Front Cover
 Table of Contents
 Dinesh Shah of Florida
 Division activities
 University of Kentucky
 Letters to the editor
 Symposium on undergraduate thermodynamics:...
 Use of slides and self-study...
 An integrated approach
 Thermodynamics with design...
 Computer-generated phase diagrams...
 Supplemental TV taped problems
 Fundamental property relation
 Residual functions and fugacit...
 A graphic look at availability...
 Putting problem solving to use...
 Book reviews
 Back Cover

Chemical engineering education
http://cee.che.ufl.edu/ ( Journal Site )
Full Citation
Permanent Link: http://ufdc.ufl.edu/AA00000383/00079
 Material Information
Title: Chemical engineering education
Alternate Title: CEE
Abbreviated Title: Chem. eng. educ.
Physical Description: v. : ill. ; 22-28 cm.
Language: English
Creator: American Society for Engineering Education -- Chemical Engineering Division
Publisher: Chemical Engineering Division, American Society for Engineering Education
Place of Publication: Storrs, Conn
Publication Date: Summer 1983
Frequency: quarterly[1962-]
annual[ former 1960-1961]
Subjects / Keywords: Chemical engineering -- Study and teaching -- Periodicals   ( lcsh )
Genre: serial   ( sobekcm )
periodical   ( marcgt )
Citation/Reference: Chemical abstracts
Additional Physical Form: Also issued online.
Dates or Sequential Designation: 1960-June 1964 ; v. 1, no. 1 (Oct. 1965)-
Numbering Peculiarities: Publication suspended briefly: issue designated v. 1, no. 4 (June 1966) published Nov. 1967.
General Note: Title from cover.
General Note: Place of publication varies: Rochester, N.Y., 1965-1967; Gainesville, Fla., 1968-
 Record Information
Source Institution: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: oclc - 01151209
lccn - 70013732
issn - 0009-2479
Classification: lcc - TP165 .C18
ddc - 660/.2/071
System ID: AA00000383:00079

Table of Contents
    Front Cover
        Front Cover 1
        Front Cover 2
    Table of Contents
        Page 93
    Dinesh Shah of Florida
        Page 94
        Page 95
        Page 96
    Division activities
        Page 97
    University of Kentucky
        Page 98
        Page 99
        Page 100
        Page 101
        Page 102
    Letters to the editor
        Page 103
    Symposium on undergraduate thermodynamics: Introduction
        Page 104
    Use of slides and self-study examples
        Page 105
        Page 106
        Page 107
    An integrated approach
        Page 108
        Page 109
    Thermodynamics with design problems
        Page 110
        Page 111
    Computer-generated phase diagrams for binary mixtures
        Page 112
        Page 113
        Page 114
        Page 115
        Page 116
    Supplemental TV taped problems
        Page 117
        Page 118
    Fundamental property relation
        Page 119
        Page 120
        Page 121
        Page 122
        Page 123
    Residual functions and fugacity
        Page 124
        Page 125
        Page 126
        Page 127
    A graphic look at availability functions
        Page 128
        Page 129
        Page 130
        Page 131
        Page 132
        Page 133
    Putting problem solving to use in the classroom
        Page 134
        Page 135
        Page 136
    Book reviews
        Page 137
        Page 138
        Page 139
        Page 140
    Back Cover
        Back Cover 1
        Back Cover 2
Full Text

i ' ' �
w �?~"f

8 -Itw�P;



&wAidA a dSiiaei of jauneds.


Department of Chemical Engineering
University of Florida
Gainesville, Florida 32611

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

Lee C. Eagleton
Pennsylvania State University

Past Chairman:
Klaus D. Timmerhaus
University of Colorado

Homer F. Johnson
University of Tennessee
Jack R. Hopper
Lamar University
James Fair
University of Texas
Gary Poehlezn
Georgia Tech

Robert F. Anderson
UOP Process Division
Lowell B. Koppel
Purdue University

William B. Krantz
University of Colorado
C. Judson King
University of California Berkeley

Angelo J. Perna
New Jersey Institute of Technology
Stuart W. Churchill
University of Pennsylvania
Raymond Baddour
A. TV. Westerberg
Carnegie-Mellon University

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

Chemical Engineering Education

The Educator
94 Dinesh Shah of Florida,
Dick Dale and John O'Connell

Department of Chemical Engineering
98 University of Kentucky, William L. Conger

Symposium: Undergraduate Thermodynamics
104 Introduction, R, G. Squires, Symposium

105 Use of Slides and Self-Study Examples,
Alan J. Brainard
108 An Integrated Approach, Thomas E.
110 Thermodynamics With Design Problems,
E. V. Cilento and J. T. Sears
112 Computer-Generated Phase Diagrams for
Binary Mixtures, Kenneth R. Jolls,
John Burnet, Jeffrey T. Haseman
117 Supplemental TV Taped Problems,
Robert G. Squires and David V. Frank

119 The Fundamental Property Relation,
Joseph J. Martin
124 Residual Functions and Fugacity,
K. R. Hall, P. T. Eubank, J. C. Holste
128 A Graphic Look at Availability Functions,
Martin V. Sussman

134 Putting Problem Solving to Use in the
Classroom, Richard D. Noble

97 Division Activities
103 Letters to the Editor
137, 138, 139 Book Reviews
97 Stirred Pots

CHEMICAL ENGINEERING EDUCATION is published quarterly by Chemical
Engineering Division, American Society for Engineering Education. The publication
is edited at the Chemical Engineering Department, University of Florida. Second-class
postage is paid at Gainesville, Florida, and at DeLeon Springs, Florida. Correspondence
regarding editorial matter, circulation and changes of address should be addressed
to the Editor at Gainesville, Florida 32611. Advertising rates and information are
available from the advertising representatives. Plates and other advertising material
may be sent directly to the printer: E. O. Painter Printing Co., P. O. Box 877,
DeLeon Springs, Florida 32028. Subscription rate U.S., Canada, and Mexico is $15 per
year, $10 per year mailed to members of AIChE and of the ChE Division of ASEE.
Bulk subscription rates to ChE faculty on request. Write for prices on individual
back copies. Copyright � 1983 Chemical Engineering Division of American Society
for Engineering Education. The statements and opinions expressed in this periodical
are those of the writers and not necessarily those of the ChE Division of the ASEE
which body assumes no responsibility for them. Defective copies replaced if notified
within 120 days.
The International Organization for Standardization has assigned the code US ISSN
0009-2479 for the identification of this periodical.



eof Florida

of Florida


DINESH SHAH IS A rebel, a philosopher, an in-
vestigator of science, a poet and a man of two
worlds. His heritage is deep in 5,000 years of East
Indian culture and his devotion is to a fledgling
nation of only two centuries.
"I was rebellious in many respects," he says.
"I didn't like some of the traditional values. I was
greatly influenced by Mahatma Gandhi and his
writings. Before Gandhi we were a society of many
castes where only people of low caste did manual
labor. Gandhi said manual labor was good for
"We had a low caste guy who cleaned our high
school and I guess he just quit or something. The
school was dirty so I told the principal that I would
clean it if he gave me the money they paid before.
He didn't see anything wrong with such an ar-
rangement but it sent a shockwave through the
"I was known as a nonconformist! But no one
had the nerve to question me. I was the top stu-
dent. I took that job in the eighth grade and kept
it for four years. My brother continued doing it."
Life for the Shah family wasn't easy. The
breadwinner was ill for a long time prior to his
death. Money was short and sacrifices had to be
made. Tradition gave way to survival.
"We had our own home so we didn't have a rent
problem. And, in India, the relatives pitch in and
help. I know my mother felt bad. If you bought

Besides being a keynote speaker on
several occasions, he has won two outstanding
paper awards at international meetings. Among his
one hundred publications are two books he
edited on enhanced oil recovery.

� Copyright ChE Division, ASEE, 1983

something in the market, it was proper to engage
a low caste to carry it to your home. I couldn't
afford a porter.
"My mother said to come home by way of the
back streets where no one would see me. I walked
through the main street with my bundles on my
College for the young Shah was, in his words,
something of a miracle. With meager savings, help
from relatives and acquaintances, and money from
academic awards earned in high school, he went to
the University of Bombay.
"There was a special boarding house there.
Heavily subsidized. No frills but adequate and at
about half the usual cost. Even with that, in six
months my money was gone.
"I walked on the beach one day, trying to find a
way to solve my problem. As I walked, I looked at
the fine houses along the shore and, without know-
ing why, I moved closer and studied the names.
These were homes of doctors, lawyers and profes-
sional people. I saw a name! An attorney who had
been prominent in our pre-independence move-
ment. And I pushed the bell."
The young man asked to speak to someone in
the family and was ushered to an audience with
the matriarch, a daughter-in-law of the late fam-
ous barrister.


University of Florida
Gainesville, FL 32611

"She listened while I told my story. That I
needed work. Washing clothes, dishes, tutoring
children. There were no children of the immediate
family but there were children of the staff. The
"Come every evening," she said, "and tutor the
children. We will not pay you a salary but when
you need money for anything just ask."
"I was overwhelmed! They were very wealthy,
indeed. And they supported me all through my
undergraduate studies. It was a miracle!
"In college there were two ways I might have
gone. Engineering or medicine. Cutting up frogs
or other "living" things was opposed by religious
sentiments and engineering appeared uninterest-
ing. I settled for physics.
"But as time went on there was nothing exotic
or mystical about physics and I became fascinated
with a new area called biophysics. Physics applied
to biological systems and processes. I thought that
would be really good.
"That year the university started a graduate
program in biophysics. I was in the first batch of
four students who were selected and I spent two
years at the Indian Cancer Research Center doing
course work.
"When I moved to graduate study I expressed
my thanks to my patron and said I could carry on
alone. I had expanded my tutoring to college stu-
dents and increased my earnings. My benefactor
was delighted with my independence. We remained
close friends.
"But in 1960 I applied for a doctoral fellowship
at Columbia, in the United States, and was ac-
cepted. To go to America meant that someone must
post a financial bond. A substantial figure. And,
without hesitation, she accepted responsibility for
my move to America. Much later, when I had
earned my degree, I received a lovely letter of
"When I first came to Columbia I was going to
work in radiation biophysics. My first summer
job, however, was with Professor J. H. Schulman
in the school of mines. He was a pioneer in surface
and colloid sciences. And I got hooked!
"This is a terrific thing! You can handle the
molecule! You can measure the molecule! And you
can feel them! You can see the effect of molecular
film on the surface tension of water. I was really
"Fortunately, the professor was also on the
advisory committee of the biophysics program. I
took him as my supervisor for doctoral research.

"I was exposed to many things in his labora-
tory that have enabled me to work broadly on such
things as oil recovery, coal dispersions, pharma-
ceutical microemulsions, contact lens solutions,
membranes and anesthesiology. Working with
such a man was my second miracle!"
Subsequently, Dinesh held a NRC-NASA Resi-
dent Research Associateship to conduct research
on chemical evolution and the origin of life at
the NASA Ames Research Laboratory. Later, he
moved to the Biological Oceanography Division of
Columbia University and investigated the disper-
sion of oil-spills, retardation of evaporation and


Shah receives Outstanding Service Award from Wayne
Chen, Dean of Engineering. Front row: John Biery, ChE
Department Chairman (deceased), Shah, Dean Chen,
K. S. Chan. Second row: Joseph Noronha, Wen-ching
Hsieh, Michael Chiang, Shih-Yung Shiao.

wave damping by thin films of surface active
In 1970, he joined the University of Florida as
an Assistant Professor and was promoted to Pro-
fessor of Chemical Engineering, Anesthesiology
and Biophysics in 1975. He has continued his re-
search love of the areas of monomolecular films,
foams, wettability and contact angle, microemul-
sions, liquid crystals, improved oil recovery, com-
bustion of coal dispersions in oil and aqueous
media, surfactant-polymer interaction, boundary
lubrication and surface phenomena in magnetic
media, membranes, lungs, vision and anesthesia.
The initiation of a multidisciplinary research
program on enhanced oil recovery jointly with
other colleagues in the department was a major
milestone in his research career. The international


recognition accorded to this program is a reflec-
tion of his relentless efforts and dedication. In the
summer of 1983, Dinesh was invited to present a
three-day short course on enhanced oil recovery at
the Imperial College, London. With frequent over-
seas visitors and students from various parts of
the world, his research group exudes a spirit of
international cooperation and harmony.
Dinesh introduced one undergraduate and two
graduate courses on interfacial phenomena to
chemical engineering curriculum which continue
to attract not only students from chemical engi-
neering but also from other engineering and basic
science departments. He has offered special topic
courses on membrane biophysics, biochemical en-
gineering and enhanced oil recovery processes.
A treat to listen to, Dinesh has presented about
one hundred papers at scientific meetings and two
hundred seminars at academic institutions and in-
dustrial laboratories. The first slide of his numer-
ous seminars (shown below) illustrates his ap-
proach to science and life. Besides being a keynote
speaker on several occasions, he has won two out-
standing paper awards at international meetings.
Among his one hundred publications are two books
he edited on enhanced oil recovery.
Dinesh's breadth of quality contributions is
remarkable. The University of Florida has hon-
ored him with its highest awards in each area of
teaching, research, and service, and the Federation
of Asian Indians in North America has given him
its "Outstanding Achievement Award".
"I am going to be an academic for my lifetime.
I could do other things but I wouldn't enjoy it. I
like the freedom. And I like the personal inter-
action with the students. You feel you are shaping
their careers. Essentially, you are expanding your

: IN


Tradional opening slide of Shah's speeches.

family. It's a great satisfaction". The common
bond of love, affection and mutual respect between
him and his students is maintained long after the
students leave his laboratory.
Perhaps Dinesh's approach to teaching, re-
search and education in general can be summar-
ized by the last sentence of his seminars, a quota-
tion from a poem by Tagore, which says "My

. . .. . ..-.

Shah and his family on a recent visit to India and the Tai

friend, drink my wine in my own cup to appreciate
its sparkling bubbles."
And Dinesh understands the meaning of fam-
ily and appreciates the support he receives from
the family in all his endeavors. His wife Suvarna
and two children are frequently seen at the chem-
ical engineering department. Guests at their home
often meet other relatives. And a delight for many
visitors is seeing the costumed children dancing to
drums tapped by their father.
Finally, there is always a verse. Deep thoughts
written mostly in Gujarati. Poetic philosophy
drafted en route in airplanes and in infrequent
quiet moments. Some to be published soon in two
languages that all in his two worlds may enjoy.
Of his adopted country he speaks positively.
"I like the general philosophy here in terms of
the appreciation of a person for his accomplish-
ments. That you are judged without consideration
of origin, race or creed.
"We see an occasional exception but by and
large this is so. You are allowed to become what
you want to become. You are the architect of your
life. There are no traditions or laws to follow and
"Wonderful!" E




The 1983 ASEE Chemical Engineering Di-
vision Lecturer was Warren Earl Stewart of the
University of Wisconsin. The purpose of this
award lecture is to recognize and encourage out-
standing 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 Lec-
ture of the Chemical Engineering Division, the
award consists of $1,000 and an engraved certifi-
cate. These were presented to this year's Lecturer
at the Annual Chemical Engineering Division
banquet, held at the Rochester Institute of Tech-
nology in Rochester, NY, on June 20. Professor
Stewart's lecture was entitled "Simulation and
Estimation by Orthogonal Collocation."

The award is made on an annual basis with
nominations being received through February 1,
1984. The full details for the award preparation
are contained in the Awards Brochure published
by ASEE. Your nominations for the 1984 lecture-
ship are invited. They should be sent to Warren
D. Seider, Chairman, 3M Award Committee, ChE
Department, University of Pennsylvania, Phila-
delphia, PA 19104.

A number of ChE's were honored with awards
at the ASEE meeting. The Chester F. Carlson
Award was given to Charles E. Wales (West Vir-
ginia University), and James E. Bailey (California
Institute of Technology) was the recipient of the
Curtis W. McGraw Award for Research. The
Western Electric Fund Awards, given on a sec-
tional basis, were: Middle Atlantic, Robert Kabel
(Penn State); Pacific Northwest, Louis Edwards
(University of Idaho; Rocky Mountain, E. Dendy
Sloan (Colorado School of Mines), Southeastern,

John Gainer (University of Virginia); St. Law-
rence, Arland H. Johannes (Rensselaer Poly-

The newly elected ChE Division officers are:
Dee Barker, Chairman; Angelo Perna, Past Chair-
man; Deran Hanesian, Chairman Elect; Bill Beck-
with, Secretary-Treasurer; Richard Noble, Pro-
gram Chairman; and H. S. Kemp, Robert Squires,
and H. Burpo, Members at Large.

1 stirred pots

Editor's Note: Some years ago a new tradition
was established at CalTech when Professor R. A.
Aris wrote a poem to honor the current lecturer
in the CalTech lecture series named in honor of
William N. Lacey. These poems, or songs, are now
performed at a banquet honoring the lecturer each
year and constitute a colorful and humorous col-
lection of tributes.
The 1983 Lacey Lecturer was Dan Luss of the
University of Houston, who was recognized with
the following poem.
Oh Danny Boy, the cusps, the cusps are calling
From tank to tank they make their winged way.
Uniqueness' gone, complexities appalling
Have risen up and, seemingly, to stay.
But came ye here with simple bifurcations,
Contact transforms and singularities,
You dazed us all with far-fetched explanations
And, Danny Boy, with such becoming ease.
From far ye came, in fact ye came from Houston,
To bring these marvels of reaction rate.
"Tex" Luss they call ye, so good are you at boostin'
The best department of the Lone Star state.
Ye also came to tell of strange perversions
Of hot-spots waxing when we thought they'd wane,
Of better feeds that yield worse conversions.
Oh, Danny Boy, you give us all a pain.
But are ye sure these stories all so racy
Lie well within the engineering ken
Or have you strayed, in these our lectures Lacey
Oh, Danny Boy, off into math again.


Central Campus

mp department


University of Kentucky
Lexington, KY 40506

of Kentucky had its beginning in an act of the
Kentucky legislature on February 22, 1865. The
act accepted the provisions of the Morrill Land-
Grant College Act and established the Agricultural
and Mechanical College of Kentucky, to be located
in Fayette County near the city of Lexington.
Six days later Governor Thomas E. Bramlette
signed into law another statute, which provided for
the consolidation of Transylvania University and
Kentucky University (a denominational school in
Harrodsburg). Transylvania, the oldest college
west of the Appalachian Mountains, had fallen on
lean years and the buildings of Kentucky Uni-

versity had burned the year before. The new
A & M College was made a college of the new con-
solidated Kentucky University.
All did not go well for the A & M College and
Kentucky University. The connection of the state-
supported A & M College with a private denomina-
tional school brought about dissension. As the situ-
ation grew worse the legislature began to look into
a solution and on March 13, 1878 passed an act re-
pealing the legislation that authorized the union
of the A & M College with Kentucky University
and providing that the Agricultural and Mechan-
ical College would forever remain a state institu-
tion free of all ecclesiastical entanglements and
control. Later Kentucky University changed its
name back to Transylvania University.
Problems were not yet solved for the fledgling
A & M College for the courts held that it had lost
all its land and buildings acquired while it was a
part of Kentucky University. A search for a new


� Copyright ChE Division, ASEE, 1983

home began and an offer from the city of Lexing-
ton to give the College fifty-two acres of the old
fair grounds was accepted. Thus the A & M College
was located on the site of the present University
of Kentucky by an act of the Kentucky legislature
in February, 1880.
In 1908 the name of the Agricultural and Me-
chanical College of Kentucky was changed to
"State University, Lexington, Kentucky" and
finally in 1916 the name was officially changed to
its present "University of Kentucky."

Although a department of chemical engineer-
ing did not formally exist until 1956, when it was
created at the request of the Chemistry Depart-
ment to replace an industrial chemistry program,
many prominent chemical engineers graduated
from the university prior to that date. Among
them are William H. McAdams, who was later
awarded an honorary D.Sc. degree, and E. V.
Just as the early years of the university did not
always go smoothly, the early years of the depart-
ment also encountered difficulties. The program
was formally initiated when Sam Hite (now at
Rose-Hulman) registered 16 freshman and 5
sophomores for the spring of 1957. The depart-
ment was housed in space made available in the
Mining Laboratory. It was not until 1966 that
Anderson Hall was completed and chemical engi-
neering was moved into the first floor of this build-
In the fall of 1958 Stan Heath and George
Crewe joined Sam. Stan remained for two years
while he finished a Divinity Degree at nearby
Asbury College. Sam and George held the fort to-
gether until Noel Moore (now at Rose-Hulman)
and Ed Litkenhouse came in the spring of 1964.
Ed taught one semester and then departed.
The early 1960's marked a major change in the
University of Kentucky. Previously the university
had emphasized undergraduate programs with
little regard to graduate education and research.
Under President John Oswald a major emphasis
was placed on the development of these areas. The
new orientation of the university translated into
major change for the department of chemical engi-
neering. Sam Hite left during the summer of 1966
and Bill Conger (now Head of Department at
VPI) and Tom Schrodt were hired as new as-
sistant professors in November 1966.
Bob Grieves (now Dean of Engineering, Uni-

versity of Texas at El Paso) joined the faculty as
Professor and Chairman in July 1967, soon fol-
lowed by Dick Kermode. With the resumes of Bob
and Dick attached, the department received ap-
proval for a Master's program in April 1967, thus
instituting its graduate program. The PhD pro-
gram was instituted in 1969 after the addition of
Charlie Hamrin (1968), Bob Brett (1968-now

Some of the ChE faculty in Memorial Coliseum, "The
House that Rupp Built." Left to right: front row, Asit
Ray, Bill Conger, Tom Schrodt; Center row, Dick Ker-
mode, Len Peters, Charlie Hamrin, Jonathan Berman;
Rear row, Dibakar Bhattacharyya.

with a consulting firm), Ed Moorhead (1969), and
Peter Skelland (1969-now at Georgia Tech).
The faculty has continued to grow with the
addition of Len Peters (1974), John Yamanis
(1975-now with Allied Chemical), Dibakar
Bhattacharyya (1979), Asit Ray (1980), and
Jonathan Berman (1982). The latest phase in the
development and growth of the department began
in 1979 when Bob Grieves moved to a position as
Associate Dean of the College of Engineering and
Len Peters took over the Chairmanship.
The first four BSChE degrees were awarded in
August 1959, the first MSChE degree in 1968, and
the first PhD degree in 1969. As of the 1982 winter
semester the department has awarded 559 Bach-
elors, 126 Masters, and 21 PhD degrees. As a point
of comparison, through 1964 the College of Engi-
neering had only awarded 576 Master of Science


In recent years a number of chemists and mathematicians have entered the graduate
program. We have developed a package which includes, in addition to the regular requirements, a core of
chemical engineering undergraduate courses . . . requiring) 3 to 3 1/2 years to finish.

and professional degrees and 6 Doctor's Degrees.
Many of chemical engineering's PhD graduates
have chosen teaching as a profession and are now
faculty members at Rensselaer, Auburn, Vander-
bilt, VPI, Iowa, and Cleveland State.
Much of the department's early development
under Bob Grieves was a result of his efforts in
obtaining Air and Water Pollution Traineeship
Grants and the Water Resources Institute. More
recently we have emphasized energy and especially
coal and oil shale. The proximity of the Kentucky
Center for Energy Research Laboratory of the
Commonwealth of Kentucky has helped in these
The present faculty of the department includes
Leonard K. Peters, Jonathan Berman, Dibakar
Bhattacharyya, George F. Crewe, Charles E. Ham-
rin, Richard I. Kermode, Edward D. Moorhead,
Asit K. Ray, and J. Thomas Schrodt.

The university is located in the heart of the
Kentucky bluegrass region, well known for its'
"beautiful horses and fast women." Lexington is
at one corner of an almost equilateral triangle with
Louisville and Cincinnati at the other two corners.
1-64, a main east-west artery, and 1-75, a main
north-south artery, intersect at Lexington-allow-
ing easy highway access to most of the eastern
The bluegrass region features a rolling grass
covered terrain dotted with horse farms. Most of
the major racing stables maintain farms in this
region. The topography of Kentucky is highly
varied, with the foothills of the Appalachians
within an hours drive to the east and the flat lands
of Kentucky several hours to the west. Kentucky is
noted for its extensive state park system and many
man-made lakes. Fishing for bass, crappie, trout,
muskie, and all kinds of panfish is available, and
all forms of boating are possible on the state's
lakes and rivers, including some good white-water
for the canoeing, kayaking, or rafting enthusiast.
Just an hour to the east of Lexington lies the
Daniel Boone National Forest where one may hike,
climb, canoe, and camp. Within the forest is the
Red River Gorge with its natural sandstone arches
and sculptured cliffs.


For the history buff there is much of interest
within the state. Lincoln's birthplace outside
Hodgensville is a state shrine, Stephen Foster's
"My Old Kentucky Home" is nearby, and there are
several battlefields of the Civil War. Daniel Boone
opened up Kentucky by leading settlers through
the Cumberland Gap; his grave can be found at
Frankfort and a replica of the fort he built is at
Boonesborough, just a half hour from Lexington.
The recreational assets of the state include the
cave country, where it is possible to explore hun-
dreds of limestone caves including Mammoth Cave.
Basketball must be mentioned when you speak
of Kentucky. It is more a religion than a sport-
there is even a rumor that Kentucky children are
born bouncing a ball.

The College of Engineering has a policy of re-
stricted entrance. This policy is in the process of
being revised, and if the revisions make it through
our university approval system, a new policy
should be in place by the fall of 1984.
Chemical engineering has proposed standards
that will be more restrictive than those proposed
by the college. Action on our restricted entrance
policy has been delayed pending action on the new
college policy. Our goal for an entrance policy in
chemical engineering is stated below.
High school applicants or transfer applicants
with less than 30 college semester credit hours
must meet all the following minimum admission
criteria: (1) an ACT composite score at or above
the 75th percentile on national (college bound)
norms, and (2) an ACT mathematics score at or
above the 80th percentile on national (college
bound) norms. All transfer students with at least
30 college semester credit hours must meet the
following minimum admission criteria: students
from UK Community Colleges, other UK pro-
grams, 3-2 programs with other universities, and
all other colleges and universities must have a
cumulative GPA of 2.7 or greater and not less than
2.5 in each area of chemistry, mathematics,
physics, and engineering.
Chemical engineering appears to get a dispro-
portionate share of the better students entering
the College of Engineering. Our students, on the


average, rank among the best in the college and
among the very best in the university.
While our program is just a little over 20 years
old, it has gone through many reorganizations and
modifications. In the 60's the College of Engineer-
ing went to core fluid mechanics, heat transfer,
and thermodynamics courses. Our students take
the first two, but we have successfully resisted the
core thermodynamics. We have maintained that
phase and chemical equilibria are so important to
our program that we must teach our own thermo.
In addition to the above courses we have 4
credit hours of stoichiometry, 5 hours of mass
transfer, and required courses in reactor design
and process control. The university requires 18
hours of general studies, and 6 hours of unre-
stricted electives. We have one further elective
that must be taken in the department. Finally, we
have the usual chemistry through P-chem, calculus,
physics, English and engineering science courses.
The result is a 4 year, 132 semester credit hour
curriculum leading to a BS in chemical engineer-
ing. In addition we have optional programs for
pre-med and pre-dent students, a 5 year co-op
program (just initiated), and an accelerated 4 1/2
year program resulting in a BS and MS. For the
fall of 1982, 325 undergraduates officially enrolled
in our department, and we graduated about 53
during 1982-83.
Kentucky has a community college system, and
a large number of students are transfers after 2
years of study. Considering this fact, for fall 1982
there were 400 undergraduates seeking a chemical
engineering degree in the University of Kentucky
system. Over 20 % of these were female.
We have active student chapters of Tau Beta
Pi, Omega Chi Epsilon, Society of Women Engi-
neers, Society of Black Engineers, and the AIChE.

We offer the MS in chemical engineering and
the PhD. The MS degree requires 24 semester
hours of course work, a thesis, and an oral exam.
There is an option to receive a MS on course work
only, but this is only used by special permission of
the faculty. In general it takes 16 to 18 months to
complete the program.
The requirements for the PhD are less specific.
There is no official course requirement, but in gen-
eral we require 30 semester hours past the MS.
The student must pass a 2 to 2 1/2 day qualifying
examination once his or her course work has been
completed, complete a dissertation on an original

research project, and successfully defend the work
in a final oral examination. Generally 2 to 2 1/2
years are required beyond the MS to complete the
PhD. A few students elect to bypass the MS and
work directly on the PhD.
In recent years a number of chemists and
mathematicians have entered the graduate pro-
gram. We have developed a package which in-
cludes, in addition to the regular requirements, a
core of chemical engineering undergraduate
courses. This program usually requires 3 to 3 1/3
years to finish.
Graduate offerings are listed in Table 1. Those
marked with an asterisk are required of all PhD
Graduate Offerings
Analysis of Chemical Engineering Problems*
Air Pollution Control
Transport I*
Chemical Reactor Design
Polymeric Materials
Advanced Chemical Engineering Process Design
Energy Engineering
Non-Newtonian Flow and Heat Transfer
Chemical Separation and Measurement for Chemical Engi-
Design of Rate and Equilibrium Processes for Water Pollu-
tion Control
Advanced Air Pollution Control
Air Sampling and Analysis
Equilibrium Thermodynamics*
Non-equilibrium Thermodynamics
Properties of Gases and Liquids
Transport II
Diffusional Mass Transfer Operations
Staged Mass Transfer Operations
Transport Phenomena in Packed and Fluidized Beds
Advanced Process Control I
Advanced Chemical Reactor Design*
Equilibrium and Rate Processes of Coal Conversion
Basic Electrode Processes in Electrochemical Engineering
Biochemical Engineering
Residence Credit for the Master's Degree
Residence Credit for the Doctor's Degree
Special Problems in Chemical Engineering

*Indicates core course in Masters Program

students. The reader will note there is an emphasis
on pollution and energy courses in the available
offerings. This relates to past and present research
interests of many of the faculty.
A full time graduate load is 9 hours, with many
students taking 12 hours. Most graduate students
are on 12 month appointments and are supported
by fellowships or research assistantships. The


Anderson Hall: The College of Engineering

current stipend is $8400/year plus tuition. A few
PhD students may teach regular department
courses with permission of the faculty and may
receive additional compensation for this service.

The graduate programs at Kentucky were
initially based upon air pollution and water pollu-
tion traineeship grants and the associated re-
search. While this is still a strong area of interest
in our faculty, most of our present emphasis is in
energy. In particular, we have faculty working in
shale oil, coal conversion, and hydrogen produc-
tion. The Kentucky Center for Energy Research
Laboratory of the Commonwealth of Kentucky,
which receives state and federal funding, is run by
the University of Kentucky and is located within
10 miles of the campus. Cooperation with this fa-
cility strengthens our energy programs. A recent
grant in this area is from Phillips Petroleum to
study eastern oil shale retorting.

Len Peters is in atmospheric transport and
chemistry on regional and global scales, and
physico-chemical behavior of aerosol systems. He
is studying the chemistry and transport of CH4
and CO in the global troposphere as a principal
subset of the carbon cycle. These theoretical stud-
ies are being compared against observations of the
CO concentration from 40�S latitude to 40�N lati-
tude obtained by an infra-red radiometer which
was flown on one of the space shuttle flights. He is
a co-investigator on that experiment.
He is also investigating the regional scale
transport, deposition, and chemistry of SO2, NOx,
and sulfates in the eastern United States. These
studies are aimed at understanding the formation
and distribution of sulfate aerosol and acid rain.
This and the previous study solve the three-dimen-
sional, time-dependent species continuity equa-
tions, including the non-linear chemistry, and are
solved on vector computers.
Asit Ray and Len are collaborating on studying
the physical and chemical processes of tobacco
smoke aerosol. Individual projects involve studies
on coagulation, growth in humid atmospheres,
physical and chemical characteristics of the aero-
sol, phoretic phenomena, the aerosol formation
processes, and deposition in the lung.
Dibakar Bhattacharyya has done extensive
work involving the development of novel separa-
tion processes with special emphasis in the area of
water pollution control. He has also worked on a
joint research project with Boliden Metal Corpo-
ration, Sweden, involving the study of sulfide pre-
cipitation systems for selective separation of toxic
metals and arsenic. His research interests are:
novel low-pressure membrane (charged and com-
posite membranes) processes for selective solute
removal and water reuse, recovery of metals by
sulfide precipitation, coal conversion wastewaters
and water recycle models, and eastern oil shale
retorting studies dealing with porosity change and
metal leachability.
Charlie Hamrin has four areas of active re-
search: determination of oxygen and nitrogen
in coal using instrumental neutron activation
analysis (joint with Chemistry Department), hy-
droliquefaction of oil shale, modeling of a catalytic,
cross-flow reactor, and solution of ordinary and
partial differential equations using computer
codes. In the first project he has measured oxygen
before and after drying by several techniques and
finds that only by assuming volatiles in addition to
water can the data be explained. The oil shale


project is an application of the tubing bomb re-
actor extensively used in coal research to study
kinetics of eastern oil shale hydroliquefaction.
Modeling of a cross-flow reactor is part of an over-
all program of a gas-liquid-solid reactor study in-
cluding the H-Coal ebullated-bed reactor. The solu-
tion of equations using computer codes has been
applied to the Graetz problem for circular tubes
and parallel plates. He has generated dimension-
less temperatures and Nusselt numbers in agree-
ment with the extensive tubulations of Shah and
London. Many problems involving transport phe-
nomena will be amenable to solution by computer
The main emphasis of Ed Moorhead's research
deals with electrochemical studies of oxidation and
reduction at conducting and semiconducting elec-
trode surfaces, and includes: investigating the
kinetic effects of surface and solution catalysis
(and photocatalysis), studies of mass transport to
various electrode geometries, development of new
or improved electronic measuring techniques (in-
cluding relaxation methods), measurement of ppb-
level trace metals, and application of in-lab mini/
micro computers for data acquisition and analysis.
He has recently developed (with NSF support)
the electromagnetically driven transverse oscillat-
ing resonant electrode ("TORE") wire for elec-
trode process studies. The vibrating wire (50
micron dia.) presents some challenging problems
in cylindrical diffusion which are presently being
addressed using finite element analysis.
Bill Conger's main interest in recent years has
been the use of the second law of thermodynamics
to analyze the energy inefficiencies in chemical
process flow sheets. In addition he is interested in
process simulations. He has combined these inter-
ests to analyze proposed hydrogen production
schemes and coal gasification processes. Presently
he is interested in using the second law analysis in
determining design alternatives.
Jonathan Berman has several areas of interest.
Among them are studies on diffusive and reactive
transport of oxygen in red blood cells and on
membrane blood oxygenators. He is presently
working on theoretical and experimental studies to
investigate the assumption normally made that the
internal contents of the red blood cell are in in-
stantaneous equilibrium with the local plasma sur-
roundings. His work on membrane oxygenators
centers around efforts to enhance the relatively
inefficient mass transfer process which results
from the separation of the two phases involved. He

is working on theoretical solutions consisting of
coupled asymptotic and numerical analyses and on
experimental verification of these solutions for
particular oxygenator configurations.
The above are examples of the interests of
some of our faculty showing the strong emphasis
of the department in the pollution and energy

We are faced with many of the same problems
that confront other departments across the coun-
try. Our undergraduate population is growing
rapidly, it is difficult to convince U.S. citizens to
continue in graduate school, and financial support
from the university is not what we would have it
to be, to name just three. In spite of these prob-
lems we feel we are a dynamic growing depart-
ment and our faculty is looking forward to what
the next five years and beyond will bring. Being a
very young department, we are experiencing grow-
ing pains; but maturing into a department that is
recognized and respected by others in our profes-
sion has made it all worthwhile. E

letters S

Dear Sir:
The possibilities for selection of reference states for
several thermodynamic functions are discussed in the
article "Reference States and Relative Value of Internal
Energy, Enthalpy, and Entropy" in the Spring, 1983 issue
of Chemical Engineering Education by Professor A. G.
Fredrickson. This letter is intended to suggest an alterna-
tive approach to that used in the article and some possible
reinterpretation and extension. My points are:
1. The results of the article can be derived more
satisfactorily from a starting point of simple closed system
equations rather than the model used, which is applicable
to complex open systems.
2. In discussion of an open system problem from
Modell and Reid's classic text, unwarranted physical
meaning is implied for the quantity total internal energy.
3. The discussion of reference states can be usefully
expanded to include Gibbs and Helmholtz free energy,
which are state functions of significantly different charac-
ter from those treated in the article.
The article starts with mathematical statements of
mass balance, first law, and second law applicable to
". . open, moving and deforming, and unsteady state
Continued on page 132.






Purdue University
West Lafayette, IN 47907

The eight papers which follow were all pre-
sented at the 90th Annual Meeting of the Amer-
ican Society for Engineering Education at Texas
A&M on June 22,1982. The Chemical Engineering
Division of ASEE sponsored a day-long series of
sessions on undergraduate thermodynamic in-
struction. The Annual Tutorial Lecture, by Pro-
fessor Joseph J. Martin, opened the day, followed
in the afternoon by a two-session symposium of
seven shorter papers.
These papers fall into two groups: the first
group presents teaching methods that, although
they are presented in the context of undergraduate
chemical engineering thermodynamics courses,
have much broader application and would be use-
ful methods in many other courses. The second
group of three papers presents application of re-
lationships that are specific to thermodynamics.
The authors in these papers emphasize the im-
portance of these specific relations in undergradu-
ate instruction.
In the first paper in the teaching methods
group, Prof. Alan Brainard describes how, at the
University of Pittsburgh, a series of over three
hundred 35mm slides, in conjunction with an
"Active-Involvement book" are used to increase
information transfer and student motivation.
Prof. Tom Daubert then describes how, at Penn
State, rather than teach a separate course in
thermodynamics, the material is integrated in the
overall curriculum. A similar idea is presented by
Profs. E. V. Cilento and J. T. Sears, who, at W.
Virginia U., after presenting the thermodynamic
fundamental concepts through standard lectures,
integrate these basic concepts with a design prob-
The next two papers discuss supplemental ma-
terials to be used in conjunction with a conven-
tional course. Prof. Jolls describes the use of com-

These papers fall into two groups:
the first group presents teaching methods
that... have... broad application and would be
useful methods in many other courses. The second
group of three papers presents application
of relationships that are specific
to thermodynamics.

puter generated two and three dimensional phase
diagrams that have recently been developed at
Iowa State. He believes that thermodynamics pre-
sents unique teaching difficulties due to its level of
abstraction and that computer generated phase
diagrams greatly aid in student understanding of
phase equilibrium. Finally, at Purdue University,
Professor Squires and D. V. Frank have developed
a series of twenty videotaped supplemental ther-
modynamic problems, covering topics from the
first law to phase and chemical equilibrium. Stu-
dent use of these problems outside of class time has
increased both the flexibility and efficiency of the
In the second group of papers, Prof. Joseph J.
Martin, the University of Michigan, contends that
the Fundamental Property Relation is one of the
four basic equations of thermodynamics. Consider-
ing its importance, it is surprising to find that the
generalization of the fundamental property rela-
tion to include effects other than thermal, com-
pression and mass change has led to considerable
confusion which this paper attempts to remedy.
Anyone who has taught chemical engineering
thermodynamics realizes the difficulty in present-
ing the concepts underlying phase equilibrium.
Professors Hall, Eubank, and Holste, of Texas
A&M, present an approach which uses the residual
functions to provide a starting point to derive the
fugacity equations.
In the last paper, Prof. Martin Sussman, Tufts
University, contends that greater thermodynamic
insights may be gained by considering a graphical
representation of the availability function. He then
applies this method to steady flow and chemically
reactive systems. O


leachsin? 2/1de,49'adA4ad T,..mrvltnMawar...


University of Pittsburgh
Pittsburgh, PA 15261

BEFORE LAUNCHING INTO a description of the STATE1- .
Methods that I utilize in my teaching, I feel
that definitions of the following terms are re-
LEARNING may be conceived of as a change, due to
experience, in the students ways of thinking, feeling,
and acting. The effectiveness of the learning process
may be thought of in terms of (1) the magnitude of the -
changes taking place in the individual student or (2) .
the proportion of students who have changed signifi- - -
cantly in one or more characteristics relevant to the ! ."
learning process. Thus conceived, education may be re-
garded as a system of learning experiences which brings :7 '
about certain desirable changes in students. [1]
MOTIVATION, in the scientific sense, may be defined
as the measure of the direction and intensity of the
expenditure of animal energy. . . . Human institutions
may be said to be formed primarily to motivate men ....
Educational systems are designed to motivate human
beings to accept a cultural heritage. [2] FIGURE 1.

The objective of my teaching can now be intro-
duced-I seek ways of maximizing the learning of


Alan J. Brainard is an Associate Professor of Chemical and Petro-
leum Engineering at the University of Pittsburgh. His M.S. and Ph.D.
degrees are from the University of Michigan. He worked for Exxon for
two years before joining Pitt. He was the recipient of the Western
Electric Award for Excellence in Engineering Education in 1976. He is
a past vice-chairman for programs of the Educational Research and
Methods Division of ASEE and continues to participate actively at both
the regional and national levels of that oragnization.

a given subject matter by providing conditions
which are motivational for my students. To be
more specific, this paper will discuss methods used
in teaching thermodynamics to students at the
University of Pittsburgh. The details of this ap-
proach have been described elsewhere [3,4] and
accordingly only the salient features will be intro-
duced here.
Three hundred and thirty nine 35 mm slides
were developed. The slides were prepared by using
pressure sensitive black letters and symbols (Tac-
type) on white cards. These cards include the
necessary definitions, postulates, laws, equations
and a limited number of applications of the sub-
ject matter. These individual cards were then
superimposed on colorful backgrounds and colored
slides were prepared from this combination. The
backgrounds include pop-art posters, colorful
wrapping papers and examples of contemporary
modern art. Figs. 1 and 2 present black and white
versions of two of the slides used in the thermo-

� Copyright ChE Division, ASEE, 1983


dynamics course.
Each of the cards used to prepare slides was
photographed and made into an Active-Involve-
ment book [5] for classroom use. Additional space
is provided on each page in this book for student
note taking. In use, the student can add relevant
material introduced by the lecturer directly in his
or her Active-Involvement book as the slides are
being shown. It has been my experience that I
communicate more information that serves to tie
the slides together and elaborate their meaning
with my continued use of them.
Now I must admit that when I first developed
my slides and their companion, the Active-Involve-
ment book, I thought that I would see immediate,
significant improvement in the ability of my stu-
dents to do problems in thermodynamics. After all,
hadn't these materials provided the motivation

namics problems; they must recognize that they
have to learn how to solve them also. Before turn-
ing to a discussion of my recent experiences con-
cerning my materials, I feel it appropriate to
spend time discussing educational objectives as I
feel they are an important element in self study
examples. Mager [7] was an early advocate of the
use of instructional (educational) objectives. Ac-
cording to Mager, a properly written instructional
objective must:
1. Describe what the learner will be doing when demon-
strating that he has satisfied the objective;
2. Describe the important conditions under which the
learner will demonstrate his competence;
3. Indicate how the learner will be evaluated, or what
constitutes acceptable performance.
The book by Mager [7] and a paper by Stice [8]
provide a good discussion on the preparation of in-

The objective of my teaching can now be introduced-I seek ways of maximizing
the learning of a given subject matter by providing conditions which are motivational for my students.
To be more specific, this paper will discuss methods used in teaching thermodynamics...

necessary to greatly enhance student learning?
For some students the answer was yes, but, un-
fortunately, for most the answer was no. I began
to see that the slides presented the theory but the
students needed additional help in applying the
theory to solve problems. If I wanted the students
to demonstrate problem-solving skills I had to pro-
vide them with lots of practice of those skills
and/or lots of examples of solved problems. The
book by Abbott and Van Ness [6] in Schaum's Out-
line series was not available so I elected to prepare
materials of my own. I generated a series of self
study examples that serve as a major input for
student learning outside the classroom. These self
study examples now number in excess of 100, with
examples both in the "British" system and SI sys-
tem of units. The examples are of two types:
1. Those having a problem statement followed by a list-
ing of the educational objectives which are appropri-
ate for the solution of the problem followed by a
detailed solution to the problem;
2. Ones similar to those described above but which leave
some of the steps of the solution up to the individual
student to complete.
The later category is necessary. Without it, too
many students just sit back and do not "dig" hard
enough with those self study examples that are
solved completely. It is not enough for them to
recognize that I know how to solve thermody-

structional objectives. Two aspects concerning the
use of instructional objectives discussed in Stice's
paper deserve our attention. First, several objec-
tions to the use of instructional objectives are
raised and shown to be without merit. Second,
Stice comments on the fact that others are too rigid
in their choice of words used to write acceptable
objectives. In particular, Walbesser et al [9] sug-
gests that only the following nine action verbs are
to be employed: to name, identify, describe, con-
struct, distinguish, demonstrate, order, state a
rule, and apply a rule. Stice suggests that words
like "derive", "explain", "calculate", and "esti-
mate" are sufficiently unambiguous to be added to
the above set. I, too, find these words convenient
and well understood when used to prepare objec-
tives for students. Certainly just which words can
be considered to be acceptable will depend upon the
subject matter of concern.
Objectives 1, 2, and 3 shown below are specific
examples of educational objectives used in my

Example 1.
The student must be able to utilize the relationship
h - u + pv
to convert the specific internal energy into the spe-
cific enthalpy and vice-versa.



Example 2.
The student must utilize the fact that two inde-
pendent intensive properties are sufficient to set the
intensive state of a simple comprehensive fluid.
Example 3.
Given a table of thermodynamic properties of a fluid,
a steam table for example, the student must be able
to correctly locate a given equilibrium state once the
conditions described in Example 2 have been met.

I am convinced of the merit of using educa-
tional objectives and encourage you to prepare
them for your students. I have found, however,
that students are largely unfamiliar with them and
some class time must be devoted to explaining their
importance and their use.
Now we get to the "bottom line"-do my ma-
terials work? I think they do and I base this judge-
ment on two sources of information:

* My own experiences in testing students with and with-
out the materials.
* Student reactions described in course evaluations.

While both of these sources are subjective, I
feel that they do provide evidence of an enhanced
learning experience for my students. Students do
demonstrate considerably more organization in the
solution of thermodynamics problems. Their ap-
proach is more direct and largely avoids many of
the errors in applying the basic principles of the
subject matter. I feel that the self study examples
are largely responsible for this.

What are the students' reactions? The follow-
ing is a summary of student response gathered
from an anonymous survey taken near the end of
the course.
The instructor was considered an interesting and dedi-
cated teacher who cared about his students. The course
was well structured and the instructor used new teach-
ing techniques successfully. The work book (Active-
Involvement book) was excellent.
The following represents individual student com-
I came into this course with apprehension. I was told
that thermo was the hardest and dullest course of all
the engineering courses I was ever to take. However,
Dr. Brainard has made this the most interesting as well
as informative course I have ever taken. His zeal for
the subject is extremely apparent and he communicates
this well to the class.
It is encouraging to see someone take as much time in
preparing a course as Dr. Brainard has.
Dr. Brainard is unbelievably dedicated and concerned
about the student. His self study examples are very

I feel these comments speak for themselves.
Will my material work as successfully for
others? I don't know. I have found that faculty
tend to develop an inertial effect in their teaching
methods. (I am no doubt guilty of this also.) Cer-
tainly individual faculty members will and should
develop their own style and that style must be one
that they believe in and are comfortable with. E

1. Bloom, B. S., "Testing Cognitive Ability and Achieve-
ment" in Handbook of Research on Teaching, ed. by
N. L. Gage, Rand McNally & Co., Chicago, 386 (1968).
2. Anon., Kaiser Aluminum News, 26, No. 2, 3 (1968).
3. Brainard, A. J., and H. T. Cullinan, Jr., "New Instruc-
tional Media for Teaching Large Classes," Engineering
Education, 62, No. 8, 930 (May, 1972).
4. Brainard, A. J., "Preparing Effective Slides for Class-
room Use," Engineering Education, 66, No. 5, 412-414
5. Brainard, A. J., A Course In Thermodynamics, Mono
Book Corp., Baltimore, Maryland (1970).
6. Abbott, M. M., and H. C. Van Ness, Thermodynamics,
Schaum's Outline Series, McGraw Hill Book Co., New
York, NY (1972).
7. Mager, R. F., Preparing Instructional Objectives,
Fearon Publishers, Belmont, California (1962).
8. Stice, J., "A First Step Toward Improved Teaching,"
Engineering Education, 66, No. 5, 394-398 (1976).
9. Walbesser, H. H., E. B. Kurtz, L. D. Goss, and R. M.
Robl, Constructing Instruction Based on Behavioral Ob-
jectives, Engineering Publications, Oklahoma State
University, (1971), p. 14.



Pennsylvania State University
University Park, PA 16802

SINCE 1972 THE CHEMICAL Engineering Depart-
ment at Penn State has attempted to eliminate
compartmentalization of basic course material by
providing a presentation which attempts to show
students the relationships between the various
parts of the sophomore and junior level required
courses. Thermodynamics has been the integrating
factor in many respects. In brief the following in-
tegration has taken place.
The first law of thermodynamics is combined
with the material balance and industrial chemical
processes as has been the case at most universities
for many years. After this point, the study of the
second law and its applications is carried out con-
currently with the study of fluid mechanics and
heat transfer such that some of the applications
can be seen immediately. Phase equilibria is
studied in the same course with mass transfer,
while chemical equilibria is covered in the basic
course in chemical kinetics and reactor design.
Table 1 notes a brief outline of the material in
these courses. As Penn State moves to a semester
system in 1983, we intend to continue this ap-
proach with the exception that the first law will
have to be separated from the stoichiometry and
coupled with the second law.

Thomas E. Daubert, Professor of Chemical Engineering at Pennsyl-
vania State University, has been at Penn State since 1961. His teaching
and research interests are in the area of physical, thermodynamic, and
transport properties. In addition to the text described in this paper he
has co-authored two other books.

Curriculum Content
Chemical Process Industries and Stoichiometry
First Law of Thermodynamics and Applications
Organic and Inorganic Chemical Processes in Brief
Material Balances
Fluid Mechanics including mass, energy, and momentum
balances and compressible flow.
Heat Tranfer including basic modes of conduction, con-
vection, and radiation and design of systems
Equations of State
Thermodynamic Properties of Real Fluids
Entropy and the Second Law of Thermodynamics Rela-
tions among Properties and Diagrams
Engines, Compressors, Refrigeration, Liquefaction
Chemical Process Thermodynamics
Homogeneous fluid mixture properties: Fugacity and
Phase Equilibria and Diagrams
Equilibrium Stage Separations: Single and Multiple
Gas-Liquid (Absorption, Distillation)
Liquid-Liquid (Extraction)
Fluid-Solid (Leachng, Adsorption)
Interphase Mass Transfer-Diffusion
Differential Continuous Contacting
Equipment Dimensions
Simultaneous Heat and Mass Transfer
Chemical Reaction Equilibria in chemical process sys-
tems for homogeneous and heterogeneous systems
and single and multiple reactions
Chemical Kinetics and Equilibrium-basic principles and
Chemical Reactors and Systems
Homogeneous Reactions in ideal batch, continuous
stirred tank, and tubular reactors including design
of reactors
Introduction to heterogeneous (catalytic) reactions,
models, and reactor designs

Does such an approach have merit? Our experi-
ence shows that two of the perennial student im-
pressions are alleviated, i.e., "Thermodynamics is
not relevent to actual situations" and "I've never
seen that equation or method before." Whether
such a method better promotes a fundamental
understanding of thermodynamics in the long run
cannot be proven except that feedback indicates

� Copyright ChE Division, ASEE, 1983


the student acceptance of thermodynamics of
equilibria are much improved by the inclusion of
this material together with mass transfer and
Following up the integrated approach is a
senior-level elective in thermodynamics which
stresses and reenforces broader applications of the
basic principles as well as giving a deeper treat-
ment of equations of state and more sophisticated
calculational methods. Included is the use of both
a physical and thermodynamic property data base
package and subroutines for solving various equa-
tions of state for various thermodynamic param-
eters with main programs supplied by the students.

"Introductory Thermodynamics for Chemical
Engineers" is a first level textbook which attempts
to summarize the aspects of thermodynamics nec-
essary to formulate, design, operate, and control
chemical processes of the 1980's. Continuous ad-
vancement of thermodynamics has occurred at
such an increasingly rapid pace that no textbook
can attempt to cover the entire field. The book de-
veloped is a textbook, not a research monograph,
and does not advance new theories; it does attempt
to summarize the salient features of current re-
search which will be helpful in using the thermo-
dynamic methods which are currently most ac-
curate and convenient.
The book begins with an introductory chapter
which provides necessary background and defini-
tions of common terms and quantities of thermo-
dynamics. The first major chapter treats equations
of state (both analytical and corresponding states
approaches) in some detail, emphasizing the meth-
ods which are now used by industry rather than
the historical perspective offered by most texts.
This allows immediate use of any equation of state
in subsequent chapters on the first and second laws
of thermodynamics, phase equilibria, and chemical
equilibria. This approach is unusual in that most
texts relegate equations of state to a later chapter
following the first and second law treatment. The
latter treatment requires that all topics must again
be considered as only the ideal gas law is available
for the first pass.
A unique feature of the book is the chapter on
estimation of auxiliary physical properties neces-
sary for thermodynamic calculations. Most equa-
tions of state and other thermodynamic methods
require critical properties and third parameters.
Densities, molecular weights, normal boiling

... feedback indicates the student acceptance
of thermodynamics of equilibria are much improved by
the inclusion of this material together
with mass transfer and kinetics.

points, and vapor pressures are often also re-
quired. Treatment of mixtures is quite necessary
in processing calculations. Quite often these data
are not readily available and sometimes experi-
mental values do not exist. Thus, drawing on work
as co-author of the Technical Data Book-Petro-
leum Refining for the petroleum industry through
the American Petroleum Institute and background
for the Data Prediction Manual for the chemical
industry through the AIChE Design Institute for
Physical Property Data, the author has included
in a separate chapter in the text, the most up-to-
date generalized prediction methods for each of
these properties.
The text is arranged in nine chapters. Treat-
ments tend to be brief so that students do not get
lost in the prose. Line drawings, diagrams, and
plots are included throughout. Exercises for the
student are liberally located throughout the text
following the appropriate subsections. Such ex-
ercises allow a student to more clearly determine
his or her understanding of the material and are
valuable for both normal classroom instruction or
self-study of the material. Lists of problems fol-
low each chapter and references to topics discussed
and bibliographies of the most important current
literature, reviews, and compendia are included in
each chapter. Appendices listing pure component
physical properties of common compounds, selected
thermodynamic properties of model compounds,
thermodynamic properties of steam, and conver-
Skeleton Table of Contents
I. Purpose, Usefulness, and Definitions of Thermody-
II. PVT Properties of Fluids-Equations of State
III. Conservation of Energy-First Law of Thermody-
IV. The Second Law of Thermodynamics and its Appli-
V. Relationships Among Thermodynamic Properties-
Graphical Representation of Properties and Pro-
VI. Estimation of Auxiliary Physical Properties of
VII. Solution Properties and Physical Equilibria
VIII. Physical Equilibria Among Phases
IX. Chemical Equilibria


sions among different systems of units are in-
cluded. Table 2 gives as skeleton table of contents
including only chapter titles. A complete table of
contents is available from the author.
The text is designed for a first course in chem-
ical engineering theromodynamics at the late
sophomore or junior college level. No previous
thermodynamic study is required. The goal is a
balanced treatment between essential thermody-
namic principles and the methods actually used in
current practice to calculate thermodynamic prop-
erties and to use modern equations of state.

My philosophy is clear. Beginning chemical en-
gineering thermodynamics should be vital, up-to-

date, and presented in as simple a form as prac-
ticable to solve problems of industrial importance,
while not compromising the underlying principles.
Since thermodynamics pervades almost all areas
of practice and many students never receive any
additional formal study in the field, it is incum-
bent upon professors to make certain that the
beginning courses in the field provide the back-
ground for students to function as working chem-
ical engineers.
The mode of presentation of the material is
variable; it may be integrated with other subjects
or presented by itself, or may be offered tradition-
ally by lecture-recitation or with modern teaching
aids or self-study. The most important feature,
however, is the content, assuring that our students
can effectively practice their profession. O


West Virginia University
Morgantown, WV 26506

THERMODYNAMICS IS AN abstract subject, which
students have more difficulty in relating to their
more concrete career objectives than studies in
subjects like unit operations. As most students will
utilize thermodynamics in the future in a support-
ing calculation mode, it was thought desirable to
emphasize the important connection of thermo-
dynamics to design concepts in a direct way. Thus
the general goals of thermodynamics course work
can be stated such that at the conclusion of their
studies the students should

* learn the important fundamental concepts of thermo-
dynamics, and
* be able to utilize the concepts of engineering calcula-
tion problems (including design).

Time was made available in the course for both


The first goal was covered through standard
lectures, using overheads etc., with the accompany-
ing text written by S. I. Sandler, "Chemical and

Engineering Thermodynamics." A synopsis of the
syllabus covered includes the common concepts:
First Law
Second Law
Real Substances
Multicomponent Mixtures
Gibbs Free Energy
Phase Equilibrium
Chemical Equilibrium
The text served the course well and has many
good features. It has an excellent presentation of

TO: Design Group
FROM: L. Brightman, Director Design Services Goal, Inc.
SUBJECT: Recirculating Solids Boiler Concept
Please analyze the recirculating solids boiler concept,
outlined on the attached sheet, as compared to a conven-
tional industrial-heat boiler. Dr. R. C. Bailie, consultant,
will present complete details at a meeting tomorrow.
List advantages and disadvantages of this system for
use in generating steam from coal, oil or waste from our
LP-7 plants. The results of your study and recommenda-
tions will serve as a basis to determine if further develop-
ment work is justified.
Include in your analysis the net steam efficiency as a
function of fuel feed, the efficiency potential for electrical
production of the steam as a function of fuel load, and
operational characteristics as a function of fuel capacity.
Your report is due five (5) weeks from Thursday, on
December 5th.

SPresently at Montana State University

� Copyright ChE Division, ASEE, 1983


phase and chemical equilibrium. It has a new ap-
proach to the development of the second law by
using a pseudoconservation equation, in parallel to
the energy balance for the first law. This perhaps
causes the instructor some difficulty, but less to the
student. As with many instructors, we desire more
example and illustrative problems.


Throughout their school years, most students
have learned to examine a problem by searching
for the appropriate equation(s) needed to solve
the problem. Conceptualizing the control volume
and stating reference conditions, are new modes
of problem solving. The students are often con-
fused by errors such as thinking all liquids are
saturated liquids, not understanding the meaning
of a sign on an answer, or misinterpreting the
steps of a flow process on a p-H diagram.
To help alleviate these types of errors, to inter-
relate thermodynamics with other engineering
course material, and to motivate the students, we
try to integrate basic concepts with a design prob-
lem. Often the problem may be multi-faceted and
the same design may be studied from a different
point of view in a companion course. Designs we
have used have focused on chemical equilibrium
limits in reactors, physical properties of materials
for portable heat paks, calculation of ionic acitiv-
ity coefficients for solubility limits, and process

.- -, .

Eugene V. Cilento is an Assistant Professor at West Virginia Uni-
versity. He did his undergraduate work at Pratt Institute, receiving his
BChE in 1973. His graduate studies were performed at the University
of Cincinnati, where he received his M.S. in 1976 and PhD in 1978.
His research interests are in biomedical engineering and include
projects in biological transport phenomena using whole organ per-
fusions and in vivo microscopy. (L)
John Sears, Professor and Head of Chemical Engineering at Montana
State University, has been active in educational innovation for over a
decade. He helped organize the PRIDE program at West Virginia Uni-
versity upon which this paper is based. (R)

.. we try to integrate basic concepts
with a design problem. Often the problem may be
multi-faceted and the same design may be studied from
a different point of view in a companion course.

lIn NOIJSniw03
- V


*u " ' . 3

- SB a nd
s'L ~

Bed-B1-Modal Size Distribution
Large Particles for Large Uif
Small Particles for Elutriation and Sensible Heat
-Combustion without Internals Disturbance
Cyclone-Return Small Particles to Bed
Heat Removal-Steam Generation
-hair/entrained particles
Schematic: Recirculating Solids Boiler

Figs. 1 and 2 illustrate a recirculating solids
boiler design concept we analyzed three years ago.
This project was analyzed by the students in con-
junction with a unit operations course. The stu-
dents were broken into small groups to analyze
and discuss the advantages or demerits of a re-
circulating waste boiler as compared to a conven-
tional fluidized bed boiler. Discussion of the fluid
flow through a packed/fluidized bed, cyclone, and
heat transfer could be emphasized by the unit


operations course. Process efficiency and Rankine-
cycle efficiency as a function of turn-down ratio
can be discussed from a thermodynamic viewpoint.
The advantages of a 6:1 turndown ratio with good
operability, lack of heat-exchange tube burnout
and reduced start-up can be discussed in terms of
process efficiency. The problem is open-ended, lim-
ited by student time and knowledge. The project
was extremely well-received by the students, who
became very interested in the design.

Major advantages of the integrated design in-
* student motivation-making the subject more con-
crete, rather than an abstract subject
* emphasis on interrelation of variables (such as ef-
ficiency) with process design operability concepts
* reinforcement of particular thermodynamic concepts
by use in the design analysis.

An ultimate test is whether the students feel
more comfortable and able using thermodynamics
in subsequent work. In one case of design problem
subsequently on separations, the students used
Debye-Huckel theory to calculate mixed-salt ionic
activity coefficients to find solubility limits in a
crystallization problem.
Disadvantages are mostly time commitments.
Design takes class time, and the philosophical de-
cision on such time must be made as to the worth
of design integration at that point in a curriculum.
If the design is done in conjunction with a second
course, then some planning and integration be-
tween faculty instructors is necessary. If an indi-
vidual instructor decides to add this design ele-
ment to his course independently, then a full un-
derstanding should be present that this component
replaces some more details on particular topics.
We are convinced that this approach is a worth-
while concept. O



Iowa State University
Ames, IA 50011

PREVIOUS PUBLICATIONS [1,2,3,4,5] have described
programs that generate projections of thermo-
dynamic phase surfaces through computer graph-
ics. Using these techniques, we have produced
diagrams representing the properties of water and
steam and the pressure-volume-temperature be-
havior of most of the common equations of state.
These programs have been used successfully with
a variety of output devices, such as CalComp and
Versatec plotters, Tektronix storage terminals,
and an Evans and Sutherland Multi-Picture Sys-
tem. In addition to making possible phase dia-
grams that have previously been unattainable, our
programs also offer several options that enable the
user to emphasize thermodynamic features of spe-
cial interest.

0On leave 1981-82 at the University of California at
Berkeley. 2Currently with Eli Lilly and Company, Lafay-
ette, Indiana.

'ErS V - Cr T C. +" ~".""
"- (RT - A - T/T 2) R Tb .

S. -- .2 pla T - s0 9.6 wR
I CopyTight, ChE Di vilo, A 198 �
4 - T '-^ -- -- - - , NEAR S0EAL IN PRESSURE AID VOL2R1

I _ ..
IL I -' _ " -: '-_ '._I. , . . - .

FIGURE 1. Benedict-Webb-Rubin equation of state for

Fig. 1 presents a P-V-T diagram drawn with
this technique. The surface is generated by the
Benedict-Webb-Rubin equation as applied to ethy-
lene. A two-phase region consistent with that equa-
� Copyright ChE Division. ASEE, 1983


tion has been superimposed on the surface through
use of an algorithm due to Balzhiser et al [6].
The principal use for these diagrams has been
in teaching. Thermodynamics, because of its level
of abstraction, has gained a longstanding unpopu-
larity among students. Even the best teaching ef-
forts have often been ineffective because of the
gap in understanding between instructor and stu-
dent. The reason for this has often been that
words, symbols, and equations have not been ade-
quate to present abstract ideas to students with
any assurance of their being grasped. Something
more tangible has been needed to catalyze compre-
hension until more of the subtleties of thermody-
namics are understood and the enormous value of
the subject appreciated.
Phase diagrams offer a vehicle for doing this.
By utilizing the geometrical interpretation of
property relationships, they provide a more con-
crete model of physical behavior than do the
theoretical statements from which they are de-
rived. While the experienced thermodynamicist
sees instinctively how properties influence pro-
cesses-inversion in a Joule-Thomson expansion,
for example-students may not understand this
and may require more explanation. On a model of
the enthalpy-pressure-temperature surface, the
Joule-Thomson inversion curve stands out as a
distinct topographic feature. If presented with
such a model, students will see this and expect a
system to behave differently on opposite sides of
the curve as experiments show.

Kenneth Jolls earned his BSChE
at North Carolina State University
and his graduate degrees at the
University of Illinois, where he
worked for T. J. Hanratty. After five
years at the Polytechnic Institute
of Brooklyn, he moved to Iowa
State University where he is pres-
ently on the faculty. His chemical
engineering interests are in thermo-
dynamics and applied electronics,
and he has held several NSF grants
related to teaching improvements in
both areas. The last of these are
supporting his current sabbatical
year at Berkeley. Outside of engineering, Dr. Jolls has a strong interest
in music. He has a degree in music from Duke University and is a
regularly performing jazz player. (L)
John Burnet studied computer science at Iowa State University and
obtained experience there in applications programming related to
thermodynamic property diagrams. He is currently a free-lance pro-
grammer in Berkeley, CA, and continues to develop graphics software

Phase diagrams... provide a more
concrete model of physical behavior than do
the theoretical statements from
which they are derived.

If problems with conceptualization exist in
pure systems, they are even more prevalent in
mixtures. Since the properties of multicomponent
systems depend on more than two independent
variables, complete phase diagrams in such cases
are beyond construction through conventional
graphics. One or more variables must be elimi-
nated and our attention restricted to subsets of the
data possessing three-dimensional character.
The loci of saturated-liquid and saturated-
vapor states in a system of two components com-
prise such subsets. These surfaces (called bubble-
point and dew-point) may be plotted in pressure-
temperature-composition (P-T-x,y) space to give
an envelope portraying all states that coexist in
liquid-vapor equilibrium. Such information is im-
portant in separation processes and also reveals
the macroscopic behavior resulting from a given
solution model.
Some notable attempts have been made to con-
struct these figures by hand [7,8], but only a small
number are available, and even these are often
limited in detail. Even through computer graphics,
solution diagrams require more effort than those
for pure components. In the latter case the gen-
erating equations are straightforward, and we are

for use in teaching. (C)
Jeffrey T. Haseman is a process engineer at the Tippecanoe Labora-
tories of Eli Lilly and Company in Lafayette, IN. For the past year he
has been associated with antibiotic synthesis and production. He
graduated from Carthage College in Kenosha, WI, with a BA in chem-
istry and is currently completing the thesis requirements for his MS in
chemical engineering from Iowa State University. (R)


able to compute and plot simultaneously. Con-
structing P-T-x,y diagrams, however, requires far
more effort, both for the acquisition and for the
management of data. Determining the gamut of
vapor-liquid equilibrium states for any binary sys-
tem would be too costly, and some type of com-
promise is necessary.

For the work reported here, the program of
M. S. Han and K. E. Starling [9] was used as a
data base for mixtures. This program is based on
the modification of the BWR equation described
by Cox et al [10]. Extension to mixture-property
prediction is through mixing rules analogous to
those developed by Bishnoi and Robinson [11] and
by means of a generalized correlation of the prop-
erties of pure fluids [12]. Predictions of density
and enthalpy departure with this program com-
pare favorably with experimental data, and vapor
pressures are also accurately determined.
An interaction parameter k1j accounts for devi-
ations from ideal solution behavior for each pair
of components accessible to this program. Since kij
strongly influences vapor-liquid equilibrium cal-
culations, its values are based on VLE data. Ref-
erence [13] presents a tabulation of k, values along
with phase-equilibrium predictions that justify
their use in this method.
As obtained from the authors, the Han-Starling
(H-S) program operated in batch mode and pro-
duced output summarizing the properties of a
pure component or mixture either in a specified
state or in a final state resulting from a specified
process. For this project, the H-S routines were
fixed within an executive program that directed
computation along paths of constant temperature,
pressure, and composition in the bubble- and dew-
point surfaces. A bi-cubic spline program deter-
mined a "best surface" through the true points,
and the projections of the smoothed isotherms,
isobars, and isopleths were produced in the same
manner as for the pure-component diagrams [14].

Fig. 2 shows the P-T-x,y diagram for the sys-
tem normal butane-normal heptane. Four complete
isothermal sections and four complete isobaric
sections are drawn. Tie lines which mark the inter-
sections between isobars and isotherms have been
added by hand to connect coexisting liquid and
vapor states. The initial estimates required by the

FIGURE 2. P-T-x,y

diagram for

normal butane-normal


H-S subprograms that perform bubble-point and
dew-point calculations were derived geometrically.
Computational difficulties with the Han-
Starling program prevented us from obtaining
convergence in the vicinity of the critical locus. It
was, therefore, not possible to construct the pre-
cise critical curves that match the P-T-x,y dia-
grams shown in this paper. The dashed curves that
are shown were obtained by using the method of
Prausnitz and Chueh [15], first to estimate critical
temperatures and volumes, and then to compute
the critical pressures from a modified Redlich-
Kwong equation. Construction of isotherms and
isobars between the pure-component critical was
begun in the usual way, but when a composition
was reached where convergence could no longer be
obtained, the section was left open at that point.
The final step in each drawing involved the
construction of dew-point and bubble-point iso-
pleths. Data for these curves were accumulated in
earlier steps, then arranged into bubble-point and
dew-point arrays, and finally fitted to smooth iso-
pleths using a 2-D spline.


s s� o �..2 .0 1 E
FIGURE 3. P-T-x,y diagram predicted by Raoult's Law.
Vapor-pressure curves are for nC4 and nC,.



FIGURE 4. P-T-x,y diagram for COz-ethane.

These procedures yielded a wireframe model of
the bubble- and dew-point surfaces with border
regions and tic marks added for completeness.
Embellishments beyond the basic structure have
been added by hand to give the result shown in
Fig. 2.

Because of their chemical similarity, butane
and heptane form nearly ideal solutions which, at
low pressures, conform closely to the model pre-
dicted by Raoult's law. This is illustrated by com-
parison to Fig. 3 where the P-T-x,y diagram pre-
dicted by Raoult's law has been constructed for a
mixture of pure components with vapor-pressure
curves identical to butane and heptane.* Having
no critical region, Fig. 3 has been left open at the
top with unterminated isopleths to signify con-
tinuing ideality. The surfaces in Fig. 2 do develop
a negative deviation at higher pressures as shown
by the bubble-point isotherm at 2900 F.
More pronounced nonideality is seen in Fig. 4
where, for the carbon dioxide-ethane system, the
Han-Starling program predicts a minimum-boiling
azeotrope over the entire range for which constant-
property sections were determined. This is in good
agreement with data reported by Gugnoni et al [16]
and by Khazanova et al [17]. Although Fig. 4 was
constructed in the same manner as the diagrams
representing nonazeotropic systems, computa-
tional procedures were sufficiently different to
necessitate a separate version of the program.

Constructing phase diagrams through com-
puter graphics gives one control over various
artistic effects. These effects can often enhance a
diagram and emphasize topographic features of
thermodynamic interest. Nonlinear scaling and
automatic smoothing are examples of this and
were both used in the construction of Fig. 1. Vari-
able orientation, adjustable perspective, variable
line structure, and the drawing of superimposed
views and stereo pairs are further options.
Controlling the degree of perspective in the
. drawings gives a depth effect to the three-dimen-
sional figures. While this is desirable in a pictorial
view, it would not be so in the side or top view one

*Fig. 3 was drawn with a Versatec electrostatic plotter
and uses heavier lines for bubble-point curves than for dew-
point curves.


-- ----

- I

52 = -.N �F 1- I
P, z 396.H
K �r

S --


O 1 s1 F i p1


- if

FIGURE 5. Pressure-composition projection of Fig. 2.

obtains by setting the orientation angles at 0�, 90�,
etc. As an example of this, Fig. 5 shows the "flat"
view of the butane-heptane diagram that com-



FIGURE 6. Temperature-composition projection of Fig. 4.

prises the pressure-composition plot. Similarly,
Fig. 6 shows the T-x,y projection for the CO2-
ethane system.


Modern computer graphics provides the means
for constructing thermodynamic phase diagrams
in number and variety never before possible.
Individually or in groups, these diagrams have
the ability to convey information about properties
and processes that would otherwise require tedious
-and often confusing-explanation. The dia-
grams described in this paper, or any of their
variants, can be compressed, expanded, molded, or
altered in any way that makes thermodynamic
subtleties easier for students to understand.
Coupled with an approach that attempts to explain
physical property behavior in terms of funda-
mental concepts, phase diagrams can complete the
picture the teacher wishes to draw. Such ideas
were not overlooked by Gibbs [18] as he began his
first paper on graphical methods in 1873:

Although geometrical representations of propositions in
the thermodynamics of fluids are in general use, and
have done good service in disseminating clear notions
in this science, yet they have by no means received the
extension in respect to variety and generality of which
they are capable.


Major support for this work was provided by
the Iowa State University Engineering Research
Institute and by the Local Course Improvement
Program of the National Science Foundation. [


1. Jolls, K. R., G. P. Willers, and L. D. Jensen, Trans.
Am. Soc. Eng. Educ., Comput. Educ. Div., 8, 10
2. Jolls, K. R., G. P. Willers, and L. D. Jensen, Educom,
12(4), 19 (1977).
3. Jolls, K. R. and G. P. Willers, Cryogenics, 18, 329
4. Willers, G. P., "The Construction of Thermodynamic
Phase Diagrams Through Computer Graphics," M.S.
thesis, Department of Chemical Engineering, Iowa
State University, Ames (1978).
5. Jolls, K. R., "Research as an Influence on Teaching,"
accepted for publication in J. Chem. Educ. (1983).
6. Balzhiser, R. E., M. R. Samuels, and J. D. Eliassen,
"Chemical Engineering Thermodynamics: The Study
of Energy, Entropy and Equilibrium," Prentice-Hall,
Inc., Englewood Cliffs, N.J. (1972).
7. Dickerson, Richard E., "Molecular Thermodynamics,"
W. A. Benjamin, Inc., Menlo Park (1969).
8. Wales, C. E., Chem. Eng. (1963), May 27, p. 120;


June 24, p. 111; July 22, p. 141; Aug. 19, p. 167; and
Sept. 16, p. 187.
9. Starling, K. E., "Fluid Thermodynamic Properties for
Light Petroleum Systems," Gulf Publishing Co.,
Houston (1978).
10. Cox, K. W., J. L. Bono, Y. C. Kwok, and K. E. Star-
ling, Ind. Eng. Chem. Fundam., 10(2), 245 (1971).
11. Bishnoi, P. R. and D. B. Robinson, Can. J. Chem. Eng.,
50, February, p. 101 (1972).
12. Starling, K. E. and M. S. Han, Hydrocarbon Process.,
51(5),129 (1972).
13. Starling, K. E. and M. S. Han, Hydrocarbon Process.,
51(6), 107 (1972).

14. Jolls, K. R., and W. C. Dowling, "Computer-Generated
Phase Diagrams for Use in Teaching Thermodynam-
ics," final report, Local Course Improvement Program,
National Science Foundation (Grant SER 78-00298),
ISU-ERI-Ames 81246, 1981.
15. Chueh, P. L. and J. M. Prausnitz, AIChE J., 13, 1107
16. Gugnoni, R. J., J. W. Eldridge, V. C. Okay, and T. J.
Lee, AIChE J., 20(2), 357 (1974).
17. Khazanova, N. E. and L. A. Lesnevskaya, "Phase and
Volume Relations in the System Ethane-Carbon Di-
oxide," Russ. J. Phys. Chem., 41, 1279 (1967).
18. Gibbs, J. W., Trans. Conn. Acad., II 309 (1873).


Purdue University
West Lafayette, IN 47907


SARGE INCREASES IN engineering enrollments in
recent years have caused instructional prob-
lems in many departments. For example, since
1974 chemical engineering enrollment at Purdue
has increased from 243 to 558 while the faculty
has gone from 19 to 21. This has resulted in an
increase in class size-the fall chemical engineer-
ing thermodynamics (Ch 311) enrollment has in-
creased from 50 to 135. This class size increase
presents particular instructional difficulties in a
problem-oriented engineering course such as ChE
311. The purpose of this project was to develop a
series of sample TV taped chemical engineering
problems which could be used by the student, out-
side of class at his or her own pace, to supplement
the course material.

ChE 311 is a semester course with 45 classes of
fifty minutes each. The 15 week course is divided
into five major sections (see Table 1). In order to
rapidly introduce the first and second law in the
beginning of the course, we use steam as the work-
ing fluid in the first two sections of the course. In
section three, additional first and second law prob-

The purpose of this project
was to develop a series of sample TV
taped chemical engineering problems which
could be used by the student, outside of class at
his or her own pace, to supplement
the course material.

� Copyright ChE Division, ASEE. 1983

Course Outline

First Law
First & Second Law
Equations of State
Phase Equilibrium
Chemical Equilibrium

lems are presented using other equations of state
including the generalized charts, other tabular and
analytical expressions. The last two sections cover
applications of interest to chemical engineers-
phase and chemical equilibrium.
The lecture material for each topic area is
covered in lectures at the beginning of the section.
In the remaining periods, a series of practical
problems of increasing complexity are discussed.
The problems are presented in three parallel
* Discussed by the professor and students in class
* A photocopied solution handed out to each student
* A video taped discussion of supplemental problems are
on file in the library and available at the student's
At the end of each section, all students simul-
taneously take a common exam. This method has
the following advantages:
* The better students may work ahead at their own
pace, checking out the video taped problem solution
from the library. They need not attend classes in
which material they already understand is being dis-
cussed. Inasmuch as these students do not attend the
problem discussion classes, the class size is reduced
and more individual attention can be given to the
remaining students.
* Students attending class but still having difficulty


with the material may also check out the video taped
problem solutions. In their case, the video tapes would
be used not to work ahead, but to reinforce the dis-
cussion of similar problems. They could, in effect,
repeat the problem discussion, via video tape, as often
as they wish. By thus spending extra time, they could
also slow down their pace through each section.
* Since all students are required to take the same exam
at the end of each section, the procrastination prob-
lem so often present in self-paced courses would not
occur. All students would be required to be at the
same point five times during the semester-at each


The thermodynamics videotapes were prepared
during a 16-month period from September 1980 to
December 1981. The twenty videotapes are divided
into five groups, as shown in Table 1. Each tape
discusses the solution to a problem similar to the
homework problems. As each new topic is begun,
students are given typed problem statements for
that topic. The solutions are available on the video-
tapes only. Table 2 shows the topic of each prob-
Each taped problem is approximately twenty
minutes long. The tapes were prepared in a Purdue
TV studio using two color TV cameras; one an
overhead showing the material being written on a
pad by the lecturer, and the other facing the lec-

Robert G. Squires is a Professor of Chemical Engineering at Purdue
University. His Bachelor's degree is from Rensselaer and his Master's
and Doctorate from U. of Michigan. He has received the Amoco
Foundation Outstanding Teaching Award and the Western Electric
Fund Award for Excellence in Engineering Instruction. He is past
chairman of the I&EC Division of ACS and was the 1982 Program
Chairman for the Chemical Engineering Division of ASEE. In his spare
time he is a jogger, a pilot and a skier.
David V. Frank is currently a graduate student in chemical educa-
tion at Purdue University. He received his BA degree from Macalester
College in 1976 and his MS degree from Purdue in 1980. His doctoral
research will be conducted in the area of problem solving in chemistry.

1. First Law
2. First Law
3. First Law
4. 1st & 2nd Law
5. 1st & 2nd Law
6. 1st & 2nd Law

7. Equation of State
8. Equation of State
9. Equation of State
10. Equation of State
11. Phase Equilibrium

12. Phase Equilibrium
13. Phase Equilibrium
14. Phase Equilibrium

15. Phase Equilibrium
16. Chemical Equilibrium

17. Chemical Equilibrium

18. Chemical Equilibrium
19. Chemical Equilibrium

20. Chemical Equilibrium

turer to give a more

Pressure Cooker
Throttling Calorimeter
Triple Point
Inventor's Process
Actual vs Ideal Compressor
Reversible Isothermal Process
-Trial & Error
Throttling Process
Throttling Process
Diesel Compression
Diesel Compression
Data vs Nomograph vs
Raoult's Law
Dew and Bubble Point
Flash Calculation
Activity Coefficient
Gibbs-Duhem Equation
Wilson Equation
Standard Heat of Reaction vs
Actual Q of a Reactor
NH3 Formation, Effect of
T, P, Composition
Multiple Reactions
Multiple Reactions with
Liquid Condensing
Multiple Reactions with Solid
Phase Reactant and Product

personal touch to his com-

A preliminary practice tape was first made and
reviewed by a panel of undergraduate students.
The changes suggested by the panel were incorpo-
rated into the final tape.
The tapes are kept in the engineering library
and may be checked out for viewing at the stu-
dent's convenience. It should be pointed out that
the TV problems are extra problems not required
of the students, not turned in, and not discussed in
class. They are, therefore, used as supplemental
material strictly for the student's benefit. Sufficient
copies of each tape are kept in the library so that
students did not queue (see Table 1).


The tapes were first made available to students
during the spring and fall semesters of 1981. We
were interested in the answers to the following
three questions:
1. Will implementation of the tapes result in
an increase in the students' test perform-
2. How often will students use the tapes?


Supplemental TV Taped Problems

3. What are the students' perceptions of the
quality of the tapes?
An experimental design was employed to
answer the first question. The students were ran-
domly assigned to two groups. Group I was allowed
to use the tapes for only the first and third topics
and Group II was allowed to use the tapes during
the second and fourth topics. (The fifth set of
tapes had not yet been made.) The exam scores for
both groups were compared following each test to
see if normal use of the tapes had a significant
effect on the student's achievement. There were 39
students in both groups who took all four exams.
Each exam consisted of two or three problems. The
average test score of a student throughout the
semester was 75.6 when he was using the video-
tapes and 74.4 when he did not have access to the
tapes. However, a t-test shows that the difference
between these two numbers is not significant.
A survey was made of the spring '81 ChE 311
class. There were 84 students in the class and 63
responded to the anonymous questionnaire. At the
time of the questionnaire 19 tapes were in use. A
summary shows that 43% of the responders saw
all 19 tapes, 81% saw more than 11 tapes, and
10% saw no tapes.
Comments from the questionnaire indicated
that most students believe that using the tapes en-
abled them to learn the material more quickly.
Many students viewed the tapes more than once.
Typically they might view a tape once when the
material was first discussed, and then view the
same tape as a review just before the exam.

The fact that no significant improvement in
test performance attributable to the tapes was ob-
served is not surprising. The tapes are but a small
part of the course and similar problems are re-
quired of all students. We were encouraged that
many students indicated that the tapes allowed
them to understand the material more quickly.
That 43% of the class saw all of the tapes and
81% saw more than half of the tapes is our best
indication that the students believed the tapes were
worthwhile. (Remember that the tapes were not
required and were not discussed in class.) At
twenty minutes per tape, this level of viewing rep-
resents a significant amount of voluntarily com-
mitted time. We conclude that the tapes are a use-
ful addition to the course and we plan to continue
their use. If any other professors would like to use
any or all of these tapes, copies can be obtained
from Prof. Squires.

We would like to thank the National Science
Foundation (Local Course Improvement Grant)
and Purdue's Schools of Engineering for their
financial support; Purdue's TV studio personnel
(in particular Robert C. Sanders and Richard D.
Light) for their help; Prof. John Lindenlaub of
Purdue's Center for Instructional Development in
Engineering for many constructive suggestions;
and the many undergraduate students who served
on reviewing panels or who participated in class
during the development of these tapes. O


University of Michigan
Ann Arbor, MI 48109

SUPPOSE ONE WERE TO try to describe the field of
thermodynamics in as simple a manner as pos-
sible. It is likely he would start with the concise
definition that thermodynamics is the science of
energy as displayed in all of its forms, transfers,
and transformations. He would probably then

*This paper was presented at the symposium prior to
Professor Martins death on Dec. 13, 1982 (see CEE Vol.
XVII, No. 2, pg. 73 for Memoriam).

invoke the famous "three laws" that are the result
of observation and some intuition, and discuss
how these lead to the field which is agreed to be
the one in question, as judged from a study of the
multitude of books that have been written on the
An alternative approach would be to assume
from prior knowledge the four basic equations of
thermodynamics, thereby utilizing from the very
start the powerful shorthand language of mathe-
matics. This would be followed by an interpreta-
tion and explanation of each basic equation.
� Copyright ChE Division, ASEE, 1983


r I-

Following the latter approach, the first and
most used basic equation is the fundamental prop-
erty relation,
dU = T dS - P dV + idmi (1)
(See Nomenclature for definition of all symbols.)
The second and more easily understood equation
is the energy balance,
d(U + u + mgz) 2
2 sys 2
6Q - 6W + J (H + + gz) 6m = dEsys (2)

The third equation is a little more sophisticated
and is known as the entropy balance,

dss = i ( + 6LW+ Sj6m (3)
Sys i i 0 j J "
while the fourth equation is the simplest of all and
is the mass balance*,

dm = 6m (4)
sys j

It is the objective in this discourse to focus
attention primarily on the fundamental property
relation because of its great utility in problems of
thermodynamic properties and physical and chem-
ical equilibrium. As it stands in its simplest form,

*The Einstein relation, m = E/c2 implies a transfer of
mass associated with work and heat; however, except in
nuclear reactions, the mass equivalent of energy is so
minute due to the vast magnitude of the velocity of light
that separate energy and mass balances are satisfactory.

An alternative approach would be
to assume from prior knowledge the four
basic equations of thermodynamics, thereby utilizing
from the very start the powerful shorthand
language of mathematics.

Eq. (1) considers only thermal, compression, and
mass change effects in any finite collection of mat-
ter or substance whose temperature, pressure, and
chemical potentials are uniform throughout. Es-
sentially, Eq. (1) says that thermodynamic prop-
erties of matter are not independent; that they are
interrelated and locked together by a differential
relationship such that if any property is changed,
at least one other property must change to pre-
serve the equality of the equation.
The generalization of Eq. (1) to include effects
other than thermal, compression, and mass change
has caused considerable confusion and difficulty,
even though all writers agree on the implications
of Eq. (1) in its simplest form. To understand the
source of confusion, let us examine first the treat-
ment of the gravitational effect in the pioneering
work of Lewis and Randall as revised by Pitzer
and Brewer [4]. They state without proof that the
reversible lifting of a weight increases its free
energy per molal mass M by an amount,

dG = gMdz


= gM

It is interesting to note here they are implying
there is a better or greater understanding of a
quantity called free energy than there is of just
energy. It is not meant that energy is a simple
concept, but it is certainly simpler than free
Preceding Eq. (6) it is emphasized that al-
though potential energy and internal energy may
be separated, their energy-content function E is to
include gravitational energy.* From their defini-
tion and later discussion the Gibbs free energy is
defined as

Joseph J. Martin (deceased) was past president of ASEE, of AIChE
and of Engineers Joint Council, and professor and acting director of
the Institute of Science and Technology at the University of Michigan.
He was graduated from Iowa State University (BS), University of
Rochester (MS) and Carnegie-Mellon University (DSc). His main area of
interest was thermodynamics.

G = E + PV - TS

*This is the opposite approach from Gibbs [2] who
wrote, "The energy of mass will now consist of two parts,
one of which depends upon its intrinsic nature and state,
and the other upon its position in space."


Their free energy relation when gravity is not of
importance is
dG = - S dT + V dP + P .dmi (8)
which follows directly from Eq. (1) with G = U +
PV - TS and the partial free energy Gi identical to
the chemical potential pi. Now if any mass m = nM
is lifted, Eq. (6) may be written

a-J = m or dG = gmdz (9)
and this may be added to Eq. (8) to give
dG = - S dT + V dP + Iidmi + gmdz (10)

If Eq. (7) is differentiated and combined with Eq.
(10), we get
dE = T dS - P dV + V P dm. + gmdz (11)
In generalizing on the terms in Eq. (11), they pre-

dE = i X dxi


where Xi is an intensive variable or force and xi is
its associated variable. A table of Xi's and xi's is
given so that one may readily construct the rela-
tion comparable to Eq. (11) as

dE = T dS - P dV + P Lidmi + gzdm (13)
It is obvious there is a contradiction between Eq.
(11) and Eq. (13) because the former contains
gmdz while the latter contains gzdm. Thus, there
is an outright error in their treatment of the gravi-
tational effect.
As a second example of difficulty the book by
Aston and Fritz [1] is considered. For a reversible
process involving a closed system (the authors em-
phasize this restriction of a closed system) the
generalized equation

dE = T dS - P dV - l X.dx.


is given with the Xi's and x,'s being respectively
the intensive and extensive variables other than
the usual ones associated with thermal and com-
pression effects. In considering the gravitational
effect they identify the intensive variable as
Xi = gz (15)

and the associated extensive variable as
xi = m (16)

When these are iserted in Eq. (14), the result is

dE = T dS - P dV - gzdm


Now here is an obvious contradiction because the
application is to a closed system where m cannot
change. Furthermore, because of the minus sign,
the equation implies that the energy somehow de-
creases if the mass is increased in a gravitational
field, a result which can be considered absurd if
they mean total energy and incorrect if they mean
internal energy which is independent of gravity.
As a last example of difficulties with the treat-
ment of effects other than thermal or compression,
let us look at the highly regarded textbook by
Guggenheim [3]. He considers the work done in
transferring dni moles of i from phase a to phase
/3, each with its own gravitational potential,

W = (0 - $a )Midn (18)
From this he deduces that terms of the form,

M i dni a
i i
must be added to the property relation (1) in
terms of moles for each phase a (and chemical
potential in place of partial free energy), so that
dUa = TadSe - PedVa + (po + M )dn (19)
Guggenheim does not explicitly say whether his U
is internal or the sum of internal and gravitational
energy. However, in view of the way he treats
electrical effects, it will first be assumed that he
means all of the energy, which is the sum E of in-
ternal and potential energy. Consequently, Eq.
(19) is rewritten as

dEa = T dS - PadVa + (PT + Mia)Ddn


Since the total energy is the internal plus the po-
tential energy,

E = U + me = U + M M n i
and Eq. (20) may be written

dEa = d(Ua + M M ini t

STadSa _ padVa + I (a + Ma)dna

This reduces to



dUa = TdSO - PadVa + p dn -iM n M de (23)
i i
Here is an equation, obtained simply by substitut-
ing the sum of internal and potential energy for
the total energy, which must be flatly incorrect,


for it says that the internal energy of matter
changes with the potential energy which is not in
accord with observation.
Of course, one might interpret Guggenheim's
U" in Eq. (19) to be strictly internal energy. In
that event
dE' = d(Ua + Mi na)
1 1
= T dS P dVa + + Mi )dn
+ M.tadna + I M.nda (24)
i i 1
This may be rearranged to

dE = T'dS' -PdV + Mn d i
+ 2 (pa + 2Mi~ )dni.


This equation with its double potential energy
term must be just as incorrect as Eq. (23), so that
either interpretation of Guggenheim's energy term
leads to ridiculous results.

It is the objective in this
discourse to focus attention primarily on
the fundamental property relation because of its
great utility in problems of thermodynamic properties
and physical and chemical equilibrium.

Now that erroneous treatments have been
shown in three well-known textbooks, let us ex-
plore a logical approach to the development of the
fundamental property relation where effects other
than thermal, compression, and exchange of mat-
ter with the surroundings are considered.
Consider as a system a uniform collection of
ponderable matter, where uniformity implies the
same chemical composition, temperature, pressure,
and any other intensive properties throughout all
regions. Let the total energy (sum of intrinsic
energy, potential energy due to position in any
kind of force field, and energy due to massive
macroscopic motion such as kinetic) be denoted
by E as in Eq. (2). This total energy may be
changed in three ways:
(1) The mass of ponderable matter may exchange heat
with its surrounding environment.
(2) It may transfer work with its surroundings.
(3) It may exchange matter with its surroundings.
The energy balance for these energy and mass
transfers may be written

dE = 6Q - 6W + C E.dm. (26)

which is just an equivalent of Eq. (2). The energy
of each component added per unit mass of that
component is Ei which is the partial total energy
of the component. The accompanying entropy
balance for the energy and mass transfer is the
equivalent of Eq. (3) for a single heat transfer
and Si the partial entropy per unit mass of each
component added, or

dS = + T + Sdm (27)

This equation simply means that the entropy
change of a collection of matter is the sum of the
heat transfer divided by the temperature, the lost
work LW divided by the temperature, and the
entropy carried in with any entering matter.
Let us now make all the energy and mass trans-
fer processes occur in such a way that the prop-
erties of the system of matter are at all times uni-
form throughout and the properties of any enter-
ing matter are identical to those of the system of
matter under observation. This means that if the
temperature of the matter is to rise, it rises uni-
formly throughout the whole mass of matter, if
the pressure is to rise, it does so uniformly
throughout, and if the concentration (and its asso-
ciated chemical potential) changes, it does so uni-
formly everywhere, and if a component is added,
it is at the same temperature, pressure, and chem-
ical potential as in the system of matter. Such a
requirement makes any process reversible because
at no point is there allowed a finite difference in
any potential driving force (i.e., all driving forces
are infinitesimal in magnitude). For such a re-
versible process there will be no lost work so that
Eq. (27) becomes in a rearranged form,

6Q = T dS - T . S.dm.
1 1


Elimination of 6Q between Eq. (26) and Eq. (28)

dE = T dS - T S dmi - W + E dmi
i i


The total energy E is the sum of the internal
energy, the kinetic energy, and any potential
energy due to position in force fields such as gravi-
tational, electrical, and magnetic,

E = U + mu2/2 + m$ - EP - HM (30)
Here by way of explanation e is the electric po-
tential or field and P is the electric polarization
while H is the magnetic field and M is the magnetic
polarization. Eq. (30) may be differentiated to


... these extended equations account for
other effects such as surface tension, tensile stress,
electric polarization, and magnetic polarization.

dE = dU + mudu + dm + md4 + Odm
- edP - PdE - HdM - MdH (31)
It may also be differentiated partially with respect
to the mass of one component at constant values of
all the intensive properties that determine the state
of matter, so that
2 - 2
Ei = Ui + U2/2 + - EP - HMi (32)

Now the work transferred between the system of
matter and the surroundings is the sum of all pos-
sible ways of doing work,

6W = P dV - P Vidmi - yda + Y admi
i i
- Fdk + F T �idmi - md$ - mudu
+ PdE + MdH (33)
Here the first term is the work done on the sur-
roundings if the system expands. The second term
is work done by the surroundings to force dm, of
matter into the system. The yda term gives the
work to overcome surface tension in creating new
area while

y a idmi
is the work to force dmi into the system of matter
when there is surface tension. The Fdl term is the
work to elongate the matter in tension while the

F iidmi
is the tensile work delivered to the surroundings
when dm, is admitted to a system of matter under
tension. An alternative more general approach
here is to set up a strain tensor that gives the
change in dimensions of an elastic material re-
sulting from all components of stress. Such a
tensor would account for tension, compression, ex-
pansion and the normal and shear components and
would give terms of the same form as that for
simple tension. The term mdD accounts for the
work to move the mass in a gravitational or centri-
fugal field. The term mudu accounts for the work
to increase the kinetic energy of the whole mass of
matter. The Pde is the work involved in moving

polarizable matter in an electric field and the MdH
is the same thing for motion in a magnetic field.
Now if Eqs. (30), (31), (32), and (33) are in-
serted into Eq. (29), and use is made of
dm = d dm.

the complete property relation is obtained,
dU = T dS - P dV + yda + Fdk + EdP
.+dM .+ (i + P - TSi
-*" y - Fi. - eP. - Hti)dmi (34)

It is worth noting that kinetic and gravitational
energy terms do not appear in Eq. (34) so that
internal energy is completely independent of these
effects, as it should be.
If Gibbs free energy is defined as
G = U + PV - TS - ye - FA - EP - HM (35)

it may be differentiated at constant T, P, y, F, E, H
and mi to give the partial extensive quantity,
Gi = Ui + PV - TS y - - F - EPi - HM. (36)

If Eq. (36) is inserted into Eq. (34),
dU = TdS - PdV + yda + Fdk + edP
+ HdM + G.dm. (37)
where the partial free energy G- is the previously
used chemical potential pi.
Since Eq. (37) is homogeneous in mass (i.e.,
doubling the mass at constant state of fixed T, P, y,
F, E, H, and Gi doubles U, S, V, d, 1, P, M, and m),
it may be integrated from zero to finite mass,
U = TS - PV + ya + Fk + EP + HMi + Gimi (38)

G = i G.m. (39)
If Eg. (35) is differentiated and compared
with Eq. (37) an alternate form of the funda-
mental property relation is obtained,
dG = - S dT + V dP - ady - �dF - PdE
- MdH + _ Gidm (40)
If Eq. (38) is differentiated and compared with
Eq. (37), the result is
SdT - VdP + cdy + RdF + Pde
+ MdH + m.dGi = 0 (41)
In summary Eqs. (34), (35), (36), (37), (38),


(40), and (41) are similar to the usual well-known
equations when only thermal, compression, and
mass transfer effects are involved, but these ex-
tended equations account for other effects such as
surface tension, tensile stress, electric polarization,
and magnetic polarization. The proper way to
handle gravitation and other field effects has been
shown and contrasted with the erroneous methods
in three well-known books.
For a more complete discussion of this subject
the reader is referred to the previous extensive
treatment of The Symmetrical Fundamental Prop-
erty Relation of Thermodynamics [5]. O

1. Aston, J. G., and J. J. Fritz, Thermodynamics and Sta-
tistical Mechanics, John Wiley & Sons, New York
2. Gibbs, J. W., Collected Works, Vol. I, Longmans, Green,
and Sons, New York (1928).
3. Guggenheim, E. A., Thermodynamics-An Advanced
Treatment for Chemists and Physicists, Interscience
Publishers, Inc., New York (1950).
4. Lewis, G. N., M. Randall, K. S. Pitzer, and L. Brewer,
Thermodynamics, 2nd Ed., McGraw-Hill Book Co., New
York (1961).
5. Martin, J. J., The Symmetrical Fundamental Property
Relation of Thermodynamics, Chemie Ingenieur Tech-
nik, 249, Vol. 5 (1972).

C Velocity of light
E Total energy (internal + kinetic + poten-
tial of all kinds)
e Electrical potential or field
F Force
G Gibbs free energy, U + PV - TS, or G = U

+ PV - TS - ya- F- P - HM
g Acceleration due to gravity
H Enthalpy, U + PV
H Magnetic potential or field
1 Length
LW Lost work irreversibilityy)
M Molecular weight
M Magnetic polarization
m Mass
n Number of moles
P Pressure
P Electrical polarization
Q Heat flow
S Entropy
T Temperature (absolute)
U Internal (intrinsic) energy of matter
u Velocity
V Volume
W Work flow
Z Height above a reference point
a Surface area
8 Quantity transferred (as heat 8Q and work
S Surface tension
S Potential energy (gz in gravitational field)
1 Chemical or mass potential (i = Gi)

- Denotes partial extensive property
a"P Points in gravitation field

Denotes different chemical species
Denotes all chemical species except partic-
ular one i being examined.


Texas A & M University
College Station, TX 77843

rpWO PROPERTIES WHICH generate considerable
confusion in thermodynamics courses are re-
sidual functions and fugacity. They are, in fact,
closely related concepts and, in this paper, we have
developed them in a consistent manner. In this

0 Copyright ChE Division, ASEE, 1983

way, the composition dependence of the fugacity
coefficient of a component in a mixture appears in
an unambiguous manner.

The property changes which we shall develop
in this paper are all of the form: real fluid prop-
erty less perfect gas property. The difference is
either at the same temperature and pressure or at
the same temperature and density. The definitions
are (using M to denote U, H, A, G, S, V).


M E M(T,p) - M (T,p)

MR E M(T,P) - M (T,P) ()

M - M = M(T,P) - M (T,Po)
= M(T,p).- M (T,P /RT) (3)

* * o
M - M = M(T,P) - M (T ,P )
= M(T,p) - M (T,P/RTo) (4)

We choose to develop these expressions in the
T-p plane because the results are then most con-
venient for computer computation. The path is

M(T,p) - M (T,0) - M (T,p)

where the real fluid and perfect gas planes inter-
sect at zero density.
The most useful working equations for this de-
velopment are

dU = c dT + T V - P dV

= cVdT + R( dp (5)

dA = - S dT - P dV = - S dT + RTZ d- (6)
We have introduced the compressibility factor to
facilitate equation of state use. Integrating these
expressions along the chosen paths provides

Kenneth R. Hall received his
BSChE from the University of Tulsa,
his MS from the University of Cali-
fornia (Berkeley) and his PhD from
the University of Oklahoma. He has
been at Texas A & M since 1974.
He became Professor of Chemical
Engineering in 1978 and Director
of the Thermodynamics Research
Center in 1979. He has approxi-
mately 60 publications, principally
in thermodynamics. (L)

Philip T. Eubank has, over the
past twenty years, conducted re-
search in the theory, correlation,
and measurement of thermophysical
properties of fluids, resulting in about 60 refereed publications. He
received the BSChE degree from Rose-Hulman Institute of Technology
and the PhD degree from Northwestern University. He is presently
Chairman of the AIChE Committee on Thermodynamics and Transport
Properties (Area 1A). (C)

U(T,p) - U (T,p) p
=U(T,p) - U (T,o) - R p
0 P(/T) p
* U*
+ U (T,0) - U (T,p) - 0

A(T,p) - A (T,p) p
= A(T,p) - A (T,0) + RT Z

*0 *
+ A (T,0) - A (T,p) - - RT

Thus, the residual functions, in
form, are

Ur = 1 3
RT T 0 (1T) p

Ar i[
RT - [Z - 1] d




Of course, the other residual functions are com-
binations of these two

Hr Ur PV - PV U
- + - +Z- 1

Sr Ur Ar

Gr r * r
G _ Ar PV - PV Ar
RT - + -




James C. Holste is an Associate Professor in the Chemical Engi-
neering Department at Texas A & M. He received his PhD in physics
from Iowa State University in 1973 and spent two years at the National
Bureau of Standards (Boulder) before joining Texas A & M in 1975. He
has approximately 20 publications describing thermodynamic properties
of fluids and solids. (R).



A consistent development
of residual functions, property changes
and fugacity reveals close relationships among
the various properties.

By definition, V' is zero so



To convert these results to residual functions
in the T-P plane requires only adjustment of the
perfect gas values

M(T,P) - M (T,P)
* * *
= M(T,p) - M (T,p) + M (T,p) - M (T,P/RT) (13)

where the required terms are

M(T,p) - M (T,p) = Mr

M*(T,p) - M (T,P/RT) =

(0 if M is U,H

-An Z if M is A,G,-S

This step is equivalent to rederiving the expres-
sions in a T-P plane.
The other types of property change (Eqs. 3
and 4) also require only adjustments of the perfect
gas values. For Eq. 3, the adjustment is

M - M = M(T,p) - M (T,p)
+ M (T,p) - M (T,P /RT) (3)


M(T,p) - M*(T,p) = M

* * 0 oif M is U,H
M (T,p) - M (T,Po/RT) = +
0n Z + kn -L

if M is A,G,-S

Eq. 4 bases the property change upon the standard
state and the adjustment is

M - M = M(T,p) - M (T,p)
o *
+ M (T,p) - M (T,P /RT)
+ M (T,Po/RT) - M (To,Po/RT)
+ M (ToP/RT) - M (To,P /RTo) (4)

In this case, it is most convenient to establish
U-Uo* and S-So* and then calculate the others from

these two. Utilizing Eq. 4, the changes are

U-U U-U 1j
o r 1 v d
U r + dT

* *
S -S S- S
o r n T


and the other functions become

H- H U - U PV - RT U - U T
o o o o + Z-- (18)
* * *
o 0 oo
* * *
U - U T[S - S] S [T - To]
0o o o0
U- U S-S S T
0 o i 0- (19)

* * * *
G-G H-H S - S S T
- - 1 - (20)

It is also very important to note that throughout
these equations the only integrals required are

1 (@Z I dp -
T P(1/T) p RT

(z - ] d= A
p RT

fT C

R *

V dT


The first two integrals are relatively simple appli-
cations of the equation of state, and the latter two
integrals involve only perfect gas specific heat.
One last point to note is the T-P plane deriva-
tion of GR/RT. Again following a constant tem-


perature path from P - O0 -> P produces

G(T,P) - G*(T,P)
=G(T,P) - G (T,0) + G*(T,O) - G*(T,P)

but the fundamental equation for G is

and the value for GR becomes

* dP
G(T,P) - G (T,P) = RT Z - RT
r0 P

Therefore, the final expression is



G dP Al'
S [Z -1 + Z - - In Z

25 and 26. Evaluation of Eq. 27 requires closer

- * - *
G. - G. G. - G. G. - G.
1 1 1 + (28)

Evaluation of Eq. 28 requires the following analy-

V T, Z

S[Gi - Gi]

- P T,z

P=0 o



The usual definition for fugacity (of a pure
component) is, in differential form

dG. = RT d Zn f. @ constant T
1 1

lim = 1.0


G. - G

-* *
G. -G.
1 1

G -Gi
RT in z.

=V -V.

i - v
i dP

= An z. (ideal solution)

+ 1 1 dP (2!


Upon integration, this expression becomes

Zn f.

dG. = RT
� Un P

d nn f.

Gi - G [
SRT-= [Z i

- ] i- - dP (22)
-lp R 1'

* =GR (24)
Gi(T,P) - Gi(T,P) = RT en = G (24)
1 1 P

Eq. 24 has an obvious relationship with Eq. 22. In
fact, we might as well have defined fugacity with
these two expressions and have extended the defi-
nition to mixtures and components in mixtures:

f G (T,P) - G.(T,P) G
kn 1 -

f G (T,P) - G*(TP) G
mn _ _ g__ M. M

f. Gi(T,P) - G.(T,P)
Pn - R

Eq. 27 thus becomes

f. Vi - Vi
an - = An zi + dP -


�RT P]d

f F .
An -P= 1-idP (30)
Furthermore, utilizing previous relationships

Furthermore, utilizing previous relationships

G. -G



Eq. 22 reveals the calculation procedure for Eqs.

-R - * -* *
S G - GC G - G
i 1 1 R i




It is also true that

-R -r
G. G.
1 1
T = RT- n Z

= (nAr/RT)
Si T,nV,nj#i

= (nZ )M

nV { ni JT,nV,nj#i


A consistent development of residual functions,
property changes and fugacity reveals close rela-
tionships among the various properties. The com-
position dependence of the fugacity coefficient of a
component in a solution is unambiguous. All prop-
erties result from integrals which are easy to de-
rive from good equations of state. D

A - Helmholz function
Cv* -perfect gas specific heat (constant volume)
fi - fugacity of pure i
fm - fugacity of a mixture



Tufts University
Medford, MA 02155

THE THERMODYNAMIC availability functions can
Sbe viewed graphically, and this view provides
valuable unexpected insights into the nature and
meaning of the functions.
To demonstrate, consider the question, "What
is the maximum work a system can perform in
moving into equilibrium with the temperature and
pressure of its environment?"
The answer is given graphically in Fig. 1. Max-
imum work is the work performed when moving
reversibly along paths (1--2) and (2--e), from an
arbitrary initial state (1) to a final state (e) in
equilibrium with the environment.

- fugacity of component i in a mixture
- Gibbs function
- enthailpy
-general property symbol
-number of moles
-gas constant
- temperature
-internal energy
-molar volume
-total volume
- compressibility factor
-mole fraction

-- T-p residual
S - T-P residual
* - perfect gas
-partial molar

I - component i
m -mixture
o -standard state
-reference state

Now this may appear to be an arbitrary choice
of paths; but it is not. It constitutes a unique com-
bination of reversible paths leading from (1) to
(e), that allow heat and mass transfer to occur
only when the system is at the potentials of its en-
vironment. These are paths that take the system
isentropically and at constant molarity, (1--2), to
the temperature of that environment; and then
isothermally, (2-+e), to the chemical potential of
the environment. And it is rather easy to prove,
again graphically, that no combination of reversi-
ble process paths connecting states (1) and (e),
can produce more work.


Curve (1-k-e) in Fig. 1 traces a reversible but
arbitrary process path taking a system from state


� Copyright ChE Division, ASEE, 1983

(1) to state (e). The area under (1-k-e) is clearly
greater than the area under the path (1-2-e) com-
prising the path producing "maximum-work".
Q (1-k-e) > Q(1-2-e) (1)
and because,
W = Q-AUie (2)
and AUie is the same for all paths; it follows that
W(1-k-e) > W(1-2-e) (3)
which appears to contradict the answer to the
above "maximum-work" question (??).
But, consider path (1-a-b-e) consisting of isen-
tropic and isothermal processes, with the isotherm,
a-b, located so that the area under (1-a-b-e) equals
that under (1-k-e), so that
W(1-k-e) = W(1-a-b-e) (4)
That any reversible progress can be replaced
by combinations of isentropic and isothermal
processes with equal heat and work effects is some-
times called Clausius' Theorem [1].
The work of process (1-a-b-e) exceeds that of
process (1-2-e) by
Area (2-a-b-e-2)
so that Eq. (3) may be written as an equality:
W(I-k-e) = W(1-2-e) + Area (2-a-b-e-2)
But process (1-a-b-e) involves an isothermal
expansion, (a-b), that must absorb heat at a tem-
perature, Ta that is higher than the temperature of
the environmental heat reservoir, Te.

M. V. Sussman is professor of chemical engineering at Tufts Uni-
versity. His work in thermodynamics includes the books "Availability
(Exergy) Analysis" (Mulliken House 1980) and "Elementary General
Thermodynamics" (Addison-Wesley 1972). He is the inventor of the
"Maxwell Demon Bottle." Previous articles in Chemical Engineering
Education are "Seeing Entropy: The Incompleat Thermodynamics of the
Maxwell Demon Bottle" and "Thermodynamic Heresies."

Where can this heat come from? If there are
other sources of heat present, than our initial
question is meaningless. The question has meaning
only if heat interactions are restricted to the sys-
tem and its environment. Such heat interaction
can occur reversibly only if a heat pump is used to
move heat from Te to Ta. The minimum work
input to this pump is that of a Carnot heat pump,
and is exactly equal to: Area (2-a-b-e-2). The net
work output from arbitrary path (1-k-e) is there-
fore equal to that from path (1-2-e). Q.E.D.
Analogous considerations hold for open sys-
tems where mass as well as heat are exchangeable
with the environment. For maximum work the


mass exchange occurs only at the potential of the
environment so that process path (1-2-e) on a
tj - ni diagram (identical to Fig. 1, except with [i
as ordinate and ni as abscissa) is analogous to the
maximum work path on a T-S diagram, and a sim-
ilar proof applies [2].
As a consequence of the Fig. 1 proof, and the
constraint of heat transfer only at Te, Eq. (2) is
transformed into an equation for maximum work
W-.-e5 = WMAx = TeASi,-AUie (5)
where the double subscript should be read as "from
state 1 to state e".
Part of this work is expended against the at-
mosphere and is therefore not available. The net
useful or available work is the difference between



the maximum work and the work expended in
pushing back the surrounding environment
WMA - PeAVe = B (6)
The symbol, B, is assigned to this quantity and
it is called the "Availability Content", "Net Useful
Work", or the non-flow "Availability" of the sys-
tem in given state (1). We may combine Eqs. (5)
and (6) to obtain the classical definition [3]
B = - [AUi.- TeASie + PeAVie] (7)

B may be represented as the area of a cycle on
a P-V plane (Fig. 2). In accord with Eqs. (5) and
(6) the cycle moves along the WMAX path, isen-
tropically from 1--2 and isothermally from state
(2) to the environmental equilibrium pressure Pe;
(2->e). A constant pressure process (e->3), from
Ve to V1, representing the atmospheric work loss,
(-P.AV1I), effectively completes the cycle. The
area enclosed is the integral around the clockwise
closed path 1-2-e-3-1. The direction of integration
is always clockwise irrespective of the placement
of state (1) with respect to state (e), so that the
enclosed area is always greater than zero. When
P, > Pe, the work output from 1->e exceeds the
input from the environment, e->3. When P, < Pe,
the work input in moving from 1--e is exceeded by
the work output gained from the atmosphere. Net
output always exceeds input.
This is also true when the temperature of the
initial state (1') is below that of its environment.
Fig. 2 shows integration cycles representing B for
states (1) and (1') having temperatures and

To examine the graphical character of (4, we
rewrite Eq. (9) by expanding the AH and A(PV)
) = - (AU,,- TeASie + ViAPie + PeAVie) (10)
Now using Eq. (7) and (10), we see that
S= B - VAP�i = B - V(P - P) (11)
Eq. (11) tells us that 4, unlike B, is greater than
zero only when the ViAPie term is negative or is
less than B; that is, for all values of P, > Pe and


pressures above and below that of state (e). The
cycles always move clockwise. Consequently
B > 0 (8)
In a steady flow system in which potential and
kinetic energy effects are unimportant, the work
that may be extracted via a shaft or cable when a
stream entering the flow system exits in equilib-
rium with its environment is
WSHAFT = - (AH - Q)
For a reversible process from (1) to (e)

and this work is a maximum if, as before, heat
transfer occurs only when the system has reached
T,. Consequently
WSH(MAX) - (AHe -TeASe) - (9)
Eq. (9) defines the steady flow availability
function, [3] to which we assign the symbol, 4.

for a limited range of values of P1 < Pe. Usually,
if P, < Pe, 4 will be negative and work will have
to be supplied to the system for it to flow into
equilibrium with the environment. This point is
illustrated in Fig. 3 by states (1) and (1') whose
pressures are both below Pe. 4 of state (1) is nega-
tive because the area of V1 (Pe - P1) exceeds that
of B. ) of state (1'), however, is positive because
area V,, (Pe - P,) does not exceed B'. On the other
hand, Eq. (11) shows that the relative magnitude
of T, and Te does not affect the sign of 4.
Eqs. (9) and (11) apply to chemical as well as
physical steady flow process as is shown in the fol-
lowing section.
In a steady flow system in which chemical re-
action occurs, but where kinetic and potential
energy effects and non-shaft work interchanges,
other than volume change, are negligible, an ac-
counting of all the energy entering or leaving the
system in a differentially small time interval yields
the equation
dQ - dWSH = dU + d (PV) (12)
which may be written as
-dWsH = dU + d(PV) - TedS (13)
if all heat is transferred reversibly at Te. But in a
reactive or diffusive system at Te
dU = TedS - PdV + Yjidn, (14)
so that Eq. (13) becomes
-dWsa = VdP + /xidni (15)
In a reversible isothermal reaction process that
is also isobaric at Pe, for example, an electrochem-
ical cell, the integral

f VdP = 0
and therefore Eq. (15) becomes

-WSH(max) = 4f idni = AGie (16)
" 1 (P,T)
A ~6~ 18/,")

... consider the question, "What is
the maximum work a system can perform in
moving into equilibrium with the temperature and
pressure of its environment?"

If, however, P varies as the system moves reversi-
bly from 1-le, as through a Van't Hoff equilibrium
reactor (Fig. 4), then

S idni = 0

across the equilibrium reactor and the reversible
turbines connected to the reactor (because ni's are
constant), so that Eq. (15) becomes

- VdP = AGe = -Ws(nmx)


Consequently, from Eqs. (16), (17), and (13)

-WSH(max) = AHie - TeASie - -4)


The subscripts (P,T) and (T) on the integra-
tion signs in Eqs. (16), (17) and (18) indicate
that the integrals are at constant pressure and
temperature, and at constant temperature, respec-
tively. Eq. (18) and the discussion leading to it
demonstrate that the steady flow availability has
the same form in chemical reactive processes as in
physical processes. The chemical potential terms
are implicit and need not be appended to the equa-

If a system can change its composition or mass
and exchange expansion work with its environ-
ment, then the differential of its internal energy is

dU = TdS - PdV + Xqidni


If in addition all mass and heat transfer occur re-
versibility at the potentials of the environment,
then Eq. (19) becomes

dU = TedS- PdV + /xid,e dn


which we rearrange and integrate to obtain an
expression for maximum expansion work that has
one more term than Eq. (5).

Wmax le f PdV =

S TedS- dU + Zx,,dni

= TeASie - AUi. + 1i,e Ani,.i


sFI crE 4


The net useful work or non-flow availability is then
found as in Eqs. (6) and (7)
Chem. Eng. Edu. Vol. 17, No. 3, Sum. 14283

B - PdV- (PeAVIe) (22)

=-[AUie + PeAVe - TeASie - /pseAn,lel]
which is the defining equation for non-flow avail-
ability found in Gibbs and elsewhere [4].
Now imagine a system that moves from an
initial state (1), through isentropic (1->2), and
isothermal (2->3) processes, into temperature and
pressure equilibrium with its environment and
then displaces its contents, wholly or in part into
that environment, if need be through a semi-
permeable membrane that allows transfer of the

to the area (1-2-3-a-1). Consequently, the second
bracket must equal zero, or

AUse + PeAV3e - TeAS3e = 2/Xt,eAni,ie



Bie = -(AU 3 + PeAV,- TeAS, 3)

where state (3) is isomolar with (1) but in equi-
librium with the environment.
For reactive systems or materials that trans-
form chemically before passing into the environ-
mental state; for example

ZaAi -> bB,
i j
in equilibrium with an environment

B = - (AUi 3 + PeAVi 3 - ToAS, 3)


- (AU3e + PeAV3e - TeASIe) j

where "i" refers to reactants, and "j" to products.
State (3) is the reaction equilibrium state and
state (e) is the environmental state. For the rea-
sons given in Fig. 3 and 5, B remains positive
definite. O

1. Zemansky, M., "Heat and Thermodynamics" fourth ed.,
p. 168 (McGraw-Hill, New York, 1957).
2. Sussman, M. V., Nature, 256, 5514, 195-198 (1975).
3. Keenan, J. H., Thermodynamics, 1st MIT Press Ed:
Cambridge, MA, 1970. Originally published by Wiley,
New York, 1941.
4. Gibbs, J. W., The Collected Works, Volumes I, II, New
York: Longsmans, Green and Co., (1931).


contents at its environmental potential or partial
pressure. The process would appear as process
1-2-3-e in Fig. 5. The work of this process is the
maximum work as given in Eq. (21), and is rep-
resented by the sum of area (1-2-3-a-1) and area
Pe (Ve - V,). The net work of the process, or the
non-flow availability, is according to Eq. (22), the
maximum work minus Pe (Ve - Vi), or simply the
area (1-2-3-a-1), that is always positive definite.
It is interesting to note that Eq. (22) may also
be written as
B = - (AUeo + PAVi 3- TeASi ) (23)

- (AUse + PeAVse - TeASoe - YPi,eAni(,e))
The first bracket in Eq. (23) is exactly equal

Continued from page 103.
systems . . .". Then some conclusions are derived about
one's freedom to select reference states for internal
energy, enthalpy, and entropy in terms of chemical com-
pounds or chemical elements, with or without the possi-
bility of chemical reaction. However, identical conclusions
are easily derived from corresponding statements applic-
able to a simple closed system. Further the open system
equations can only be obtained by derivation from the
closed system relations. Thus the derivation of reference
state constraints from the open system equations is not
so much a proof as it is a partial check on the deriva-
tion(s) which led to the open system equations.
To illustrate the closed system approach, consider the
familiar first law statement:

E2 - El = Q - W


As Kestin points out [1]:
". . .The concept of energy is connected with two
different states of a single closed system and a numerical
value can only be ascribed to the difference E2 - El be-
tween the energies in the two states, because only this
difference, or its negative, can be measured by means of
an adiabetic, irreversible process . . ."
Thus for any closed system, we may arbitrarily choose
to assign an absolute numerical value to any one state of
the system. Most often this is a numerical value of zero
at a so-called reference state. Because of the requirement
to satisfy equation #1, we have no more freedom of choice
and corresponding absolute energy values are determined
for all other possible states of our single closed system.
The conclusions about reference state selection reached
in the article follow in a direct way from equation #1 and
the corresponding second law statement. As one example,
let us define a reference state for a single closed system to
consist of a collection of sub-systems, each of which
contains one pure element in some arbitrary state. If we
assign a numerical value of zero to the energy of each
sub-system, we have set the value of reference state energy
equal to zero for the entire closed system. Clearly this
choice of reference state is alawys available, regardless of
what particular chemical compounds might be present,
and further there is no constraint on what specific refer-
ence states we select for the individual pure elements. So
this method of assigning absolute energy values is always
acceptable in principle, whether or not chemical reactions
are possible in a particular closed system. Similar results
can be obtained in the case of entropy.
Not only is the closed system approach a simpler way
to obtain information about acceptable reference states, but
it also avoids possible misleading interpretations of total
energy or entropy values. As Kestin points out [2]:
". . .no physical meaning can be attached to the
difference between the energies of two different systems,
even if the two systems merely represent different masses
of the same homogeneous system . . ."
In the CEE article, Profesor Fredrickson uses the
notions of total internal energy and total entropy in de-
riving reference state constraints. Then the results are
applied to interpretation of a problem from the classic text
by Modell and Reid [3]. The problem involves computation
of heat transfer to the helium in a tank which will main-
tain total internal energy at a constant value despite the
flow of gas from the tank. The comment is made that
". . we cannot know how to adjust the heat transfer rate
to the gas so that its absolute total internal energy remains
constant as its mass changes . . .". The implication of this
and other remarks in the article is that there does exist a
unique absolute energy value for any particular collection
of matter, even though we cannot in principle determine
what it is. But as discussed above, there is no one unique
absolute internal energy for a particular system. We can
assign absolute energy values, but the only unique values
are for changes of state of a simple closed system. If we
allow changes of system mass to occur, as in an open
system, there is no physical meaning even to the numerical
value of changes in the system (total) internal energy. By
our freedom to select reference states, we can force an
open system energy change to have whatever numerical

value we may desire. Even the notion of holding the
energy of an open system constant has no physical mean-
The lack of direct physical meaning for total internal
energy does not invalidate the open system equation which
contains such a term. Rather in that equation, the input,
accumulation, and output terms in combination have the
effect of making the open system balance equivalent to a
closed system balance in disguise. The open system equa-
tion is valid, but the total energy term by itself has no
physical meaning.
Finally, it can be noted that not all "state functions"
are created equal. We commonly refer for example to
internal energy, specific volume, and Gibbs free energy as
state functions. But these are really not the same. The
volume term, in common with pressure and temperature, is
accepted as an inherently absolute quantity, except for
choice of units. There is no issue of a reference state. In-
ternal energy, however, can take on any desired numerical
value at any one state. It is only changes of internal energy
that must always be the same. Another such function is
enthalpy. Clearly the product of two absolute quantities,
PV is also an absolute quantity, and so the linear sum of
internal energy and PV which we call enthalpy preserves
the property that changes of enthalpy depend only on
state changes and not upon choices) of reference statess.
Still a third kind of "state function" is exemplified by
Gibbs free energy, defined as:
G = U + PV - TS (2)
An arbitrary set of absolute values for G is deter-
mined by the selection of reference states for internal
energy and entropy. But these absolute values do not be-
have in the same manner with respect to changes of state
as do internal energy or entropy values. Comparing two
different states, we have:
G2 - G1 U2 - U1 + P2 V2 - P1 V1 -
T2 S2 + T1 S1 (3)

Clearly it is only in the case that T2 = T1 that we can
be assured that changes in G depend only on changes in
state. In any other case, it is generally possible to affect
the numerical value of the change in G by an arbitrary se-
lection of the reference states) for entropy. Since we are
always free to make such selectionss, and since no legiti-
mate thermodynamic conclusion can be thereby affected,
we conclude that Gibbs free energy is a third kind of state
function. If the system is isothermal, free energy changes
are unique. If the system is not isothermal, there is no
physical meaning to the numerical value of free energy
changes. This lack of meaning is a fact whether the system
is open or closed.
W. H. Abraham
Iowa State University

1. J. Kestin, "A Course in Thermodynamics," p. 157
(Waltham, Massachusetts: Blaisdell Publishing
Company, 1966).
2. Ibid pp. 158-159.
3. M. Modell and R. C. Reid, "Thermodynamics and its
Applications," p. 141 (Englewood Cliffs, N.J.: Prentice-
Hall, Inc., 1974).


jPl classroom



University of Colorado
Boulder, CO 80309

PROBLEM SOLVING HAS become an area of in-
tense interest and study [1-10]. Textbooks have
been written on the subject and separate courses
are being offered. While it would be impractical
for all engineering educators to attempt separate
offerings in problem solving, the concepts and ap-
plication of problem solving can be utilized in ex-
isting courses. This can be done without any loss
of material coverage.
The objective of this paper is to indicate spe-
cific areas in a course being taught where the
problem solving approach can be utilized and why
this approach can be useful.

There are a large variety of problem solving
strategies but most contain the elements initially
described by Polya [11] and expanded by Woods
[1]: 1) Define the problem, 2) explore possible
solution procedures, 3) develop a solution plan,
4) carry out the plan, and 5) check your results.
This is often not a straight linear process since
the problem solver may have to loop backwards
at any stage of solution process to redefine the

Richard D. Noble received his
B.E. degree in 1968 and M.E. degree
in 1969 from Stevens Institute of
Technology. In 1976, he received
his PhD degree from the University
of California, Davis. His current
research interests include facilitated
transport in liquid membranes,
transient heat transfer, and problem
solving skills.
O Copyright ChE Division, ASEE, 1983

problem or develop new solution strategies if the
initial attempts fail. The degree of difficulty in
solving problems can be related to the level of
difficulty outlined in Bloom's taxonomy of
knowledge [12] (see Table 1). As problems re-
quire higher levels of thinking, students ex-
perience increased difficulty since they have had
little or no practice in problems at higher think-
ing levels. Most problems at the end of a chapter
in an engineering textbook require application.
Problems requiring analysis and synthesis are
rarely encountered by students. Once encountered,
students have no structured process for solving
these problems. Even problems requiring applica-
tion of material presented can be difficult.
Students expect exactly the right amount of in-
formation given to solve the problem and a de-
finitive statement of what the problem requires
for a solution. Even at this point, if students
cannot plod straight through to the solution, they
sometimes become confused and cannot develop a
solution. Overcoming anxiety and frustration then
also becomes an important component of problem
solving [13, 14].
This paper will present a series of different
approaches which can be used with a class to de-
velop their problem solving skills. These tech-
niques require some time and effort to imple-

Refering to Bloom's taxonomy (Table 1),
most problems at the end of a textbook chapter or
on an examination require application. Typically,
the exact amount of information required to solve
the problem is given and the student applies
knowledge learned in the chapter to the problem.
Higher levels of thinking such as analysis and
synthesis, are normally not encountered. There-
fore, students get no practice in applying newly
learned knowledge as part of a more complicated
or vague problem.
To overcome this limitation, a mixture of


problems requiring application, analysis, and
synthesis will reinforce a student's learning and
use of this knowledge in expanded situations. This
will require some additional work on the part of
the instructor since development of analysis and
synthesis problems would be required.

The type of question given a student on an
examination can certainly put to use the problem
solving skills of the students. Using problems
which just require comprehension or application
do very little to test the student's problem solving

Bloom's Taxonomy of Knowledge
Knowledge-Recall memorized information.

What is Fourier's law of
heat conduction?

Measure velocity of fluid in
a pipe at five points along
the cross-section.

Comprehension-Solve recognizable problem.

If the temperature gra-
dient through a place
wall is tripled, what is the
resulting change in the
heat flux ?

Compare the measured ve-
locity distribution with
laminar flow theory.

Application-Use memorized knowledge to solve un-
familiar problem.

What is the steady-state
heat flux through a com-
posite wall, given k's and
boundary temperatures.

Determine the relevant data
needed to test the laminar
flow theory in pipes.

Analysis-Bring together remote relationships to solve
Course Laboratory

A fire breaks out in a
room adjacent to a fuel
tank. How long before
the fuel explodes ?

Determine why the experi-
ment for flow through a
pipe does not agree with
laminar flow theory.

Synthesis-Create alternative solutions to an open-ended
problem and select best one.
Course Laboratory

Design a heat exchanger. Design an experiment to
Specify type and con- measure the velocity dis-
struction details. tribution in pipes.

To overcome this limitation, a
mixture of problems requiring application,
analysis, and synthesis will reinforce a student's
learning and use of this knowledge
in expanded situations.

skills as well as knowledge. Adding a problem
which requires analysis provides the framework
for students to make better use of their problem
solving skills since the degree of difficulty in-
creases. This is not to say that solving problems
requiring comprehension or application do not
make use of problem solving skills but adding
more difficult problems can increase a student's
problem solving skills. If we test students on prob-
lems requiring analysis or synthesis, it is im-
portant that we have provided some prior practice
in solving problems at these thinking levels.


The use of example problems can serve as a
tool for developing problem solving skills as well
as knowledge. All aspects of a problem solving
strategy can be utilized in an example problem.
Once the problem statement is read from the text
or hand-out, I ask the class to determine the given
facts, what we are asked to find, and draw a
diagram. Once this is completed, I ask the students
to provide the solution steps. If a step is incorrect,
we will still follow it until the class realizes that
something is wrong. This shows students that it is
OK to make a mistake, a common emotional block
to creativity. By testing each solution procedure,
we can determine errors in reasoning and also
show alternate solutions. We check our results at
each step in the process to determine the reason-
ableness of our answer. Different heuristic tech-
niques can be utilized with different example
problems to aid in the solution process [15] (see
Table 2 for examples). Students can be asked to
provide heuristics. Another approach is to try at
least one new heuristic each week in class. Once
the solution is obtained, the answer is checked to
insure reasonableness and accuracy. If difficulty
arises at any step in the process, this is the time
to let the students loop back through the process
or use heuristics to become "unstuck." Once the
solution is complete, I ask the students questions
which relate to the problem to increase their
understanding. Which variable can we control?
What happens to the solution if various variables
are changed? It may be necessary to guide the


students in this process. As their skills develop,
the guidance can be reduced.

One key aspect of problem solving is the
realization that people usually do not progress
directly through a solution process to the answer.
There can be false starts, redefining the problem,
alternate solution paths, and finally, checking the
answer. The point of this is that people need
sufficient time to allow the problem solving pro-
cess to be fully utilized. By assigning difficult
problems and allowing a relatively short period of
time for the student to respond, the student can be
placed in a high anxiety situation where his
performance will be low. One method to deal with
this problem is to allow two hours for a one hour
examination. If a student makes a mistake, this
allows sufficient time to recover and proceed
through to a proper solution. My experience has

Some Heuristics or Guides
1. Solve a simpler problem. Many times a student can be-
come immersed in a complicated problem and become
"stuck." Simplifying the problem to a stage where
the student recognizes the solution approach can aid
in developing the actual solution procedure.
2. Overcome excess anxiety. When a student becomes
"stuck," they can develop a large amount of anxiety
which prevents effectively developing a solution.
Awareness is the first step to combating this.
3. Communicate your difficulty to another person. It is
sometimes very beneficial to try to explain your situ-
ation to another person who is familiar with the
subject. Describe what you have done and what you are
trying to do. Often this will help to point out ad-
ditional information or errors in reasoning.
4. Brainstorming. When "stuck" on a problem, generate
a list of words or phrases which immediately come to
mind. Write everything down and defer judgment until
you have exhausted the flow of information. Once this
is completed, analyze the list and use judgement to de-
termine any new relevant information.
5. Personal analogy. Pretend that you have entered the
system under study. Try to imagine what you see, feel,
etc. This helps to "visualize" the situation.
6. Look at extreme cases. Ask yourself a lot of "what if"
questions to get a "feel" for how you think the system
will respond. Have will to doubt. Focuses attention
on different aspects of problem.
7. Incubation. Sometimes it is helpful to stop actively
working on the problem when "stuck." Let the problem
"incubate" for awhile. Some insight may "pop up"
into your conscious domain or, upon your return to the
problem you can see errors in reasoning or other ob-
stacles to the solution that were not previously ob-

been that students will respond very well to taking
evening exams with the extra time allotted.
Engineering problems, especially in junior
and senior level courses, require more than a few
minutes to complete a good solution procedure.
Allowing the extra time allows the instructor to
assign problems requiring analysis instead of just

The method that you use to grade exams and
homework problems can influence a student's
problem solving behavior. If the major credit is
given for a right answer, a student will become
mainly concerned with the answer and not the
solution process. If a student stops getting credit
as soon as he or she makes a mistake, they can
develop a great deal of frustration and anxiety.
Fear of making a mistake is an emotional block
to creativity. They lose perspective on the problem
solution and deal mainly with frustration. If the
student receives the major portion of credit for
a proper solution, the student will work at de-
veloping a correct solution without a high degree
of anxiety over making a mistake.

If a student comes into your office for as-
sistance, it is very easy to simply show them how
to do the problem and have them leave. A more
effective technique would be to help them work
through the method of solution. Whimbey and
Lockhead's problem-solving pairs is one example
[4]. By guiding the student but not giving them
the answer, you help them not only to solve the
problem but to develop problem solving skills
along the way. Wankat [16] and Miller [17] de-
scribe some useful approaches in talking with
students that could prove helpful in these situ-

The use of instructional objectives in a class
can be a major asset to problem solving. Out-
lining the major concepts and explaining what is
required for a particular topic gives the student a
framework for developing a solution strategy. In-
structional objectives can also include such items
as ability to check reasonableness of an answer
or the ability to develop an alternative solution
procedure. Mager's book [18] is an excellent source
to learn about using instructional objectives.


There are also additional references concerned
specifically with instructional objectives for engi-
neering classes [19, 20].


The use of problem solving skills in various
class situations has been discussed. It has been
shown that the thinking level of assigned
problems, type of examination questions, example
problems in class, time factor in examinations,
grading, help outside the classroom and be-
havioral objectives are all areas where problem
solving skills of students can be incorporated.
This allows the class experience to be one where
both an increase in knowledge and problem
solving skills can be attained. FO

1. McMaster University Problem Solving Group, "De-
velopment Stype in Solving Problems," Engineering
Education, Vol. 69, No. 7, April, 1979.
2. Greenfield, L. B., "Student Problem Solving," Engi-
neering Education, Vol. 69, No. 7, April, 1979.
3. Rubinstein, M., "Patterns of Problem Solving,"
Prentice-Hall, Inc., 1975.
4. Whimbey, A. and J. Lockhead, "Problem Solving and
Comprehension: A Short Course in Analytical
Reasoning," Franklin Institute Press, 1980.
5. Adams, J. L., "Conceptual Blockbusting," W. W.
Norton and Co., Second Edition, 1979.
6. McMaster Problem Solving Group, "What is Problem
Solving," Chemical Engineering Education, Summer
1979, pp. 132-137.
7. Woods, D., "On Teaching Problem Solving, Part I:
What is Being Done?" Chemical Engineering Edu-
cation, Spring, 1977, pp. 86-94.
8. Woods, D., "On Teaching Problem Solving, Part II:
The Challenges," Chemical Engineering Education,
Summer 1977, pp. 140-144.
9. Noble, R. D., "Mathematical Models in the Context of
Problem Solving," Mathematical Modeling, Vol. 3,
1982, pp. 215-219.
10. "Problem Solving," AIChE Symposium Series, Edited
by D. R. Woods, J. T. Sears, and R. D. Noble, 1983.
11. Polya, G. "How to Solve it," Second Edition, Double-
day Anchor, 1957.
12. Bloom, B. S. and L. G. Broder, "Problem-Solving Pro-
cesses of College Students," Supplementary Edu-
cational Monographs, No. 73, Univ. of Chicago Press,
13. Richardson, S. A., R. D. Noble, and M. Hawkins, "The
Use of Relaxation in Overcoming Anxiety in Problem
Solving," Engineering Education, Nov. 1980.
14. Richardson, S. A., and R. D. Noble, "Anxiety: Another
Aspect of Problem Solving," AIChE Symposium Series
on Problem Solving, 1983.
15. Schoenfeld, A., "Explicit Heuristic Training as a
Variable in Problem Solving Performance," J. for
Research in Mathematical Education, May 1979.

16. Wankat, P. C., "The Professor as Counselor," Engi-
neering Education, November 1980, pp. 153-158.
17. Miller, P., "Nonverbal Communication: How to Say
What you Mean and Know What They're Saying,"
Engineering Education, November 1980, pp. 159-161.
18. Maker, R. F., "Preparing Instructional Objectives,"
Fearson, 1962.
19. Leuba, R., "Instructional Objectives-A Guide to Ef-
fective Teaching," American Society for Engineering
Education publication, 1980.
20. Stice, J., "A First Step Toward Improved Teaching,"
Engineering Education, Vol. 66, No. 5, Feb. 1976, pp.

O book reviews


By Charles D. Holland
McGraw-Hill Book Company, NY
626 pgs, $39.95
Reviewed by
William L. Bolles
Monsanto Company, St. Louis, MO
This book may be regarded as the "Bible" on
calculating the detailed mass and energy balances
on a plate-to-plate basis for distillation columns
processing multicomponent systems. It may also
be regarded as the prime textbook for those writ-
ing computer programs for the same.
The book is intended to completely replace the
1963 volume by the same author, entitled "Multi-
component Distillation".
The principal problem attacked is achieving
the complete component mass and energy balances
for the "complex distillation column": i.e., one
with multiple stages, multiple feeds, multiple side-
draws, either liquid or vapor, and multiple stage
heat exchangers. Also, it is assumed that any
multicomponent nonideal phase equilibria and
enthalpy models may apply. The approach is
rigorous insofar as the Frst Law of Thermo-
dynamics is concerned.
The author develops his subject in a very
orderly manner, including the following major
topics: introduction to the fundamentals, develop-
ment of computational convergence methods, ap-
plication of convergence methods to complex col-
umns, systems of columns, the Newton-Raphson
method application, azeotropic and extractive dis-
tillation, systems of columns with energy exchange
between streams, distillation accompanied by
chemical reaction, optimum design and operation,


the problem of minimum reflux, and thermody-
namic relationships for multicomponent mixtures.
There are also chapters on the fluid mechanics
and mass transfer efficiency relationships of com-
mercial equipment, including the design of sieve
and valve trays.
The approach used throughout the book is to
begin with established theoretical realtionships
such as the First Law, and then proceed with
complete mathematical derivations of all the equa-
tions required in practice.
There are numerous numerical examples, as
well as many problems for classroom and home-
work assignments. There is also available, from
the publisher, a "Solutions Book" to the problems,
free to educators. El


By Bruce A. Finlayson
McGraw-Hill Chemical Engineering Series
366 pages
Reviewed by
A. G. Dixon
Worcester Polytechnic Institute
This graduate-level text, which provides an
introduction to modern methods of obtaining solu-
tions to nonlinear ordinary and partial differential
equations, is a welcome addition to the ranks of
chemical engineering mathematics books. The
author's aim is to teach students how to apply such
techniques as perturbation, orthogonal collocation,
finite difference and finite element methods to
typical chemical engineering problems. He demon-
strates these using case studies drawn largely
from his own experiences in chemical reaction
engineering, heat transfer and polymer flow in-
In a brief introduction (Chapter 1) the author
illustrates the types of equations considered in this
book: initial-value and boundary-value ODEs,
parabolic PDEs and elliptic PDEs. Hyperbolic
PDEs are, unfortunately, not covered.
In Chapter 2 a short discussion of the solution
of nonlinear algebraic equations is given, to pro-
vide background for the methods which follow in
later chapters. Only the successive substitution
and Newton-Raphson methods are presented, and
some convergence proofs are given. No worked
examples are provided.

Chapter 3 presents standard methods for
initial-value ODEs with special attention being
paid to concepts of step-size control, stability and
stiffness. Computer subroutine packages are ex-
amined and a comparison of methods is made.
This chapter is a reasonable review for those
familiar with the material, but will make rather
dry reading for beginners. The presentation is
similar to that in mathematics texts, and no chem-
ical engineering examples are worked out to il-
lustrate the methods.
The main value of the book lies in the final
three chapters, which together make up two-thirds
of the whole. Chapter 4 deals with boundary-value
problems, while Chapter 5 and 6 treat parabolic
and elliptic PDEs respectively. Each chapter fol-
lows the same pattern: the various methods are
introduced through such examples as diffusion and
reaction in a catalyst particle and packed bed re-
actor analysis, some case studies are described,
and a comparison of methods is made based on
operation counts and convergence rates. At times
the discussion of errors and computation times
seems rather lengthy for a text directed to engi-
neering students.
Particular attention is paid to the method of
orthogonal collocation for spatial approximation
in Chapters 4 and 5, especially when combined
with a finite element approach. In Chapter 6 the
Galerkin finite element method is thoroughly de-
scribed, different types of element being illustrated
and compared.
At the end of most chapters the author pro-
vides study questions, homework problems, a short
bibliography and some references. The study ques-
tions give the reader a convenient "check list" of
the more important points in the development,
while the homework problems serve to extend the
formal material. Many of the problems ask for
derivations of results used earlier, while other ex-
tend the case studies, often requiring the use of
FORTRAN computer programs provided in an
appendix. Some of these programs are general
matrix inversion subroutines, while others solve
specific problems.
The layout of the book makes it pleasant to
read; the text is interspersed with tables and
diagrams to illustrate the results, and the print
does not tax the eyes. There seem to be fewer typo-
graphical errors than one might expect in such a
mathematical work. Professor Finlayson's style is
clear and direct, making the book suitable even for
beginning graduate students.


In summary, the book will make a good text for
a graduate-level chemical engineering mathe-
matics course oriented towards numerical meth-
ods. The instructor will find it necessary to amplify
some parts of the book, and will generally wish to
use a broader range of examples and homework
problems than it provides. O

By M. V. Sussman
Mulliken House, Lexington, MA 02173
Reviewed by
J. D. Seader
University of Utah
This is a 100-page self-instruction manual,
which is divided into four parts. In Part I, the
concept of availability, also referred to as exergy,
is defined, explained, and related to enthalpy and
entropy. Applications are given for a number of
simple physical processes. In Part II, changes in
availability for chemical-reaction processes are
analyzed, with the results presented in graphical
form. Second-law efficiencies based on availability,
are defined in Part III. Available energy costing
(thermoeconomics) is considered in Part IV. An
appendix tabulates standard chemical availabil-
ities referred to 25�C, latm and a set of final ref-
erence products for 137 different compounds. Pro-
fessor Sussman advises the reader to read the
manual in a sequential manner. However, keyword
or short summaries placed in the margins permit
the reader to readily skip material that is already
In order to follow the presentation of material
in the manual, the reader should have at least a
fundamental understanding of the first and second
laws of thermodynamics and be able to compute
changes in enthalpy and entropy for pure com-
pounds and ideal mixtures. Such background is gen-
erally the subject of an undergraduate course in
engineering thermodynamics. In addition, some
elementary knowledge of solution thermodynamics
would be helpful. A pretest, included before Part
I, permits the reader to determine if he (she) is
properly prepared to proceed. At the end of each
of the four parts, exit tests, with detailed solutions,
are provided to help determine if the reader has
mastered the material.
In Part I, the following points are developed in
a lucid, interesting, and sometimes historical

1. Both quantity and quality of energy should be con-
2. The quality of energy refers to the fraction of that
energy that can be extracted as useful work.
3. The first law makes no distinction based on the quality
of energy.
4. Maximum work extraction occurs in an ideal (reversible)
5. The availability, which is a state property closely related
to the Gibbs free energy, is a quantitative measure of
the quality of energy and depends on the choice of the
environmental reference (dead) state.
6. The change in availability is independent of the process
path and the choice of dead state.
Throughout Part I, the chemicals considered
are mainly water, air, nitrogen, and oxygen; that
is, chemicals that are found in the environment.
For these, examples are given of calculations of
both availability and change in availability. When
other chemicals are involved, only the change in
availability is considered. Part I is concluded by 12
excellent examples of the calculation of availability
or the change in availability for process involving
no chemical reaction. Of particular importance are
some additional concepts that are presented in: 1)
Example (c)iii, which illustrates the effect on
availability of bringing the material of a given
composition to a different dead-state composition;
2) Example (k), which defines the work equiv-
alent of heat; and 3) Example (1), which notes
that shaft work and electrical energy are exactly
equivalent to availability. It is unfortunate that
these very important concepts are buried in ex-
amples and are not discussed thoroughly in the
main text.
In Part II, chemical reactions are considered,
and it now becomes necessary to carefully eluci-
date the composition of the environmental refer-
ence (dead) state. This has been the subject of
much discussion and controversy among research-
ers, with no general agreement. As an example,
Gaggioli and Petit [Chem Tech 7, 496-506 (1977)]
use the following dead state:
T = 25�C, P = latm


Mole Fraction

Liquid: Pure H20
Solids: CaCO., CaSO, . 2H20, NaCI, etc.
Sussman uses a different dead state; namely,


the standard products of combustion, e.g., H2O (1)
CO2 (g), SO2(g), etc., in their pure state at 25�C
and 1 atm. Thus, he does not deal with a single
dead state, but with a collection of dead states.
These two approaches can lead to different values
for the standard availability of a pure chemical in
a particular state of aggregation at 25�C and 1
atm as shown in the following table:
Standard Availability,
Btu/lb mole

Chemical Species
H,0 (g)
H,0 (1)
CH, (g)
SO, (g)

Gaggioli & Petit Sussman



The differences are considerable for CO. (g)
and particularly SO,(g). If only the change in
availability is of importance, then the dead state
basis cancels out and is not a factor. If the actual
availability is of importance, then the choice of
dead state is very important. Gaggioli and Petit
assume that the ultimate dead state of the sulfur
atom is as CaSO4.2HO(,) and not as pure SO,(g).
Also, they assume that CO2 (g) ultimately becomes
CO2 (g) at a mole fraction of 0.0003 and not pure
CO2 (g), which serves as Sussman's basis. To ob-
tain Sussman's values for standard availability,
one need only compute, from free energies of
formation, the negative of the standard change in
free energy for combustion of the particular com-
pound. Calculated values for 137 different com-
pounds appear in the Appendix.
The major portion of Part II is devoted to a
series of three excellent detailed examples involv-
ing chemical reaction, the last of which deals with
a complete methane reforming process. Availabil-
ity diagrams are used to conveniently illustrate
availability flows, and particularly availability
losses, in each process example. It is made clear
that while energy is conserved, availability is not.
The exit test involves further calculations on the
methane reforming process and directs the reader
to assess the points of greatest availability loss
and to find ways of reducing availability losses.
Just prior to the exit test, Sussman lists some
reasons why availability losses occur.
Part III is a short chapter, which begins by
defining an overall second-law efficiency for a
process as the ratio of availability outputs to
availability inputs. By means of examples, this
efficiency is contrasted to that given by the first

law. Sussman shows clearly that this definition of
second-law efficiency can give negative results
when the chosen reference state does not cor-
respond to that of the lowest free energy. An
alternative definition extractivee second-law ef-
ficiency) is also presented, but it is not general
either because it only applies when streams enter-
ing a process do not mix with other streams. The
exit test questions are relatively short exercises.
An introduction to thermoeconomics is pre-
sented in the final chapter, Part IV. The problem
is how to determine a cost for a stream of energy.
Based on availability considerations, a joule of
electricity should be worth more than a joule of
high-pressure steam, which should be worth more
than a joule of low-pressure steam. Methods for
assigning costs are developed by applying various
costing rules to a process that cogenerates these
three energy streams. The simplest rule presented
assumes that all three energy streams have the
same cost per unit of availability. The resulting
costs per kwh of energy content are $0.0211,
$0.0080, and $0.0053 for electricity, 250 psia
steam, and 50 psia steam, respectively. Other cited
costing rules involve such matters as whether the
energy streams are for internal or external use
and if they must compete with the open market.
The exit test at the end of Part IV involves the
application of one of these alternative costing rules
to the same cogeneration process.
Although written by a chemical engineer, the
chemical engineering literature on second-law
analysis is essentially ignored in the manual. In
particular, the paper by Denbigh [Chem. Eng. Sci.,
6, 1-9 (1956)], in which he derives the availability
function and availability loss by combining the
first and second laws, is not mentioned. Denbigh's
derivation is much more general than the deriva-
tion of Equation (8) in the manual.
Separation processes, such as distillation,
which are very important industrially and gen-
erally inefficient from a second-law analysis, are
almost totally ignored. Nevertheless, the beginner,
who knows little or nothing about second-law
analysis will find his time well spent by studying
the concise text and the many execellent, detailed
examples and exit tests. He can then strengthen
his understanding, learn of other viewpoints, and
see other applications by reading the previously
mentioned papers by Denbigh and by Gaggioli
and Petit, in addition to de Nevers [Chem. Tech.,
12, 306-317 (1982)] and Smith and Van Ness
["Introduction to Chemical Engineering Thermo-
dynamics," McGraw-Hill (1975), Chapter 13]. E

'5 rA





Departmental Sponsors: The following 146 departments contributed
to the support of CHEMICAL ENGINEERING EDUCATION in 1983 with bulk subscriptions.

University of Akron
University of Alabama
University of Alberta
Arizona State University
University of Arizona
University of Arkansas
Auburn University
Brigham Young University
University of British Columbia
Brown University
Bucknell University
California State Polytechnic
California State U. at Long Beach
California Institute of Technology
University of California (Berkeley)
University of California (Davis)
University of California (Santa Barbara)
University of California at San Diego
Carnegie-Mellon University
Case-Western Reserve University
University of Cincinnati
Clarkson College of Technology
Clemson University
Cleveland State University
University of Colorado
Colorado School of Mines
Columbia University
University of Connecticut
Cornell University
University of Dayton
University of Delaware
U. of Detroit
Drexel University
University of Florida
Florida Institute of Technology
Georgia Technical Institute
University of Houston
Howard University
University of Idaho
University of Illinois (Chicago)
University of Illinois (Urbana)
Illinois Institute of Technology
Institute of Paper Chemistry
University of Iowa
John Hopkins University
University of Jordan
Iowa State University
Kansas State University

University of Kentucky
Lafayette College
Lamar University
Laval University
Lehigh University
Loughborough University
Louisiana State University
Louisiana Tech. University
University of Louisville
University of Maine
University of Maryland
University of Massachusetts
Massachusetts Institute of Technology
McMaster University
McNeese State University
University of Michigan
Michigan State University
Michigan Tech. University
University of Minnesota
University of Missouri (Columbia)
University of Missouri (Rolla)
Monash University
Montana State University
University of Nebraska
New Jersey Inst. of Tech.
University of New Hampshire
New Mexico State University
University of New Mexico
City University of New York
Polytechnic Institute of New York
State University of N.Y. at Buffalo
North Carolina State University
University of North Dakota
Northeastern University
Northwestern University
University of Notre Dame
Nova Scotia Tech. College
Ohio State University
Ohio University
ITniversity of Oklahoma
Oklahoma State University
Oregon State University
University of Ottawa
University of Pennsylvania
Pennsylvania State University
University of Pittsburgh
Princeton University
Purdue University
University of Queensland

Queen's University
Rensselaer Polytechnic Institutc
University of Rhode Island
Rice University
University of Rochester
Rose-Hulman Institute
Rutgers U.
University of South Carolina
University of Saskatchewan
South Dakota School of Mines
University of South Alabama
University of South Florida
University of Southern California
Stanford University
Stevens Institute of Technology
University of Sydney
Syracuse University
Teesside Polytechnic Institute
Tennessee Technological University
University of Tennessee
Texas A&M University
Texas A&I University
University of Texas at Austin
Texas Technological University
University of Toledo
Tri-State University
Tufts University
Tulane University
University of Tulsa
University of Utah
Vanderbilt University
Villanova University
University of Virginia
Virginia Polytechnic Institute
Washington State University
University of Washington
Washington University
University of Waterloo
Wayne State University
West Virginia Inst. Technology
West Virginia University
University of Western Ontario
Widener College
University of Windsor
University of Wisconsin (Madison)
Worcester Polytechnic Institute
University of Wyoming
Yale University
Youngstown State University

TO OUR READERS: If your department is not a contributor, please ask your department chairman to write CHEMI-
CAL ENGINEERING EDUCATION, c/o Chemical Engineering Department, University of Florida, Gainesville, Florida

University of Florida Home Page
© 2004 - 2011 University of Florida George A. Smathers Libraries.
All rights reserved.

Acceptable Use, Copyright, and Disclaimer Statement
Powered by SobekCM