projections of the models
are used to relate the process conditions to the
change in a state property. The students response
to the question, "Did you find the emphasis on the
graphical representation of each process helpful
in understanding the material?" varied from
"definitely"; and "very helpful"; to "yes, I can
picture what is happening"; "yes, it was some
thing basic to refer to"; and 'yes, I need a physi
cal feeling for something to really understand it."
In all, twentysix students found this graphical
approach helpful, two others liked the approach
but were confused by the great number of graphs
presented.
Programs Free the Teacher
Designed as carefully as they are, you would
expect programs to teach a subject and teach it
well. The response of my students to the question
"Do you think the programs helped you learn
more than you usually do?", bears this out. The
students' reply was a unanimous yes.
When asked if the programs helped them un
derstand more than usual, twentyseven students
said yes; one was undecided. Part of the students'
reactions can probably be attributed to the Haw
thorne effect, but I'm not willing to admit that
this is a major factor. I don't think engineering
students are that naive. The fact that graduate
students ask me for copies of my programs to
study for their qualifying exams is further sup
port for the value of the programs.
Hopefully, by now I have convinced you that
programs can be of significant value in an engi
neering course. If not, let me tempt you with one
final attribute of programmed instruction. Dur
ing the past semester I taught an entire course in
thermodynamics using the set of programs I have
developed. Each program and its accompanying
problem set were assigned as homework. There
were no lectures in this course, class time was
completely free for other activities. In a typical
class meeting I spent from five to twenty minutes
answering the students' questions about the ma
terial in the program and discussing the home
work problems. During the rest of the period we
did a variety of things; we probed the concept to
greater depth, we extended the concept to new
situations and we applied the concept to indus
trial type problems. Those of you who would like
to find time to put some engineering in the engi
neering curriculum should be especially eager to
try programs. By increasing the efficiency of
the transmission of knowledge, the programs can
give you the time you need for other activities.
This, I might point out, is exactly the role
the psychologists predict for programmed instruc
tion. Ernest Hilgard, a former chemical engi
neer, head of the Department of Psychology and
CHEMICAL ENGINEERING EDUCATION
dean of the Graduate Division at Stanford put it
this way4. ". . . the program does not replace the
teacher but can hopefully free the teacher from
routine exposition, and give time for doing the
things that only the teacher can do," teaching
students to think for themselves.
Programmed instruction can help you give
your students a better education; I hope the in
formation I have presented here will encourage
you to try programs in your classroom.
References
1. Skinner, B. F., Harvard Educational Review, 31, (4),
1961.
2. Ausubel, D. P., The Psychology of Meaningful Verbal
Learning, Grune & Stratton, New York, 1963, (pp. 213,
208, 212).
3. Resnick, L. B., Harvard Educational Review, 33, (4),
1963.
4. Hilgard, E. R., Stanford Today, Series 1, (6), Sept.
1963.
Dr. Charles E. Wales is an associate professor of engi
neering and the President's assistant for educational re
search and development at Wright State University. His
present assignment includes organizing and presenting a
series of seminars on effective teaching techniques for
the Wright State faculty. He was educated at Wayne
State (BSChE), University of Michigan (MSChE), and
Purdue University (PhD).
Professor Wales has written programmed instruction
material in the areas of material balance calculations and
basic thermodynamics. His programs have been or are
being used on an experimental basis at Purdue, Kansas
State, West Virginia, Ohio, and Wright State universities,
at the Universities of Texas and Missouri (Columbia), and
at Ohio College of Applied Science.
3 book reviews
Engineering Thermodynamics
M. W. Zemansky and H. C. Van Ness,
McGrawHill (1966).
Professors Zemansky and Van Ness have writ
ten a text on thermodynamics with the "common
core" course in mind. As such, the text repre
sents a combination of and selection from the ma
terial offered in the conventional beginning cour
ses in thermodynamics in the chemical and me
chanical engineering curricula. In following this
path, the authors had to judge that certain topics
included in these portions of the typical chemical
engineering program would either be deleted, or
discussed in other courses. A similar statement,
but with different topics in mind, applies equally
well to the typical mechanical engineering pro
gram.
Viewed against the background of the typical
chemical engineering program, there are certain
features which make this book different. First,
there are a number of applications discussed in
the text which are not presently included in this
part, if indeed in any part, of the chemical engi
neering program. In this category are such top
ics as "bars in tension and compression" (chap.
2), "work in straining a bar" (chap. 3), "work
in changing the polarization of a dielectric in a
parallel plate capacitor" (chap. 3) "work in
changing the magnetization of a magnetic solid"
(chap. 3) and some of those discussed in "ap
plications" (chap. 14).
Secondly, a number of the classical experi
ments are discussed. This includes the determina
tion of "J" factor mechanical equivalent of heat
(chap. 4), determination of (3U/3P)T of a gas
(chap. 5), reversible change of volume of a gas
(chap. 7), and the measurement of latent heat of
vaporization (chap. 11) to cite a few. By the
discussion of experimental methods and the in
clusion of experimental data in some figures, I
believe the authors are attempting to impress on
the student the physical significance of the quan
tities which are later used in the solution of prob
lems. This is a part of education which is ap
parently being phased out in the fundamental
sciences and mathematics.
Looking at the other side of the coin, the
missing material, the chemical engineer will note
that fugacityy" is not mentioned. The theorem
of correspondence states is introduced and used
only in one problem11.1. Also, only mixtures
of ideal gases are considered. Nothing is in
cluded on heats of solution, or properties of real
mixtures, and very little on thermochemistry.
Also, the development and use of the humidity
SUMMER, 1968
TL l
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but as a tourist attraction.
Several Fluor employees and their families
toured this part of Spain during 1967. Why
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building a refinery for Rio Gulf de Petroleos
at La Rabida, the site from which Columbus
actually sailed. The Rio Gulf project is just one
of some thirty foreign jobs currently under way
by Fluor.
Fluor's principal engineering centers are
located in the United States and Europe. Almost
every plant Fluor builds is engineered in one
of four support facilities... Los Angeles, Hous
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eventually end up at a foreign jobsite (if he
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chart and calculation of dewpoints and bubble
points using Raoult's lawtopics common to
practically all initial chemical engineering cour
sesare not considered.
Undoubtedly, many mechanical engineers re
viewing this book would find that some of their
favorite topics have been omitted or treated with
brevity and, conversely, some topics have been
covered more extensively than is usually the case.
The book is well written and the level of
mathematicssome partial differential equations
are usedsuch that the second year, or certainly
the first semester third year, student should have
no trouble. If a student cannot learn the the
principles of thermodynamics from this book, it
should certainly not be due to the mathematics
used. Each chapter is concluded with a number
of problems which appear to offer the user a rea
esonable choice; i.e. some difficult ones and some
not so difficult. Apparently, the problems were
selected so a slide rule is the only type of com
puter necessary.
The usage of this book by chemical engineers
depends upon how our programs develop over the
next few years. If we move to more common core
coursesand thermodynamics is one of the prime
areas where such movement is possiblethis
book "Engineering Thermodynamics," should be
seriously considered for use.
James H. Weber
University of Nebraska
IM problems for teachers
The following solutions to thermody
namics problems published in CEE Spring
quarter, pp. 9596, 1968, were prepared by
Professors R. K. Irey and J. H. Pohl at the
University of Florida. We continue to so
licit questions on subjects of general en
gineering or scientific interest to be pre
sented in this department.
1. (a) Consider u as u(s,xi),
du = \ds + :f d ,
7asj I '
By analogy with
du = Tds  di j
T and  =M w Fl ,(N+l eqs.)
(b) The Maxwelf relations are
aTN a
/at,  aF)
(c) i) N+l, for a total of 4(N+1) eqs.
3N(N+l)
ii)  , for a total of 2N(N+1) eqs.
iii) Take the derivative of 4 q and sub
stitute du into the equation
d q = sdT 
Consider the total derivative of
'q = ' q(T,x.), i= 1,  ,N.
d +q  ( dT + t'
thus, T s and .
Since 2
we have _ 5
1' _1) JJ T/)
\aT ig,! ta2RT,
2. (a) Consider s = s(T,5L) and s = s(T,FI).
Then A(
ads = dT d +j (i)
and ( / and
ds = dT + 'I (ii)
= = T 1 , and
S = = T (iii)
Use the Maxwell relations,
and the relations (iii) in (i) and
(ii). Then set the right of (ii)
equal to the right of (i).
If F is constant,
^. T4 ;x ,,
If xZ is constant, the result is the
same.
(b) From (i) above
dJ= i dT ( Ell .ti
From the exactness of this equation
Hold T constant in this equation and
integrate with respect to all 5%.
The lower limit is a reference value,
Ci. The upper limit is variable.
SUMMER, 1968
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CHEMICAL ENGINEERING EDUCATION
views and opinions I
THERMODYNAMICS:
DEATH AND TRANSFIGURATION
JAMES L. THRONE*
Ohio University
Athens, Ohio 45701
In a recent article1 I criticized vehemently
present approaches to the teaching of thermo
dynamics. In particular, I argued that thermo
dynamics at present is based on mysticism and
magic when dealing with the fundamental con
cepts such as temperature, energy, and entropy.
I argued that what was needed was a rational
approach to the development of concepts and
their application to chemical engineering and
that, for the nonthermodynamicist, in particular,
thermodynamics should be viewed as a hand
maiden to the major chemical engineering areas
such as kinetics, process design and control, and
transport mechanics.
In this paper, then, I offer a program which
attempts to prepare the graduate engineer for
a career in which thermodynamics plays an im
portant, but not dominant, role. While this pro
gram also has limitation, I should hasten to point
out that it has been used successfully at Ohio
University on a firstsemester graduate level for
some time.
Statistical or Mechanical Approach?
As I pointed out in the earlier paper, I con
sider that the fundamental concepts of thermo
dynamics are three in number:
1. The concept of temperature
2. The concept of energy
3. The concept of entropy
Traditionally, there are two major ways of intro
ducing these concepts:
1. The intuitive approach, sometimes referred to as
a phenomenological approach, in which, for example, the
concept of temperature is regarded as a primitive con
cept, like force and displacement, and therefore, not re
quiring definition, merely illustration.
2. The statistical approach, in which it is necessary to
identify a constraint in the system of describing equations
*A biography of Dr. Throne is available in CEE 2,
92, 1968.
with one of the concepts. The describing equations may
deal with energy in kinetic form (classical approach), or
quantum form, or even level of information form (Tribus).
As I stated earlier, probably the only time the
statistical approach is applied in traditional grad
uate level chemical engineering first courses is in
shoring up otherwise weak and faltering develop
ments of the concept of entropy. It is apparent
that if the proper approach to the development
of the concept of entropy is employed, no shoring
up is needed and, hence introduction of statistical
concepts into a first course is not needed!
Traditionally, the intuitive approach to chemi
cal engineering thermodynamics has been "mole
culeless mechanical thermodynamics," with em
phasis on steadystate operations of system con
taining continue of material. To say that this ap
proach represents a crazyquilt of sterile applica
tions of sound principles of mathematics and clas
sical physics and empirical rulesofthumb so
typical of chemical engineering in the thirties
would undoubtedly insult many socalled chemical
engineering thermodynamicists. In this program,
I attempt to establish a firm, rational basis for
the determination of a working program (no
pun intended). I emphasize establishment of
rigorous axioms on which we can evaluate the
empirical concepts presently in vogue in the
literature.2 Undoubtedly, I cannot hope to pre
scribe a single remedy that will cure the multiple
ills plaguing authors of articles and textbooks in
one, introductory course. It is my primary goal
to make the average graduate student aware of
the maladies, so that he can intelligently evaluate
work in his chosen field of endeavor.
Our Program: Goals and Gaols*
We begin the course by reviewing the funda
mental laws of thermodynamics as primitive con
cepts, requiring no definition. We then construct
concepts total and path differentiation from a
mathematical viewpoint. Concepts such as work
*The texts we have been using, along with the support
ing reference material, are listed in Table 1.
SUMMER, 1968
I~ihE'k
_....... __._. _   
introduced in metric form as being the result of
relationships between generalized forces and
differential displacements.** The close relation
ship between fluid mechanical systems and ther
modynamic systems is then discussed, and the
generalized concepts of enthalpy and heat capa
cities (in terms of generalized forces and dis
placements) are developed, with specific examples
in linear extension, surface extension, and pres
surevolume. The theorems of Caratheodory,
Pfaff, inaccessible states, and mathematical de
velopment of constitutive equations for entropy,
reversible heat and temperature are developed.
Shaw's method of Jacobian of Transformation5
and the development of Maxwell's equations are
presented, with extension of Shaw's method to
multicomponent systems. These equations are
then applied to the generation of equation such
as the GibbsDuhem Equation.
Partial molar properties, multicomponent sys
tems, and the natural appearance of the chemical
potential are presented. With special emphasis on
gases, rules for the development and evaluation
of constituitive equations are presented, along
with fugacity and perfect mixtures of perfect and
nonideal gases. It is emphasized that fugacity is
the true thermodynamic pressure. The role and
limitation of chemical potential, the phase rule,
and degrees of freedom are then developed.
We then consider first and higher order phase
transitions, developments of Clapeyron and Er
henfest equations from direct integration of Max
well's equations and from L'Hopital's rule, and
their physical implications in single component
and multicomponent systems.
We then expend considerable effort in apply
ing the GibbsDuhem equation to the selection of
constitutive relationships between partial pres
sure, composition and temperature, emphasizing
Raoult's law of ideal systems, Henry's law of
equations. It is important to note here that we
emphasize the approximate empirical nature of
these constitutive equations; we do not let these
equations live by themselves, as it were.
Application of constitutive equations to engi
neering systems such as heat of mixing and
volume change, depression of freezing point, os
**It is important to note that standard approaches to
work utilize affine coordinates. While developments of
concepts in affine coordinates are satisfactory for explicit
problemsolving, development of general concepts, par
ticularly when thermodynamics is used in transport me
chanics, must be made in metric coordinates.3,4
TABLE I.
Books Used in First Course in Graduate Thermodynamics
Required Texts:
1. Denbigh, K. G. The Principles of Chemical Equi
librium, 2nd Ed., Cambridge 1966.
2. Tribus, M., Thermostatics and Thermodynamics, D.
Van Nostrand, Co., 1961.
Recommended Reading Reference:
1. Zemansky, M.W., Heat and Thermodynamics, 4th
Ed., McGrawHill, 1957.
2. Guggenheim, E. A., Thermodynamics, 3rd Ed., North
Holland Publishing, 1957.
3. Dodge, B. F., Chemical Engineering Thermodynam
ics, McGrawHill, 1944.
4. Smith, J. M., Introduction to Chemical Engineering
Thermodynamics, McGrawHill, 1949.
5. Coull, J., and Stuart, E. B., Equilibrium Thermo
dynamics, Wiley, 1964.
6. Lewis, G. N. and Randall, M., Pitzer, K. S. and
Brewer, L., Thermodynamics, 2nd Ed., McGraw
Hill, 1961.
7. Bosnjakovic, F., Technical Thermodynamics, Holt,
Rinehart and Winston, 1965.
8. Gibbs, J. W., The Scientific Papers of., Volume 1,
Thermodynamics, Dover, 1961.
9. Weber, H. C., and Meissner, H. P., Thermodynamics
for Chemical Engineers, 2nd Ed., Wiley, 1957.
10. Van Wylen, G. J., Thermodynamics, Wiley, 1959.
11. Fong, P., Foundations of Thermodynamics, Oxford,
1961.
12. Bridgman, P. W. The Nature of Thermodynamics,
Harper, 1961.
13. Fermi, E., Thermodynamics, Dover, 1956.
motic pressure, and such, follow. Thermodynamic
consistency tests and their relative reliability are
stressed.
Finally, we introduce concepts of thermo
dynamics of the steady state, dealing with the
concept of entropy production and the phenome
nological coupling tensor between fluxes and
forces. We discuss "Curie's theorem" and its
logical basis as a fundamental theorem of tensor
calculus,6 and the faults of the present state of
irreversible thermodynamics (linear "Onsager
ist" approach) and its future role in thermody
namics. We conclude by examining real engi
neering examples of steadystate thermodynamics
in coupled systems such as heatmass transfer,
kineticsfluid flow, and fuel cell technology.
To implement the development of the course,
I present, in flow diagram form, apparent inter
actions in the major areas of thermodynamics.
This diagram is shown below. While I do not
pretend to imply that this flow diagram is wholly
correct or complete, it does serve graphically to
illustrate chemical engineering thermodynamics.
CHEMICAL ENGINEERING EDUCATION
THERMODYNAMICS
Thermodynamics: Who Cares?
First, it is important that the above program
makes no mention of cycles, refrigerators, en
gines, TS diagrams, Mollier Charts, compressi
bility curves, etc. This is done deliberately. Em
phasis is placed on understanding of underlying
mathematical, mechanical, chemical, and physical
principles. Interrelationships between thermo
dynamics, kinetics, and mechanics are continu
ally emphasized and illustrated through engineer
ing examples. Why? It is my belief that rational
understanding of the role of thermodynamics in
the overall concept of chemical engineering comes,
not from the ability of the student to calculate
coefficients in equations of stategiven critical
properties, but from his ability to understand the
usefulness and limitations of the present concepts
of thermodynamics. It is his ability to intelli
gently and rationally question existing practices,
not blindly calculate and manipulate empirical
equations, that will make him a valuable member
of the chemical engineering community.
Conclusion
Classical thermodynamicists with their minds
intently focused on new PVT correlations or
nth degree refinement in the current Mollier dia
gram for steam or ammonia, are being bypassed
and circumvented by people who need to answer
thermodynamic questions dealing with biological
metabolism, kindey or fuel cell operation, kinetic
fluid flow interaction, cyclic operation of non
ideal transport systems, thermomechanical foun
dations of nonlinear visocelastic media, nonFick
ian diffusion, sewage disposal and antipollution
systems. We cannot afford to ignore the challenge
of modern chemical engineering by offering ma
terial that was designed to support chemical en
gineering Edisonianism of the 30's.
It is my opinion, then, that Dr. Bates' ap
proach ("First Aid to Ailing Thermodynamics")
will eventually lead to the death of thermody
namics as it is traditionally taught. To this, I
say, good riddance. For, like the Phoenix of
Egyptian mythology, from its ashes shall rise
anew a thermodynamics founded on the rational
principles of Gibbsian mechanics.
REFERENCES
1. Throne, J. L., Chem. Eng. Ed. 1 7071, (1966).
2. Giles, R., "Mathematical Foundations of Thermo
dynamics," The Macmillan Co., New York, 1964.
3. Throne, J. L., "Applications of Tensor Calculus in
Chemical Engineering," McGrawHill Book Co., New
York, to be published.
4. Brillouin, L., "Tensors in Mechanics and Elastic
ity," Academic Press, New York, 1964.
5. Tribus, M., "Thermostatics and Thermodynamics,"
D. Van Nostrand Co., Inc., New York.
6. Fitts, D. D., "Nonequilibrium Thermodynamics: A
Phenomenological Theory of Irreversible Processes in
Fluid Systems," McGrawHill Book Co., New York, 1962.
SUMMER, 1968
WHERE ARE THE ENGINEERS?*
T. B. METCALFE
University of Southwestern Louisiana
Lafayette, La.
In spite of our usual confident reliance upon
the balance between supply and demand, the re
lationship between the output of our engineering
colleges and the need for practicing engineers does
not seem to be following the rule. All of the
factors which we would expect to contribute to a
great demand for engineers seem to be present.
Engineering employment has reached new highs
and graduating students of engineering colleges
are offered a half dozen or more jobs upon gradu
ation. There are complaints from many potential
employers that they are unable to fill their quotas.
Indeed, the meteoric rise in the employment of
technicians in the engineering field, while largely
due to a heretofore unfilled need for this kind of
service, is also greatly influenced by the unavail
ability of young engineers.
Incentives are certainly present in the current
situation. The satisfaction to the individual of
making a contribution to technical advancement
has never been greater and recognition on the
part of the general public of the contribution of
engineers is well established. Salaries and other
remuneration for engineers are at new peaks,
higher than those for most other career profes
sionals, at least in the years immediately follow
ing graduation. Engineering starting salaries are
increasing and at a rate higher than the rate of
increase for other professionals.
Thus, the high and unsatisfied demand seems
to have created the expected result of increased
incentives for the study of engineering. Why
then, should there be any shortage of engineers?
Many contend that there is no shortage, or rather,
they cite statistics to show that there is a consis
tent increase in the number who choose to study
engineering. They conclude that we should not
fear a shortage as long as the trends continue.
A comprehensive study published in the Janu
ary, 1966 Journal of the American Society for En
gineering Education, by the ECAC (committee
for analysis of engineering enrollment) presented
data in total engineering enrollments between
1949 and 1962. They note the large contribution
of veterans under the government educational
*Presented to the Spring Meeting of the GulfSouth
west Section ASEE, College Station, Texas, 21 March
1968.
Dr. T. B. Metcalfe is Head of the Department of
Chemical Engineering at the University of Southwestern
Louisiana. His background and experience includes de
grees from Georgia Institute of Technology and the
University of Texas; faculty positions at West Virginia
Institute of Technology and the University of Houston;
and professional experience with Shell Oil Company,
U. S. Naval Reserve (WW II) and Dow Chemical Com
pany.
programs who swelled the enrollment in the years
immediately following World War II and also
during 195456 subsequent to the Korean military
involvement. This analysis illustrated that if the
enrollment of veterans was not included in the
totals, the fluctuations in enrollment of engineer
ing students are much reduced and a definite and
consistent trend was evident. It was concluded
that the apparent appreciation in engineering
enrollments of about 13,500 each year ( during the
entire thirteenyear period covered) might be con
fidently extrapolated for another few years.
It becomes the responsibility of engineering
educators to perceive the changes in trends, and
to exert the necessary influence to reverse unde
sirable ones. Two conditions which contribute
markedly to the rate of output of engineers are
(1) the number of entering college students
choosing engineering as a career and (2) the re
tention of those students through graduation
from engineering college. The desirability of, and
the incentive to, study engineering must be com
municated to the high school and junior high
school public (student, parent, and counselor).
Depending upon the success of this contact, more
(or fewer) students may choose the profession of
engineering. The statistics upon which Figure 1
is based illustrate that in the years 1949 to 1952
there was indeed a marked decrease in the total
enrollment in universities in our country. This
was undoubtedly due both to the then declining
number of World War II veterans enrolling and
the decrease in the enrollment of younger men
CHEMICAL ENGINEERING EDUCATION
FIRE I
Tal Enrollments By Year
T  Total College Enrollmnt
E  Total Engi�erng Enrollment
1950 52 54 56 58 60 62 64 66
FGURE 2
Englenring Prcealagr of
Taal Collea Enollmnat
by year
" O0
\
\
S .... EnrolluntTrend
(ae Fipre 1)
195 52 54 56 58 60 62 6 66
 674
5323C mo
n5 Is 5e6Iw I Es OL 60 6_
6156
.9. 6 b6
7\
1067 1 x
1956 5o 56 56 60 62
,� / ^
students due to the Korean involvement. Subse
quent to that period, however, from 1952 to the
present no disregard of veterans or any other
group is necessary to allow the recognition of a
consistent, rapidly upward trend in the total en
rollment of college men students in our colleges
and universities. Comparison of trends in the
total college enrollment and in engineering enroll
ments show the same fluctuations, with variations
in the trend for the most part occurring at the
same times. However, the variations are greater
in the case of the engineering enrollment and the
ECAC prediction of an appreciation of 13,500
each year has been exceeded considerably each of
the last 4 years, with an ever increasing rate. A
significant difference in total enrollment and engi
neering enrollment is the occurrence of a peak
in engineering enrollment in 1957 and a subse
quent fouryear decline in that enrollment, during
which four years, the rise in total college enroll
ment slowed only slightly.
In 1961, while total college enrollments con
tinued to climb (due, no doubt, to the coming of
college age of the unusually large number of post
war babies), engineering enrollments began again
to rise. Each year since, the rise has been at a
larger rate.
Since our analysis of incentives has been dis
cussed earlier in terms of comparison to other
professions and careers, it is logical to evaluate
the trends in engineering enrollments in terms of
comparison to the overall enrollment. The sig
nificance of the 1957 reversal in the upward trend
of engineering enrollments is clarified by the
curve of Figure 2 which represents the fraction
SUMMER, 1968
of total enrollment represented by engineers. The
percentage of engineers in the total college popu
lation reached a peak in 1957 after having risen
consistently during the postKorean period. Sub
sequent to 1957, this percentage has persistently
dropped, until at the present time, it is little more
than half of the 1957 value of nearly 15 per cent.
This is taken to be a clear indication of a ser
ious and dangerous lack of rapport with the po
tential college student on the part of engineering
educators. There is small comfort in the existence
of an upward trend in engineering enrollments in
view of the fact that the shortage of engineers is
not being relieved and the increase in engineering
enrollments falls so far short of the increase in
total college enrollment.
To be most meaningful the statistics must be
expressed in terms of the various disciplines. The
classical disciplines of Chemical, Civil, Electrical,
and Mechanical Engineering account for about
half of all engineering students. Industrial and
Petroleum Engineering are the only other disci
plines with appreciable fractions of total engi
neering enrollments. In 1952, there were in
ECPD accredited departments 3,822 entering
freshmen students who wished to study Chemical
Engineering, and in 1962, at the end of the re
porting by ASEE, there were 3,862, an only
slightly larger number (see Figure 3). Reflecting
the difference in total engineering enrollments at
the start and at the end of this period, the nearly
equal numbers of students in Chemical Engineer
ing represented 8 per cent (of total engineering
enrollment) in 1952 and hardly more than 7 per
cent in 1962. Thus, while maintaining the num
ber of its students, Chemical Engineering has de
clined slightly in public acceptance as an engi
neering discipline.
By comparison, and considering the absolute
numbers for the beginning and end of the ten
year span as well as the trends, it is evident
from the curves (Figure 3) that enrollments in
Civil Engineering have dropped slightly, while
their percentage has dropped from 111/2 to 91/2
per cent. There has been a more marked drop in
the number of Mechanical Engineers and their
percentage is down from 17 to 12 per cent of
the total. Both Industrial and Petroleum Engi
neering disciplines have shown large decreases in
the number of students and in their fraction of
the total engineering enrollment during this per
iod. Only Electrical Engineering has shown a
marked increase in number of students. This has
resulted in an increase in its fraction of the total
from 16 to 20 per cent.
It becomes evident that the classical disci
plines are not generally increasing in spite of the
marked increase in total engineering enrollments.
The increase is distributed among the newer dis
ciplines, each representing smaller numbers of
engineering students. These newer disciplines,
while offshoots of the classical disciplines, have
completely divorced themselves from the parent
departments except in the case of Electrical Engi
neering. The growth of the Electrical Engineer
ing discipline can be attributed to their absorp
tion of a number of new interests such as Elec
tronics and Communications.
This action on the part of Electrical Engineers
to retain within a single discipline the widely
varied interests which represent different appli
cations of the same engineering principles is con
sidered a wise one and one which should be emu
lated by other disciplines. New branches of engi
neering often are created because of the recog
nition on the part of their practitioners that their
interests stem from more than one of the classical
disciplines, and therefore, they consider them
selves separate from both. Preferable to this
proliferation of engineering disciplines would be
an interdisciplinary interest on the part of the
parent disciplines. This would tend to unify and
strengthen engineering instead of weakening it as
does the current practice of splintering.
Having determined the total enrollments as
the potential with which we have to work, it is
now interesting to observe the retention of this
group of students. Over a tenyear period, the
average retention for Chemical Engineering
144
 EUR4
T6DE Ti AniE I0
. 
(Figure 4) shows that after the first year the
number of students enrolled for their second year
is only 90 per cent, and those persisting to the
third year only 73 per cent of the entering fresh
men. Sixtyseven per cent persisted to their
fourth year, and finally 61 per cent were gradu
ated with the B.S. degree after four years. In
Civil Engineering, 5 per cent were lost in the
first year, with 95 per cent remaining; 90 per
cent remained for their third year and a slight ap
preciation then resulted in the fourth year class
of 92 per cent of their entering freshmen. At the
end of four years, 80 per cent of the entering Civil
Engineering classes were graduated. Mechanical
and Electrical Engineering appreciated 6 and 7
per cent, respectively, in the second year after
which their number declined so than Mechanical
Engineering Departments graduated 85 per cent
of their entering freshmen and Electrical Engi
neering, 83 per cent. Thus, among these disci
plines only Chemical Engineering shows no in
crease at any level during the college career.
Rather, the number dropping out of Chemical En
gineering during each year is significant.
We can conclude that engineering educators
must face up to the fact of a declining acceptance
of engineering as a course of study by college
students. Instead of fatalistic acceptance, we
must strive to reverse this trend and provide
greater numbers of graduated professionals by
stronger recruitment of high school and junior
college graduates and by greater retention of
entering students who choose an engineering
course of study.
CHEMICAL ENGINEERING EDUCATION
MARATHON: DYNAMIC PROGRESS
;r**r31i ~n*rri*1 L vII"�WE L"YL1" ~��*��*
""~i� L~ U
r'E. 
Marathon Oil Company was founded in Find
lay, Ohio in 1887; however its ultramodern
Denver Research Center is located at the foot
hills of the Rockies. The company is a producer,
transporter, refiner and marketer of crude oil and
petroleum products on five continents throughout
the world.
The Denver Research Center was established
to make discovery of new petroleum reserves more
economical, to help recover a larger percentage
of oil in present fields, to develop more profitable
refining and chemical processes, and to develop
new products.
Marathon employs more than 8,000 persons
at its offices around the world including its head
quarters in Findlay. There are over 300 em
ployees at the Denver Research Center of which
more than half are scientists and engineers.
CHEMICAL ENGINEERING AT MARATHON
Using engineering research to determine ways
to recover more of the oil from known deposits
is an important part of the work at the Research
Center. It includes projects aimed at stimulating
wells so they will produce more oil; in situ com
bustion; and fluid injection processes, such as
miscible displacement, which are more efficient
than conventional techniques where gas or water
are used to drive oil to a production well.
Reservoir mechanics comprise another signifi
cant part of the engineering work at the Denver
Research Center. The transient behavior of oil
reservoirs and the flow of fluids through porous
media are important phases of this work. Mathe
matical models, which simulate reservoir behav
ior, provide insight into future behavior of oil
bearing reservoirs.
Chemical engineers are also engaged in the
pilot plant study of existing refinery and chemical
processes as well as in the evaluation and devel
opment of new processes and new chemicals.
Projects are underway, for example, on petro
chemical processes to make monomers and other
basic components for polymers.
At Marathon's Research Center, qualified en
gineers are provided with both the challenge and
incentive in supplying answers to these problems.
Your further inquiry is invited.
Mr. L. Miles
Personnel Supervisor
Dept. CE1, P. O. Box 269
Littleton, Colorado 80120
AN EQUAL OPPORTUNITY EMPLOYER
MARATHON
MARATHON OIL COMPANY
DENVER RESEARCH CENTER
LITTLETON. COLORADO
..1
'5,:
4;,
f*
* i
If
i'.~
Professor, What Do You Think?
Process Design Oilfield Production
Technical Sales Plant Design
Refinery Engineering Development
Research Technical Service
With all the opportunities available today
you probably often hear this question from
your students. You can be a major factor
in his career.
If you find yourself in this situation why
not consider an industry that can offer
a full range of Chemical Engineering
assignments and advancement opportunities?
Standard Oil Company of California has
challenging assignments in just about any
area that would interest Chemical Engineers.
These initial assignments will test their
ability and can lead to advancement
in many areas.
Should you or any of your students wish additional
information on our industry or Company write to:
Mr. Robert E. Rodman
Coordinator, Professional Employment
Standard Oil Company of California
225 Bush Street
San Francisco, California 94120
Standard Oil Company of California
An Equal Opportunity Employer
