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Professor Olaf Hougen ( PDF )
University of Washington, R.W. Moulton ( PDF ) Irreversible Thermodynamics, C.M. Sliepcevich and H.T. Hashemi ( PDF ) Approaches to Statistical Thermodynamics, M.V. Sussman ( PDF ) The New Stoichiometry, E.M. Rosen and E.J. Henley ( PDF ) ChE Kinetics Laboratory, Kenneth B. Bischoff ( PDF ) Programmed Instruction in Thermodynamics, Charles E. Wales ( PDF ) Book Reviews ( PDF ) Thermodynamics: Death and Transfiguration, James L. Throne, Where are the Engineers?, T.B. Metcalfe ( PDF ) ( PDF ) 
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DR.JOSEPH JOFFE,CH.E. DEPT NEWARK COLL ENGG 323 HIGH ST NEWARK,NJ 07102 SUMMER 1968 CHEMICAL PROCESS PRINCIPLES TODAY C9a1 /omf" : PIONEERING EDUCATOR CREATOR OF TEACHERS INSPIRE OF RESEARCHERS %'T. , S"It is more important to carryon research Than itisto pay S' dividends The speaker was Lammot du Pont. The year was gloomy 1932, and he was president of Du Pont. A proposal had been made to pare the research budgets in order to protect the dividend. As it turned out, the company was strong enough to pay for both, and it hasn't missed paying for either in the past sixty years. But there was no doubt which way Lammot du Pont would have decided back in 1932. And today, we invest more than $100 million a year in the quest for new knowledge and better products. It is precisely this attitude towards research and development that attracts so many graduates every year. And that makes Du Pont such an exciting and rewarding place to work. There is no formal training period. Our men go into responsible jobs from the first day. They work in small groups where individual contribu tions are promptly recognized and rewarded. Promotions come from within the company. They do significant work of positive benefit to society. And they work with the best men in their fields in a crackling technical environment that provides every facility needed. If our attitude towards research and work agrees with yours, why not suggest that your students sign up for a talk with a Du Pont recruiter? Or that they write our College Relations Manager, Wilmington, Delaware 19898, for additional information on opportunities in their fields. CU P0r ? I ~~ _<*' Chemical Engineering Education VOLUME 2 NUMBER 3 EDITORIAL AND BUSINESS ADDRESS Department of Chemical Engineering University of Florida Gainesville, Florida 32601 Departments Editor: Ray Fahiein Associate Editor: Mack Tyner Business Manager: R. B. Bennett Publications Board and Regional Advertising Representatives: WEST: William H. Corcoran Chairman of Publication Board Department of Chemical Engineering California Institute of Technology Pasadena, California 91109 SOUTH: Charles Littlejohn Department of Chemical Engineering Clemson University Clemson, South Carolina 29631 EAST: Robert Matteson College Relations Sun Oil Company Philadelphia, Pennsylvania 19100 E. P. Bartkus Secretary's Department E. I. du Pont de Nemours Wilmington, Delaware 19898 NORTH: J. J. Martin Department of Chemical Engineering University of Michigan Ann Arbor, Michigan 48104 J. A. Bergantz Department of Chemical Engineering University of Buffalo Buffalo, N. Y. 14200 CENTRAL: James Weber Department of Chemical Engineering University of Nebraska Lincoln, Nebraska 68508 99 Editorial 98 Letters from Readers 104 Departments of Chemical Engineering University of Washington, R. W. Moulton 100 The Educator Professor Olaf Hougen 139 Views and Opinions Thermodynamics: Death and Transfigura tion, James L. Throne Where are the Engineers?, T. B. Metcalfe 129 The Classroom Programmed Instruction in Thermody namics, Charles E. Wales 126 The Laboratory ChE Kinetics Laboratory, Kenneth B. Bischoff 135 Book Reviews 137 Problems for Teachers Feature Articles 109 Irreversible Thermodynamics, C. M. Sliep cevich and H. T. Hashemi 113 Approaches to Statistical Thermodynamics, M. V. Sussman 120 The New Stoichiometry, E. M. Rosen and E. J. Henley 107 DIVISION ACTIVITIES Scriven Delivers Annual Lecture CHEMICAL ENGINEERING EDUCATION is published quarterly by the Chemical Engineering Division, American Society for Engineering Education. The publication is edited at the Chemical Engineering Department, University of Florida. Application to mail at secondclass postage rates is pending at Gainesville, Florida, and at additional mailing offices. Correspondence regarding editorial matter, circulation and changes of address should be addressed to the Editor at Gainesville, Florida 32601. Advertising rates and information are available from the advertising representatives. Plates and other advertising material may be sent directly to the printer: E. O. Painter Printing Co., 137 E. Wisconsin Ave., DeLand, Florida 32720. Subscription rates on request. SUMMER, 1968 SUMMER 1968 I ' New from RONALD Mack Tyner and Frank P. May, both University of Florida An introduction to linear control theory for college students and practicing engineers. Emphasis is on the universality of the control problem in process engineer ing through mathematical equations that apply equally to components from all technologies. Linearization of nonlinear forms and its limitations are discussed early in the book. Both the root locus method and the fre quency response method are stressed as means of control system analysis, and Nyquist diagrams, Bode plots, and Nichols charts, which serve as useful analytical tech niques, are demonstrated in many of the illustrative examples. Attention is directed to the use of both digital and analog computers. An Instructor's Supplement is available. 1968. 472 pages. $14.00 Publishers since 1900 The Ronald Press Company 79 Madison Avenue New York. N.Y. 10016 from the READERS Editor: Please refer to the article on the common thermody namics course by Manning and Canjar in your winter issue, page 11. Why should the chemical engineering staff at Carnegie have to put up with (a) a compromise, (b) conferences to make the compromise work? I advise the staff to scream loudly and try to get out of the bed of Procrustes. Ernest W. Thiele University of Notre Dame Editor: The ASEE might render a real service to our country if it could get pages 78 and 79 Spring CEE into the hands of every senator and congressman in the country, with a forceful letter of transmittal calling attention to the analogy of General Hershey and Adolph Hitler as implied in "The Rise and Fall of the Third Reich" and alluded to in the last paragraph on page 78. John E. Kiker, Jr. University of Florida Acknowledgments The following have donated funds for the sup port of CHEMICAL ENGINEERING EDUCA TION: Atlantic Richfield Company C. F. Braun and Company Dow Chemical Company Mallinckrodt Chemical Works Monsanto Company Olin Mathieson Chemical Corporation The Procter and Gamble Company 3M Company Standard Oil (Indiana) Foundation The Stauffer Chemical Company CHEMICAL ENGINEERING EDUCATION IPRCS from the EDITOR Since we wanted our first issues of CHEMI CAL ENGINEERING EDUCATION to have as broad an appeal as possible, we included articles in a number of areas of modern chemical engi neering. But in this issue, we are using a dif ferent approach: we are emphasizing the areas of thermodynamics, kinetics, and stoichiometry the subjects that were joined together many years ago in a threevolume work called "Chemical Pro cess Principles." As our "ChE Educator" we are featuring one of the brilliant authors of that work, Professor Hougen, and, as our "ChE De partment" his Alma Mater, the University of Washington. Olaf Hougen might well be called the inspira tional and intellectual father of modern chemical engineering: he is the inspire of many promi nent chemical engineers who were his students; he developed the areas of chemical engineering thermodynamics and kinetics; and he played an important role in the development of transport phenomena when he brought Professor Bird back to Wisconsin and charged him with the responsi bility of placing the engineering computation of heat, mass, and momentum transfer on a sound theoretical and scientific basis.* In this day of continued debate on the merits of the socalled "chemical engineering science" approach, there are lessons to be learned from the example of this great man. The first and most important lesson is that we cannot expect to know what is at the end of the research path before we get there; i.e., no one could know a priori what applications would arise from the first course in mass transport which Professor Bird began to teach back in 1954; nor could Professors Hougen and Watson initially know the extent to which the theoretical subject of chemical kinetics could be extended and applied to the flow, batch, and fluidized reactors of chemical engineering practice; nor could the profession know many de cades ago that chemical plants would be designed on the basis of the thermodynamic properties of substances that were predicted by the theoretical methods developed by these same two men. Al though talk about the "practicality" of thermody *Professor Bird recognized the inspiration and incen tive placed before him by Professor Hougen in the pre face of his text on "Transport Phenomena" with the coded acronym: "This book is dedicated to Olaf Hougen." namics persisted throughout the 1950's, today not even the Neanderthals of the profession ques tion the importance of thermodynamic informa tion on enthalpies, free energies, heats of reaction and PVT data to modern industry. The lesson we must again learn is that chemical engineers and particularly young teachers and graduate stu dentsmust be provided an opportunity to delve into those areas of science that are unexplored even if applications are not clearly visible. (An important area of this type today is the en tire field of bioengineering and biomedical engi neering). It is certainly destructive to stifle the curiosity and dull the initiative of our young scholars by harassing them with demands that they show the immediate application of their work. These men need instead the same kind of encouragement Professor Hougen provided Pro fessor Bird and others. But another lesson that can be learned from Professor Hougen's career is one that must be learned by many of these same young scholars; namely, that the work of the engineering scholar should ultimately be placedby himself or by othersin a form that is usable to the practicing engineer. For the real utility of the work of Hougen and Watson lies in the fact that these authors prepared numerous charts that could be easily used by the engineer in practice (e.g. to find the final conditions in a Joule Thompson expansion or to predict enthalpy or PVT changes in a process.) Without such a step, the important work of the scholar may long go unheeded by engineers in industry who do not have the time or academic background to use it. The AIChE Research Committee is currently studying the problem of the industryacademic gap. President Max Peters has often spoken of it and it was forthrightly discussed in the last issue of CEE by Bob Lenz. Perhaps one answer lies in our thinking again about the work of Olaf Hougen in not only developing the Chemical Pro cess Principles but also in further making them applicable to real engineering problems. CHEMI CAL ENGINEERING EDUCATION in this issue is proud to present articles on the "Chemical Pro cess Principles Today" and to acknowledge the debts of the profession to a pioneering educator and a very warm and sensitive human being. R. W. F. SUMMER, 1968 A GREAT TEACHER OLAF A. HOUGEN Olaf Andreas Hougen, Emeritus Professor of Chemical Engineering at the University of Wis consin, has pursued a distinguished career in the field of chemical engineering education. He has been one of the leaders in bringing the profession from a state of empirical practice to a state where it is firmly based upon sound basic prin ciples of chemistry, physics, and mathematics. He was born in Manitowoc, Wisconsin, on October 4, 1893, the son of a prominent pastor, who was a pioneer in the development of the Norwegian Evangelical Lutheran Church of America. When Olaf was four years old, his fa ther was assigned a pastorate in Decorah, Iowa, and it was there that Olaf received his elemen tary grade school education. While the material resources of the Hougen family were limited one of Olaf's daily chores was to take the family's cow to pasture and backit was a family rich in intellectual and social activities, with constant encouragement to the children to achieve high educational attainments. Proximity to Luther College and the fact that he had several attrac tive sisters made the Hougen home in Decorah the center of much lively social activity. The family later moved to the State of Washington, where Olaf graduated from Tacoma High School. He then decided to enroll at the University of Washington in the Department of Chemical En gineering, which was headed by Dr. H. K. Benson, one of the early leaders in the development of chemical engineering as a separate educational discipline. At the University of Washington, Olaf established a distinguished career, both aca demically and in extracurricular activities. He received his BS degree in 1915, cum laude, and was a member of Tau Beta Pi, Phi Beta Kappa, and other honorary societies. After graduation, he spent one year with the American Smelting and Refining Company, at their Tacoma plant. Then, with the encourage ment of Dr. Benson, Olaf decided to take up graduate work in chemical engineering. He chose the University of Wisconsin because of the na tionally recognized work of C. F. Burgess (founder of the Chemical Engineering Depart ment and of the various Burgess companies, in cluding the Burgess Battery Company), O. L. Kowalke (prominent in gas manufacture re search; Chairman of the Chemical Engineering Department for 25 years), and 0. P. Watts (leader in the field of applied electrochemistry). After two years at Wisconsin, first as a Graduate Fellow and then as a full time Instructor, he served in World War I, 19181919, in the Chemi cal Warfare Service, assigned to chemical engi neering work at the Saltville, Virginia, plant. Following his discharge from the armed forces, he spent one year with the Carborundum Com pany, in their research laboratories at Niagara Falls, New York, where his work was largely focused upon the development of refractory ma terials. The post war upsurge in student enrollment that was felt throughout the country resulted in an invitation being extended to Olaf to resume his Wisconsin connection. He accepted, and re turned to Madison in the fall of 1920, as an As sistant Professor. Since that time until his re tirement in 1964, he has been associated continu ously with the University of Wisconsin, except for several leaves of absence. He rose through the various academic ranks, and served three terms as Chairman, totaling to 8 years. His first graduate degree, Chemical Engineer, was earned in 1918; his PhD was received in 1925, number 4 in a list that now includes over 200 names. When Olaf Hougen started his career as a teacher, chemical engineering courses were large ly qualitative in character; the pioneering texts of Walker, Lewis and MacAdams and of Badger and McCabe had not yet been published. Through CHEMICAL ENGINEERING EDUCATION S educator This article was contributed by an anonymous associate of Professor Hougen. The Academic'Tamily Tree"of a Great Teacher S0.A.NHOUGEN I SHAW Z WHATLEY 3 BOCHINSK/I ARSON 5 WILEY 6 KOERNER 7 BARHIUSEN B9OSTIAN 9 BC/MEN/HERA o NADIO 11 KINNEY 2 SHARP 13 BETHEA SSiONAKER 15 ORAY iTIVTERMAMN 2 KANO SDICKSON 1 BYDAL S GORE 6 ORE/ER 7 SCHINLER WILLIAMS STALWALAR 3DA OIS I WETHERN SJACOW/ 3 LEE 4 ALSEICK S /WIMNM 6 CORINO 7 KIM 8 DENNY 9 I/M COBERLY 2 COFFEE SMUTZ 4 ADLER RANZ 6 STOUT 7 TATE  DIFFIE 9 WETZEL 0 NICHOLS G IBSON LEADER BRODKEY 14HERRING 15 DARNELL 16 HOLCOMB 170HARItESWMn CROSBY 19 OWYN 20MILLER 21iReUZTINGER 22 THOMAS 23 MOORE 24 LAMBERT 25 AMRNELL 26 AIlRVIN 27 DICKINSON 28 KIM DOWNING BISWAS 32 RANALL SDAMON I RAO OOP/CHAND SVENKATESAKMRD 4RAMA SWAMI VENKATESMARMs SMANI MTYAAARAYAWA GARMA 8PALKR/ISNA SEN GUPTA ROY OUHA KAURA RA4GMVENDRA RA1rT OIRADKER RAJA A4HADEVAN I CLARK HS// 3 AERTNER 4 D#AISK8S 5 BENJAMIN 6 WELCH 7 HOSLER ORELL 9 THOAM8 0O KIRBY I 81UEHL A YEN 13 OLAS IS YATABE 16 PETERSON 17 HALEY BOCER B VENIKATSWIU ACHARYA MURTY 4 RAO SRAO AA 0 6 ATAPATHY 1MURTY e RAO SCHIRANJIVI/ RAO SJAANwNADHA RAO 3 RAO 4 SUBBA KR/SHNA 16 RAO 7 REDDY 18 RAO 19 AfNYAM zo wAI/RTY 21 MI/RTY 21 MURTY WESTWAZER GROHSEE 3 OAZLEY F CARfENFR 3 RAO 6 JORDAN 1 GIFFORD CORRIGAN SDOSNO0 2 MASSEY 3 SNOWALA RAS 4 W/N 4 KLASSEN 5RAINES SBARVER 6 MILLER 1 FAIR Z OLDENBUS R 3 PERKINS 4 POZZ/ HALL SOTTMENS 7 SAY L I OLSON I LI/IHTNER SCOLBURN 2 EARLE 2 RAO JACKSON CEAVLSK"E PIKE ANOAERSON LANDOREN MARS LPHILLIPS 1 ERICKSON A 7 LEE I ARLA6E CASKEY 5 ROWE 6 60RDON 7 BAIN SGAMSON THODOS WILKE BECKMANN 12 P/FAH 13 BROWN TAECKEA SWONO KIRK 17 FRIDMAN 18 ANDERSON 19 FE/N 20 BICKLING 21 BAKER ZZ YANG 23 DORAISWAMY RAO TAO 26 NELSON TREACY 8 8DDCK TSCHERN/TZ 30 RE/I 31 BABCOCK 32 K/RCHER 33 JOHNSON CHNAO OR ENKORN SAWYER 37 POLEJES 38 ROGERS 1] ENQEL 40 C/# cOHITTENDEN 42 MILAY RAMIASNAMI LIN ORELLO ANJAR IOTARD /IIRKE IBSON LDAIAN WICKS PARKAS '(LEY MITH HWA IPPEL USSTIN rUNo 1Wsrw/ AOWIN 'AISER LESSON JOHNS SKEW eDRICK IRMA4N *RMAK 'LLIS AOTOTO TALMLitE BRISKEY SCHNELLE LANDIS 6 GESER 9 KAMAL MKOSTECKI CAMP 1 RIMPEL 13 SUTHEOR SAMHBER rWELTYII SMEYER II .LANAI J BER 10 it 8 A 668 9H 10 M 23 8 13 A 14 M 15 LA 7 BROWN W/LCOX POTER 99 AE 2 MM 1oLYmCH I S SHANSON =R RTSON F PERS 7 BROWE 'OO3TEPJ/,II The above academic family tree indicates those persons who have held university professorships by white numbers on a black background. Over the years Professor Hougen has been advisor for 44 PhD's of which nearly half are now in educational work. SUMMER, 1968 I SIMKOVICH Z COZEWITH *I GOTFI/NER 2 WH/TE 1 FOK Z FOSTER RWILLNS CLEMEOS JUSTICE 3 ELKNO 86877 ~L~'~T~3 f f IHOBSON PERONA 3 LASER 4 RIGAS rOYER 5 /IMOTAKE EM/IO 6 FORMAN NWI/CK 7 TALLER lAB AII / TIEN 9 MEAHRA 10 YEN ORIEVES 23 SEN O/PrA 24 WENTZ 15 MIS/C 16 REYNES 17 DASTUR :AWOSON 19 EKINER B SE WI/T MATH/IR 22 MATSEHKE SHAMR/N Despite his many honors, Olaf remains a modest person, with a warm and outgoing personality; with a host of friends not only in University circles, but in the Madison community as well. out his career at Wisconsin, Olaf was a leading force in bringing about a constant modernization and upgrading of the undergraduate curriculum, including the establishment of unit operations theory and laboratory courses, chemical engi neering thermodynamics, and kinetics and re actor design. It was through his influence that Bird, Stewart, and Lightfoot wrote their text, Transport Phenomena, which has had such a widespread impact in chemical engineering edu cation in recent years. When Olaf started his teaching career at Wisconsin, graduate enrollment in chemical engi neering was low, being generally limited to one or two graduate fellows and to the young mem bers of the teaching staff working for their de grees. While some growth took place, it was greatly accelerated when Olaf, in recognition of his substantial research contributions with limi ted support, received a grant in 1941 of $100,000 from the University Research Committee, using funds given by the Wisconsin Alumni Research Foundation. This grant enabled him to start a program of graduate research that not only re sulted in a sharp increase in the number of gradu ate students, but also enabled him to initiate a program of staff additions. He was largely re sponsible for bringing in K. M. Watson (who later resigned), C. C. Watson, W. R. Marshall, E. N. Lightfoot, W. E. Stewart, and R. B. Bird, all of whom contributed greatly to making Wiscon sin's Department of Chemical Engineering one of the leading ones in this country. When Olaf Hougen joined the Wisconsin staff, his unusual talents as a classroom teacher became apparent at once. While his courses were de manding, his enthusiasm, his clarity of exposi tion, his excellent organization of subject matter, and his fresh approach to solving chemical engi neering problems won him immediate acceptance by the students as being one of the outstanding teachers in the College of Engineering. Olaf has always treated his students with courtesy and respect, and has encouraged them to do original analytical thinking in solving difficult problems. Olaf Hougen early recognized that the ideal teacher strikes an effective balance between class room teaching and research, and he constantly strove to match this ideal, with the high degree of success that his associates fully appreciate. Over the years, he has trained 44 PhD's, with somewhat less than half now being in educational work. The widely disseminated influence that Olaf has had in graduate education in illustrated by his academic "Family Tree," shown in the ac companying figure, which was prepared by R. B. Bird and presented to Olaf at a recognition dinner given in his honor on October 8, 1966. On this chart, the white numbers on a black background indicate those persons who have at sometime held university professorships. Olaf's publications cover a wide diversity of subjects in the field of chemical engineering, and total to over ninety. Olaf Hougen's influence in the field of chemical engineering education has been felt not only through his classroom teaching and his direction of graduate research, but also by the publication of a series of widely used text books. Industrial Chemical Calculations, published in 1931 with K. M. Watson as coauthor, was later followed by the three volume series, Chemical Process Princi ples (Material and Energy Balances; Thermody namics; Kinetics), again with K. M. Watson as coauthor. These texts have been highly success ful, and have been translated into Italian, Japan ese, and Spanish. Many honors and awards have come to Olaf Hougen because of his distinguished career in engineering education and research. He has de livered many invited lectures at other universi ties, and before industrial groups. His major awards are as follows. Awards Based on Contributions in Engineering Education 1. The Warren K. Lewis Award of the American Institute of Chemical Engineers, 1964. Second recipient of the award. 2. The Lamme Award of the American Society for Engineering Education, 1961. This is considered the major award of the ASEE. 3. Appointment to the Burgess Research Professor ship at the University of Wisconsin, 19551961. 4. Benjamin Smith Reynolds Award for Excellence in Teaching Future Engineers, 1955. An award of $1,000 given annually to an outstanding Wisconsin Faculty member. First recipient of the award. CHEMICAL ENGINEERING EDUCATION n"  Ir f ..* i.I' Professor R. B. Bird presented the academic "family tree" to Professor Hougen at a dinner in his honor. Awards From Professional Societies 1. American Chemical Society Award in Industrial and Engineering Chemistry, sponsored by the Esso Research and Engineering Company, 1961. 2. Founders Award, American Institute of Chemical Engineers, 1958. 3. Institute Lecturer, American Institute of Chemical Engineers, 1950. The second lecturer to receive this honor. 4. William H. Walker Award of the American Insti tute of Chemical Engineers, 1944. International Recognition and Awards 1. Scientific Attach6, U. S. State Department. As signed to American Embassy, Stockholm and cov ering Denmark, Finland, Iceland, Norway, and Sweden 196163. 2. Honorary Doctor of Science Degree from the Nor wegian Institute of Technology, Trondheim, Nor way, at 50th Anniversary Celebration, 1960. 3. Honorary member, Indian Institute of Chemical Engineers, 1958. 4. Fulbright Professorship To Norwegian Institute of Technology, 1951 To Kyoto University, Japan, 195758. 5. Invited to give keynote address before the Deut sche Bunsen Gesellschaft, Duisberg, West Ger many, 1953. Despite his many honors, Olaf remains a modest person, with a warm and outgoing per sonality; with a host of friends not only in Uni versity circles, but in the Madison community as well. Olaf Hougen was married in 1919 to Olga M. Berg, and one daughter, Esther, was born to them. Esther is married to F. G. Taylor, and has 3 children, in whom the Hougen grandparents take great pleasure. One of Olaf's brothers, Joel O. Hougen, is presently the Alcoa Professor of Chemical Engineering at the University of Texas. A nephew, Wendell T. Berg, is a chemical engi neer with Union Oil Company. The nationally known CBS commentator, Eric Sevareid, is one of his nephews. Because of his Norwegian ancestry, Olaf has taken a prominent role in NorwegianAmeri can activities, as well as developing and main taining strong ties with Norway. He is a member of Sons of Norway and of Ygdrasil Literary So ciety. Because of his activities in 194045 as Wis consin Treasurer for American Relief for Nor way, he received a citation from King Haakon of Norway. As a result of his father's influence, religion has been a strong and continuous force in his life. He has participated extensively in the activities of Luther Memorial Church, a large church located in the University area. Olaf is a long standing member of the Optimist Club, and has served as an officer. Golfing is his chief out door recreation, and keeps him in excellent physi cal condition. Though Olaf retired in 1964, he is still actively interested in his department and in the chemical engineering profession. He frequently is at his office, and the members of the staff have the bene fit of his counsel and advice. He truly is one of the revered elder statesmen of the chemical engi neering profession. SUMMER, 1968 1 Department UNIVERSITY OF WASHINGTON R. W. MOULTON, Head History (19001968) In 1895 the University of Washington moved from downtown Seattle to its present location about 4 miles northeast of the city center. Denny Hall was the first structure built and in its base ment there were facilities for what was known then as the Chemistry Department. Chemical Engineering at the University of Washington had its roots in the Chemistry Department. In 1904, Dr. Henry K. Benson joined the faculty of the University and while his educational background was in chemistry his interests were motivated strongly toward industrial chemistry. Dr. Benson was interested in the application of chemistry to agriculture and he was a leader in the chemurgy movement in the Pacific North west. He was extremely conscious of the pulp and paper industry locally and throughout the world. He did much research during his lifetime in fields related to the production of pulp from wood and other forest products. In 1919, Dr. Benson was appointed executive officer of the Department of Chemistry and Chemical Engineering as it was known at that time. He served in that capacity until 1947. In 1911, an organization called the Chemical Engineering Club was formed at the University of Washington. At that time leaders from chemi cal industry in the Pacific Northwest together with appropriate faculty members at the Univer sity of Washington established the first chemical engineering curriculum. This curriculum was somewhat weighted toward pulp and paper and also coal and gas technology. This curriculum was the precursor of the chemical engineering program as it is known today. In 1922, Professor Warren L. Beuschlein joined the faculty of the department. Professor Beuschlein had received his Bachelor of Science in Chemical Engineering degree from the Uni versity of Washington and his Master of Science degree in Chemical Engineering from the Cali fornia Institute of Technology. Professor Beu schlein became a dominant figure in the thinking of the faculty of the department during his tenure on the campus. He died suddenly in September 1944. Professor Beuschlein's research interests were quite broad. He made important contribu tions in the areas of the manufacture of charcoal from wood waste, the high pressure hydrogena tion of coal, the fixation of nitrogen from air, and in the manufacture of pulp from forest products. The first doctorate degree in Chemical Engi neering on record was that awarded to Dr. Cal vert D. Wright in 1931. Dr. Wright joined the faculty at Pennsylvania State University and was active in research dealing with the utiliza tion of coal during his tenure there. During the 20's the department graduated a considerable number of individuals, some of whom obtained significant national prominence in their profes sional careers. Among these are Mr. Samuel G. Baker, Dr. Olaf A. Hougen, Mr. Victor Mills, and Dr. Waldo Semon. Mr. Baker had important re sponsibilities with the DuPont Company before his retirement. Dr. Hougen became a leading educator and spent most of his professional life at the University of Wisconsin. Mr. Mills was employed at the Procter and Gamble Company for most of his professional life and made sig nificant contributions to their new product de velopment. Dr. Waldo Semon was associated with the Goodrich Rubber Company and was their research director before retirement. Accreditation of chemical engineering de partments was initiated originally by the Ameri can Institute of Chemical Engineers in 1925. The University of Washington's department of Chemi cal Engineering became the first department ac credited in the Pacific Northwest and this action took place in 1926. In the middle 30's accredi tation was first carried out by AIChE for the new organization, the Engineers Council for Pro fessional Development. In 1930, Dr. Kenneth A. Kobe, a new PhD in Chemical Engineering from the University of Minnesota joined the faculty. Dr. Kobe was a very energetic, enthusiastic faculty member. Du CHEMICAL ENGINEERING EDUCATION Many prominent chemical engineers, including Olaf Hougen received their education at the University of Washington in Seattle. ring his eleven years on the faculty he published well over 100 significant papers dealing with his area of research and related works. Dr. Kobe resigned from the department in 1941 to accept a position on the faculty of the Department of Chemical Engineering at the University of Texas. Dr. Frank B. West joined the department in 1939. He left later during the war years. The author became affiliated with the department in 1941, as did Dr. Joseph L. McCarthy. Both Dr. McCarthy and the author are still active mem bers of the Chemical Engineering faculty. The postwar years have produced extensive changes in the department. There has been a dramatic increase in the number of faculty mem bers, the size of the undergraduate classes, the size of the graduate program, and the amount and kind of facilities devoted to the department. These changes have created the department as it exists today. Chemical Engineering Today The faculty of the Department of Chemical Engineering now number fourteen individuals. Four of these men have joint appointments; two with Nuclear Engineering, and two with Forest Resources. The College of Forest Resources has developed within the last few years a Bachelor of Science degree program in Pulp and Paper Technology. Because of the long and deep in terest of the Department of Chemical Engineer ing in the field of pulp and paper these two joint appointments were established and serve to main tain close and good working relationships in this area. The Department of Chemical Engineering played a significant role in the formation of a Nuclear Engineering Department at the Uni versity of Washington. The first courses in nu clear engineering on this campus were given by the Department of Chemical Engineering. An early interest in the facilities at Richland, Wash ington dating back to about 1950 initiated some of this enthusiasm for the nuclear industry. Nu clear Engineering evolved into a group effort of five engineering departments and was eventually established as a separate department wholly at the graduate level. Dr. A. L. Babb, a member of the Chemical Engineering faculty, serves as its chairman. The joint appointments in Nuclear Engineering serve to emphasize the close tie of chemical engineering to nuclear engineering. In 1953 the Department of Chemical Engi neering was established as a separate department. Prior to 1953 there had been what was then called the Department of Chemistry and Chemical Engi neering under one chairman who reported to the Dean of Arts and Sciences for Chemistry and the Dean of Engineering for Chemical Engineering. While this was a reasonably good arrangement it was decided in 1953 to formally separate the two departments. After separation the two depart ments occupied the same facilities and for all practical purposes continued in the same manner as before. The Department of Chemical Engi neering owes much of its tradition and strength to the Department of Chemistry which has always been a strong department at the University of Washington. After literally decades of effort in planning and study a new building for the Department of Chemical Engineering was authorized and com pleted in September 1966, in time for the 196667 school year. This new building increased the gross square feet allocated to the department from 30,000 square feet to 72,000 square feet. SUMMER, 1968 The first courses in Nuclear Engineering were given by the Department of Chemical Engineering ... Dr. Babb's involvement in the development of the artificial kidney has received international recognition. Not only was there an increase in space but the space was now functionally suited for the needs of the department. Each faculty member now has his own office, and his own research areas. There are also many types of specialized research areas built into the building for the needs of the depart ment. The philosophy followed in the design of the building was to provide for a maximum de gree of flexibility. The building committee and the faculty as a whole felt that it was unwise to be highly precise about how space would be used five and ten years in the future. The undergraduate program in the depart ment has undergone a major revision in the last few years. The changes that have been made in the curriculum provide for more options in plan ning the students' programs. There is a core of required courses for the department (which is not common to all engineering departments). On top of this quota of required courses both in chemical engineering and related fields the stu dents have the option of choosing technical elec tives amounting to 15 quarter credits and electives in the area of humanistic and social sciences amounting to 30 quarter credits. By judicious choosing of electives the student can plan his undergraduate program to be a foundation for graduate work or alternatively he can plan for direct employment in industry following gradu ation. Following this latter course he can spec ialize to some extent depending upon his interests. If he so chooses, he can take some courses in the field of pulp and paper technology, or he can en hance his background in fluid mechanics, heat transfer, or other selected chemical engineering areas. The graduate program of the department is the one that has changed most significantly in the last twenty years. At the end of World War II there were from four to six graduate students. At the present time there are of the order of sixty graduate students in attendance. Current re search activities of the faculty encompass the areas of reaction kinetics, transport phenomena, fluid mechanics, heat transfer, mass transfer, bio engineering, interfacial phenomena, polymers, cellulose and lignin, thermodynamics and phase equilibria, process dynamics and control, and ap plied mathematics. None of the faculty members exactly duplicate each other's interests, although there is some overlapping. The fourteen faculty members received their doctorate degrees almost entirely from different schools. Schools repre sented are the University of Illinois, the Univer sity of California, Yale University, the Univer sity of Minnesota, Massachusetts Institute of Technology, Princeton University, the University of Wisconsin, McGill University, the University of Washington, the State University College of Forestry at New York, and the University of Michigan. It is obvious from the spectrum of research interests and the backgrounds of the faculty that there is a considerable breadth built into the faculty of the department. Future Trends It is risky to predict the future with any degree of definiteness. Within the College of Engineering and within the Department of Chem ical Engineering there is considerable interest today in various interdisciplinary areas. The most prominent of these at the present time is the cooperative programs being developed with the medical school. Fortunately, the University of Washington has on the same campus a very good medical school. This school has been de veloped since World War II. Many cooperative programs are already established. A prominent example of one of these is Dr. Babb's involve ment with Dr. Scribner in the development of the artificial kidney. This work has received na tional and international recognition. Other re search areas are being jointly prosecuted at the present time and it is certain that this work will expand in the future. The area of marine sciences is another inter disciplinary area that is receiving a high degree of support on the campus at this time. The Uni versity has an outstanding department of ocean ography and has recently received federal fund ing through a seagrant award. A new division of marine science has been established with vari ous segments of engineering being a part of this program. Other areas of cooperation will certainly de velop. About the only thing that can be stated with some conviction is that chemical engineering will be different in the future than it is today. CHEMICAL ENGINEERING EDUCATION 4Qa CHEMICAL ENGINEERING DIVISION ACTIVITIES Scriven Delivers Annual Lecture The 1968 ASEE Chemical Engineering Divi sion Lecturer is Dr. L. E. Scriven of the Univer sity of Minnesota. The purpose of this award lecture is to recognize and encourage outstanding achievement in an important field of fundamental chemical engineering theory or practice. The 3M Company provides the financial support for this annual lecture award. Bestowed annually upon a distinguished engi neering educator who delivers the Annual Lecture of the Chemical Engineering Division, the award consists of $1,000 and an engraved certificate. These were presented to this year's Lecturer, Dr. L. E. Scriven, at the Annual Chemical Engi neering Division Banquet held June 19, 1968 at the University of California, Los Angeles, Cali fornia. Dr. Scriven spoke on "Flow and Trans fer at Fluid Interfaces." A paper based upon his lecture will be published in an early issue of CHEMICAL ENGINEERING EDUCATION. PREVIOUS LECTURERS 1963, A. B. Metzner, University of Delaware, "NonNewtonian fluids." 1964, C. R. Wilke, University of California, "Mass transfer in turbulent flow." 1965, Leon Lapidus, Princeton University, "As pects of modern control theory and applica tion." 1966, Octave Levenspiel, Illinois Institute of Tech nology, "Changing Attitudes to Reactor De sign." 1967, Andreas Acrivos, Stanford University, Matched Asympototic Expansions." BIOGRAPHIC SKETCH L. E. Scriven was born in 1931 in Battle Creek, Michigan. He graduated from the University of Cali fornia, Berkeley with honors in 1952, where he won the University Gold Medal for academic achievement and was elected to Tau Beta Pi and Phi Beta Kappa. He went on to do graduate work in chemical engineering at the Uni versity of Delaware and received the MChE and the PhD degrees in 1954 and 1956 respectively. While there he was elected to Phi Eta Kappa and held NSF and Shell predoctoral fellowships. After three years as a Research Engineer with the Shell Development Company, Emeryville, California, Dr. Scriven joined the faculty of the University of Minnesota where he is now Professor of Chemical Engineering. In 1963 he was Guest Investigator at the Rockefeller Insti tute and in 1967 Visiting Professor at the University of Pennsylvania. In 1960 he was corecipient (with C. V. Sternling) of the Colburn Award of the American In stitute of Chemical Engineers for the outstanding paper published by the Institute. His teaching abilities were recognized in 1966 by the Distinguished Teaching Award of the University of Minnesota Institute of Technology. In research and scholarly activities his interests have centered about fluid mechanics, some associated mathe matical methods and the application of engineering to biology. He has published highly significant papers on continuum theory of transport and transformation pro cesses, interface physics, interface transfer and dynamic instability and pattern. Dr. Scriven is Advisory Editor for the PrenticeHall Series in the Chemical and Physical Engineering Sciences and is widely known for his editor ship of Theory of Energy and Mass Transfer by A. V. Lykov and Y. A. Mikhaylov, translated in 1961 from the Russian by W. Begell. Many industrial firms have called upon him as a consultant or lecturer. SUMMER, 1968 ni neers grow with the growing world of Sohio We need talented people immediately to work on important projects in: Research on Products and Processes Process and Product Development Economic Analysis Process Design Plant Design, Construction and Operation Market Research Sales and Marketing Management. Sohio is'a progressive company whose growth is based on continuous research, development and marketing of products for transportation, industry, agriculture and construction; not boomorbust military or space projects. That means we rely on your technical talent to help us grow, and we offer rapid advancement to those who are willing to work hard to achieve it. WRITE SOHIO TODAYI Join the Sohio team...where you can get ahead fast because we're moving fast. We assist you with direct aid for education, too... so you can get where you want to go as quickly as your growing interests and abilities will take you. We are the number one marketer of petroleum products in Ohio; our sales equal those of the next four oil companies combined! Our patented singlestep acrylonitrile process accounts for more than 75% of the free world's supply! Sales have risen over 35% in the last four years! Profits over 135%. Write in strict confidence, stating education, experience and salary requirements to: Elwood G. Glass, Jr. Mgr. Technical and Professional Recruitment O H IO 7889 Midland Building ^S H Cleveland, Ohio 44115 THE STANDARD OIL COMPANY (OHIO) An Equal Opportunity Employer (M&F) 108 CHEMICAL ENGINEERING EDUCATION IRREVERSIBLE THERMODYNAMICS* C. M. SLIEPCEVICH and H. T. HASHEMI University of Oklahoma Norman, Oklahoma 73069 The macroscopic approach to irre versible thermodynamics originally pro posed by Sliepcevich and Finn in 1963 is amplified to demonstrate that, of the four possible alternatives for obtaining the re ciprocal relations, fluxes and forces for systems under the simultaneous influence of two potential differences, one alterna tive is identical to the results obtained by Onsager. IN A PREVIOUS PAPER by Sliepcevich and Finn9 a macroscopic approach for deriving the linear laws, which relate the fluxes to the forces for irreversible processes under the simultaneous influence of two potential differences, was pro posed. Subsequent to this publication a number of readers raised questions regarding the validity of this derivation and whether the fluxes and forces so derived had any physical significance. More recently Andrews1 has published a negation of the macroscopic derivation as extended by Sliepcevich and Hashemi"1; however his para phrasing of the macroscopic approach does not appear to be tenable. In an attempt to amplify the macroscopic derivation, a simple example of a onedimension al, onecomponent system under the influence of two potential differences will be used. Multi component systems will not be considered since in these cases the definition of heat is at best am biguous2, 5 and therefore, it is meaningless to re late the fluxes to physically significant quantities. Furthermore, systems under the influence of viscous dissipation forces or external fields (e.g., magnetic) pose some unresolved problems on their inclusion in the energy balance equations. An analysis of the complications introduced by the presence of electrical and magnetic fields has been presented by Martin.6 *Presented at the Annual Meeting of ASEE, June 1922, 1967. N GENERAL, the literature of irreversible thermodynamics raises some profound questions as to its range of practical usefulness; an excel lent review has been published by Wei.2 In order to circumvent definitional dilemmas associated with more complex systemswhich would serve no purpose other than to detract from the prin cipal focus of this paperattention will be given only to a simple process familiar to chemical en gineers. Until agreement can be reached on the validity of the derivation for the simplified sys tem treated herein, it would be folly to attempt to cover the more complex cases. The system to be analyzed in this paper is a onedimensional, onecomponent system in which the properties such as temperature T, pressure P, and chemical potential p. are assumed to be uniform throughout. Likewise, the properties of this same component which composes the sur roundings are assumed to be uniform throughout and are denoted by the subscript i, viz. Ti, Pi, p.i, which in general are different from the pro perties of the system. Obviously, then, disconti nuities in the properties exist at the boundaries, and for this reason it has been called a discon tinuous system.4 Neglecting kinetic and potential energy effects (without loss in generality) the following equations apply when a quantity of mass 8Mi, having a specific enthalpy, hi, and a quantity of heat 8Q, are transferred simultaneous ly and irreversibly across the boundary of the system at Ti such that no work is done. Energy balance: hi Mi + 6 (uM) = 8Q (a) Entropy balance: 8 (sM) = 8( ) + iSMi + 8 (b) Mass balance: 8M = 8Mi (c) Gibbs equation: 8u = T8s P8v (d) SUMMER, 1968 Defining equation: / = h Ts = u + Pv Ts (e) where u, s, v are the specific internal energy, en tropy and volume, respectively, is the chemical potential, and Iw is the lost work as defined in 81w Equation (b) so that T= S, = total entropy production. Combining these equations yields 81w = [8 ( + si8M] (Ti T) + M(i ) (f) Replacing the potential differences by A's, noting that APT = siAT + As and converting to the differential form Equation (f) becomes dlw = (AT) d + (APT) dM (1)* Ti Equation 1 is valid to the extent that Equations (a) through (e) hold, and no other restrictions are required. Although Equation 1 was derived for the discontinuous system the same form of the equation holds for steady state systems. How ever, in the latter case it is customary to replace the A's in Equation 1 by the gradients, namely grad T and grad Ip. Another aspect of Equation 1, which is com monly overlooked, is that it is perfectly valid subject to the aforementioned restrictionsir respective of whether dlw is path dependent or path independent. In general, dlw for closed systems is regarded as path dependent because heat Q and work W are path dependent. How ever, if either Q or W is zero, then the nonzero quantity becomes path independent, as required by the first law energy balance, and in this case dlw becomes path independent. For open systems in which a transfer of mass occurs across the boundaries as well as a transfer of heat and work, then it is conceivable that the energy term associated with mass transfer is path dependent if the properties of the mass being transferred vary with the amount of mass transported. How ever, for discontinuous or steady state systems, the properties are invariant at the boundary so *Since _' s, then it follows that si (Ti T) + (/pi /) () Pi,T ( P.,T + (i Pi,T P,T P= i' P,T P,T AT that the energy term associated with mass trans fer is path independent. Therefore for the case of either discontinuous or steady state, open sys tems in which no work is done, dlw is an exact differential.** In reality it is not essential to the objectives of this paper to argue further regarding the ne cessity and sufficiency of the conditions for which dlw can be treated as path independent or an exact differential. As will be seen in the follow ing development, the subsequent restrictions to systems under the influence of very small po tential differences or gradients (or fluxes) is equivalent to considering only those processes for which dlw is an exact differential; in other words the linear laws and the bilinear form of the en tropy production or lost work equation are tanta mount to the assumption that dlw is an exact differential. Therefore, it is permissible to ex press Equation 1 as dlw = (AT) d (APT) dM Ti Ca lw Ti SQ d T M ( alw dM + QMT Ti Once the conditions of exactness implied by Equa tion 2 are recognized, the remainder of the macro scopic derivation of the reciprocal relations is almost trivial. FLUXES AS INDEPENDENT VARIABLES EQUATION 1 CAN BE expressed in rate form: 1w = (AT) + M(AT) (3) Ti where the dot above the symbol denotes the time (8) derivative. From Equation 3 and wellestablished thermo dynamic concepts, four postulates can be in ferred:9 I. lw = lw Since both T and M are continuous functions of AT and A[T, **It is interesting to note that the form of Equation 1 is similar to the decrease in availability or maximum work which is an exact differential.8 Likewise, dlw is path independent for a process between two prescribed states in which no work is transferred. In other words the lost work, 1w, can be no greater, nor less, than the maximum work that could have been transferred if each step of the process was carried out reversibly. CHEMICAL ENGINEERING EDUCATION Iw can be expressed as a function of two inde pendent variables, namely ( M (AT, Ti / AMT), ( A/T) or (M, AT). II. lw (0,0) = 0. If Q and M are each equal Ti to zero, so is Iw. alw alw III. (0,0) = 0 and (0,0) = 0. Q 3M & Q Ti Since 1w is always positive and is a continuous, even function, with continuous derivatives, Tw Iw  and w (M) = lw(M). Ti Ti) a lw a2lw IV. The equivalence a Q ZM aMa Q Ji Ti of the cross partial follows immediately from the first postulate. Referring to Equation 3 and recalling that ac cording to Fourier's law, Q AT, and according to Fick's law, M I A/AT, it is postulated that 1w is a homogeneous function of the second degree in Q and M (or in AT and A/LT) at least to a first Ti approximation for small fluxes or forces. Thus Equation 3 can be expressed in general functional form for the case in which 1w is time indepen dent, such as for discontinuous or steady state systems,10 lw = w M (4) T It is to be noted that Equation 4 implies that dlw is an exact differential in and M. Ti Applying Euler's theorem for homogeneous functions of the second degree to Equation 4: alw Q 1/ Ti 4 Ti M /2 ( ) Ti Recalling the definition of the time derivative d(z) /do = z so that dz = zd0, Equation 5 be comes, after multiplying through by dO alw Ti dlw = 1/ d Ti M + / w ( dM \M / Q T, Since dlw is exact, the coefficients of the dif ferentials of Q and M in Equations 2 and 6 Ti can be equated. Thus, alw AT= Q M A[w ah T, alw =1/2 7^ 2( T) ( TT, M aM)w  ( 9 _ The righthand partial differentials of Equations 7 and 8 can be expanded in a MacLaurin series neglecting terms higher than second order. AT 1/ M T1 M 1 ( 2lw Ta 0,0 a2lW Ti 0,0 AT = Li, + L21 M Ti  2a lQ Ti ( It Ti + 7A \ 8 o + 1/2a2 1 8M20,0 (9a) (9b) Q Ti 0, 0 (10a) SUMMER, 1968 AT = L21 + L2, M4 Ti (10b) where the L's are substituted for the second order, partial differential, constant coefficients. Note particularly that since the second order cross par tials are equal, then L12 2 La1. Equations 9b and 10b can be solved for Q and M without des Ti trying the symmetry (equivalence of cross par tials) to obtain S= L11 AT + L12 ArLT (11) Ti M =L LA. AT + L, AIT (12) where the L's denote the terms containing the L's. It can be shown easily that La,, L21, since Lt = L21. The forces as defined by Equations 7 and 8 and the fluxes as given by Equations 11 and 12 are identical to those of Onsager.3 7 SELECTION OF OTHER INDEPENDENT VARIABLES A S NOTED in Postulate I above, 1w could just as well have been expressed in terms of other independent variables. For example, instead of Equation 4, one could have started with lw = 1w(AT, A/,T) (13) By utilizing the same procedures as above, it can be shown that Equations 11 and 12 will result. In this case the fluxes and forces are defined as Flux = Q= ( 1/2 w) and Force= AT (14) \i AT M Flux = M = 1/2 aw and Force = Ar (15) Ti In the paper by Sliepcevich and Finn9 the fluxes and forces were defined in the above manner. It can also be shown that these definitions are equiv alent to those of Onsager.*** Similarly, Equations 16 and 17 could have been used as starting points. ***In reality, the definitions of the fluxes and forces as given by Equations 14 and 15 are more consistent with the treatment of the Onsager coordinates in the bilinear form of the entropy equation as intensive, rather than ex tensive, variables. Ti ) (16) (17) or 1w = lw(AT, M) to obtain Equations 11 and 12. Of the four possibilities, Equations 4, 13, 16 and 17, Equation 17 would represent the most logical choice since AT and M are the quantities that can be measured directly. CONCLUSION IT IS SUBMITTED that the foregoing macro scopic approach constitutes a valid derivation of the Onsager reciprocal relations without re course to the theorem of microscopic reversibility. Recent experimental evidence has caused some physicists to question the validity of the time re versal invariance principle on which the theorem of microscopic reversibility is based. Notwith standing, the assumptions and postulates for the macroscopic derivation presented herein are Dr. C. M. Sliepcevich is George Lynn Cross Research Professor at the University of Oklahoma. He was edu cated at the University of Michigan (PhD '48) and has taught at the University of Oklahoma since 1955. He has received many awards for outstanding contributions to research and teaching in engineering and in 1967 won the University of Michigan Sequicentennial Award for dis tinguished alumni. Dr. Sliepcevich's interests include thermodynamics, re action kinetics and catalysis, high pressure design, energy scattering, process dynamics, cryogenics, and flame dy namics. (Photo on left). Dr. H. T. Hashemi is a consulting engineer and vice president of University Engineers, Inc., Norman, Okla homa. He was educated at Abadan Technical Institute, Tulsa University, and University of Oklahoma (PhD '65). His interests include the fields of cryogenic processing and storage, hydrodynamics, thermodynamics, secondary recovery of petroleum, and soil mechanics. (Photo on right). CHEMICAL ENGINEERING EDUCATION 1W = 1' equally tenable to those involved in the micro scopic derivation since both are consistent with empirical observations on related physical phe nomena. The principal result of the Onsager develop ment is that the reciprocal relations, derived by application of the theorem of microscopic re versibility, permit a direct comparison of fluxes and forces with physically, identifiable quanti ties. On the other hand, the macroscopic deriva tion presented herein achieves the same result by virtue of the fact that dlw and dlw can be treated as exact differentials for the conditions under which the equations of irreversible thermody namics hold and to the extent that the funda mental laws of classical macroscopic thermody namics are valid. In other words, since the lost work is already known a priori to be path inde pendent (when no work is done at any stage of the process) no new information is gained by re sorting to the theorem of microscopic reversi bility. ACKNOWLEDGMENT The criticisms of F. Andrews and F. Mixon were invaluable. This work was supported in part by the Air Force Office of Scientific Re search, Grant AFAFOSR56365. REFERENCES 1. Andrews, F. C., Ind. and Eng. Chem. Fund. 6, 48, 1967. 2. Bearman, R. J. and Crawford, J. G., J. Chem. Phys. 28, 136, 1958. 3. Coleman, B. D. and Truesdell, C., J. Chem. Phys. 33, 28, 1960. 4. deGroot, S. R. and Mazur, P., Non Equilibrium Thermodynamics, Chapter XV, Interscience Publishers, Inc., New York, 1962. 5. Kirkwood, J. G. and Crawford, B., Jr., J. Phys. Chem. 56, 1048, 1952. 6. Martin, J. J. "The Symmetrical Fundamental Prop erty Relations of Thermodynamics," Presented at the San Francisco meeting of the American Institute of Chemical Engineers, May 1965. 7. Onsager, L., Phys. Rev. 37, 405, 1931; 38, 2265, 1931. 8. Sliepcevich, C. M. and Finn, D. in Chemical Engi neers' Handbook, 4th ed., pp. 442, 444, and 469, McGraw Hill Book Co., Inc., New York, 1963. 9. Sliepcevich, C. M. and Finn, D., Ind. Eng. Chem. Fund, 2, 249, 1963. 10. Sliepcevich, C. M., Finn, D., Hashemi, H., and Heymann, M., Ind. Eng. Chem. Fund. 3, 276, 1964. 11. Sliepcevich, C. M. and Hashemi, H. T. "Recipro cal Relations in Irreversible Processes." Presented at the Philadelphia meeting of the American Institute of Chemi cal Engineers, December 1965. 12. Wei, James, Ind. and Eng. Chem. 58, 55, 1966. APPROACHES TO STATISTICAL THERMODYNAMICS* M. V. SUSSMAN Tufts University Medford, Mass. Statistical thermodynamics connects classical thermodynamics which describes the energetic interactions of macroscopic systems with the properties of the microscopic or molecular con stituents of a system. The connection expands the application of thermodynamics to extreme temperature, solid state, thermoelectric, and other phenomena. It permits derivation of equa tions of state, and calculation of thermodynamic properties from spectroscopic data. It provides insights to many thermodynamic properties, par ticularly the entropy. Like many other worth while goals, statistical thermodynamics may be approached in a number of ways. The various approaches each have their strong proponents and detractors and the selection of an approach is often a subjective decision reflecting the user's mathematical sophistication, epistemological phi losophy and teacher's prejudice. My purpose here is to outline the more com mon approaches to statistical thermodynamics, necessarily in qualitative terms and with more emphasis on the similarities than the differences. My point of view is summarized by the mountain scape sketched in Fig. 1. In the brief time avail able I will run you over the various trails, passes and pathways which have been used to connect microscopic to macroscopic thermodynamic ba havior. *Presented at the Annual Meeting of ASEE, June 1922, 1967. SUMMER, 1968 Statement of Basic Problem All approaches to the problem start from the following common ground. 1. Recognition that every macroscopic system has a fantastically detailed microscopic structure, and that the existence of this micro structure makes possible an astronomically large number of different arrange ments of the microscopic elements (quantum states) which are completely consistent with the macroscopic system's properties. 2. A realization that there is no way of knowing which arrangement or state actually represents the system and therefore, all (or a most representative portion of) the possible microstates must be con sidered in determining the system's properties. The basic problem of statistical thermody namics is therefore the assignment of a weight (a probability) to each possible microstate which reflects its contribution to the properties of the macroscopic system. It is in the rationalization of the averaging technique, that is, in the derivation of the func tion (called a "distribution" function) assigning weight or probability to each micro state, that a variety of approaches are used. All approaches arrive at essentially the same result: For a closed constantvolume system in equilibrium with a heat bath the probability of the i'th micro state is equal to 1 Pi  exp / Ei (1) where E, is the energy of state i and P and Z are constants of the equilibrium system. The sum of all the probabilities = 1, and therefore 1 2 Pi = 1 = i exp /E, Z = exp /E, (2) Z is called the "partition function," or "sum over states." /3 is shown to be 1/kT. The expected energy of the macroscopic system is equal to: CHEMICAL ENGINEERING EDUCATION (E) = Z(3) and the entropy of the system is equal to S = kIPi In P, (4) (or S = k In W) (5) From here the expressions of classical thermo dynamics are obtained by straightforward, unso phisticated mathematical techniques. Ensemble of States Let us now explore the Fig. 1 mountain be ginning at its basethe concept of an ensemble of all possible microscopic states of a macroscopic system. In quantum mechanics, the Schr6dinger equation specifies the possible discrete macro scopic or quantum states of a system. The totali ty of these states is the quantum mechanical representation of the ensemble. An alternate and older view of the ensemble is provided by classical mechanics where a many dimensional hyperspace is used to chart the total spectrum of mechanical states of all the microscopic constituents of the system that are consistent with the macroscopic knowledge about the system. This hyperspace is called the "phase space" of the system. Having set up the ensemble of all possible states in either quantum mechanical or classical mechanical terms, it becomes necessary to con nect the ensemble to the macroscopic system of interest. The connection is made in the ways indi cated in Fig. 1. QuasiErgodic Hypothesis The average properties of an ensemble are re lated to the properties of a given macroscopic system by making an assumption about the actual mechanical behavior of the macroscopic system, viz: A property measurement (for example pres sure) made on a macroscopic system is a time average property measurement rather than an in stantaneous property measurement. The measure ment time is long on a microscopic scale and with in the measurement time interval the system visits (or comes arbitrarily close to) all points in the phase space of the ensemble. It therefore fol lows that a time average property of a macro system is the same as an ensemble average prop erty. condition '" n2= I En.= 4 Znei 3+2=5 S= =4 w 3111 =4 condition "B" n,=i n2 no= 2  n.=4 Y n.E4 = 5 W = 4! 12 b 2! I I! E=3 3 E=3 3 Figure 2.Most likely "condition." Condition "B" is more likely than condition "A" because Wb > Wa. The validity of the ergodic hypothesis is ques tionable particularly because systems can be imagined where the hypothesis does not hold; for example, an ideal gas in a rigid parallel wall con tainer whose particles are so arranged as to move perpendicular to the parallel faces of the con tainer, and in such a manner that no collision oc curs between the particles. This system would not visit all regions of phase space, that is go through all configurations of its particles' positions and velocities consistent with the total energy of the system. Equal APriori Probabilities Another method of connecting the ensemble to the macrosystem of interest is to assign equal statistical weight or probability to all equal micro states of the ensemble. This is a reasonable as sumption because knowing only the energy of the system, we have no basis for choosing one micro state over any other microstate having the same energy. The system has an equal likelihood of being in all such microstates. Therefore, its average property is the average over all the equally likely states. A corollary of this approach is that the prob ability of a microstate is a function of the energy of that state only, that is, SUMMER, 1968 P 2 i 'a ZP = 7P 'a lb Figure 3.Moment of a distribution. Pi = f (Energy of state i) (7) The third way of connecting an ensemble to the system of interest indicated in Fig. 1 is the information theory approach which implicitly agrees with the equal probability assumption, al though it does not make the assumption explicitly. More will be said about this later. True Ensemble Average We now turn to the trails ascending from our base camp to the "distribution function" (Fig. 1). Given that ensemble average properties are the same as the macroscopic properties of a sys tem, the system property (M) is found by inte grating over phase space M f p(p,q,t) M(p,q) dpdq (8) where p and q are the generalized coordinates of phase space; t is time and p is a density function which gives the probability of finding a state point in any unit volume of phase space. A mathematical theorem due to Liouville is then used to show that the density function is inde pendent of time dp/dt = 0 if p is a constant or a function of the energy of the entire system. (When this condition prevails the ensemble is said to be in statistical equi librium). A suitable function is p = exp  (X + PE) which leads to the conclusion that the probability of a state is proportional to exponen tial (PEstate). This is the route taken by the professional statistical mechanician. It requires considerable mathematical sophistication. It is thorough, ele gant, rigorous, and generally unsuitable for pre senting the useful concepts of statistical thermo dynamics to undergraduates. Most likely "Condition" An alternate route to the "distribution func tion" I have called the "most likely condition." It is supposed to be a short cut since it attempts to evaluate the average property of an esemble, not by covering all states in the ensemble, but only the most likely states, as represented by the most likely "condition." The "condition" of a system is the set of occupancy numbers (ni) which designate the number of microscopic particles in each of the energy levels accessible to a system's particles. For example, Fig. 2 shows a system which has only four particles. The "acondition" of that system is given by the set of occupancy numbers (n) ; ni = 3; n, = 1. The sum of the ni is equal to the total number of particles in the system, in this case 4; and the energy of the system is equal to E = ni Ei = (3 x 1) + (1x 2) = 5 energy units Now, three 1energy unit particles and one 2en ergy unit particle can be permuted in 4!/3!1! = 4 ways. (The general rule for the number of per mutations of N total objects where N is equal to nni; is W N!/Trni!) Condition "b", given by n, = 1, n, = 1, no = 2, allows for 12 accomoda tions or permutations. Therefore, if we were betting on condition "a" or "b" we would put our money on "b" as the more likely "condition." Quite clearly, the most likely "condition" of any system is that set of ni's (consistent with the system's energy) which produces the maximum number of permutations. It can be shown that as the number of particles becomes very large the likelihood of any condition other than the most likely condition becomes very small. There fore, the ensemble as a whole can be described with reasonable accuracy in terms of its most likely "condition" and the set of ni's that cor respond to that most likely condition is simply found by maximizing the number of permuta tions W or In W taking into account the fact that Xni = N and Y ni Ei = Et. This technique if fol lowed carefully, and if certain pitfalls are avoided, eventually leads to an expression for the partition function of a multiparticle system in CHEMICAL ENGINEERING EDUCATION terms of the allowed energy levels of its consti tuent particles. The pitfalls and somewhat odd rationalizations* used to arrive at this final result offset the shortcut promised by averaging over the most likely condition rather than over the en tire ensemble. In this approach S = kln W. Mathematical Necessity Using the equal apriori probability assump tion, the probability of a state is a function only of its energy (see eq. 7). If we have two systems at equilibrium with a thermostatic bath whose size is such that fluctuations of the energy of one system will have no effect on the energy of the bath or the energy of the other system, then we can state Pi =f(Ei) (7) Pj = f (E,) (9) where Ei represents an allowed energy state of the first system and Ej represents an allowed energy state of the second system. Now, considering both systems together, the probability of the first sys tem being at Ei and the second system at Ej must be Piandj = f(Ei + E) =Pi P (10) therefore f(Ei+ Ej) = f(Ei) f (E,) (11) The only function satisfying (11) is an expo nential 1 Therefore Pi = f(Ei) = exp PEi (1) and we are again at the top of the mountain. A mathematical consequence of (1) and the classi cal definition of entropy is that S, can be shown to be equal to S = klPi In Pi (13) This is the approach taken by Denbigh,2 An drews,1 and others. It is straightforward enough to be taught to undergraduates, requiring only acceptance of the fact of the existence of a multi tude of quantum states and the assumption of the equal probability of equal energy quantum states. A maximization computation is avoided. Information Theory Approach The Information Theory approach, while us ing exactly the same mathematical forms estab lished in the older statistical thermodynamic literature, has a somewhat different philosophical or logical orientation. It states that statistical *Particles are assumed to be distinguishable. Also, Stirlings approximation, In n! = n In n n, is used. thermodynamics is not a physical theory whose validity depends either on the truth of additional basic assumptions, such as ergodic behavior or equal probability, or on experimental verification. It is instead a form of statistical inference; a technique for making the best estimates on the basis of incomplete information. If experiment al verification is not obtained this is not a short coming of the statistical thermodynamics, but of the information supplied. The relationship S = kPPi In Pi (13) occupies the primal position in this approach. The equation is the basic equation of Shannon's "Mathematical Theory of Information" and is identified with thermodynamic entropy. Maxi mizing (13) subject to the constraints that Pi = 1, (The system must be in some state) and ZPiEi = E; (The system has energy (E)) leads immediately to 1 Pi = exp P8Ei Z It is the contention of the information theo rists that maximizing P In P subject to con straints produces the least biased distribution of probabilities; a distribution which is maximally noncommital with regard to missing informa tion. An identical technique using a different ra tionale was suggested by Pauli who showed that the distribution functions are obtained by mini mizing the Boltzmann H function H = PPi In Pi subject to constraints. The latter technique is discussed in detail by Tolman.3 Taking $ P In P to an extremum is not a new idea. The "informa tion theorists" however give it new importance by insisting that it is the most fundamental ap proach to statistical mechanics, because evaluat ing the Pi is a problem in guessing (i.e., statistics) and not physics, and therefore there need be no further concern with Ergodicity or Equiproba bility and their justification. From an undergraduate teaching point of view, the information theory approach is almost as simple as the previously mentioned mathemati cal necessity approach. The student is asked to accept, without proof, the axiom that maximizing S subject to the known properties of a system produces a minimally biased set of Pi's. The mathematics of maximization are reasonably straightforward. The trouble with the axiom is that it does not relate to much in the undergradu SUMMER, 1968 ate's experience whereas other thermodynamic and mathematical axioms usually have some in tuitive acceptability. Smoothing Function A way of making the axiom more acceptable is to demonstrate qualitatively that maximiz ing Pi In Pi or minimizing +PPi In P is a smoothing operation which tends to minimize the "moment" (lower the center of gravity) of a plot of Pi vs. i. As qualitative example, assume that we have a system which is capable of existing in a great number of possible states, and we are asked to arbitrarily assign probabilities to each of these states. The states can be ordered in a sequence, and indexed by an integral subscript i. Assume that all we know about this system is that it must be in some state Pi. In Fig. 3, line b is an arbitrarily assigned distribution for this system which is constrained only by the fact that the sum of the ordinates equals unity, that is IPi = 1. This is not an unbiased distribution because I have put maxima and minima in this distribution, that is, I have given some states more weight than others, without information that would jus tify so doing. The relative smoothness of the arbitrary curve in Fig. 3, can be represented by the mathematical index EPi2 (14) which evaluates the "moment" of the distribution about the horizontal axis. The "moment" in creases as the magnitude of the singularities or extrema in the system increase, and conversely, decreases as the center of gravity of the distribu tion drops, that is, as the curve becomes more uniformly smooth. In fact, it is a straightfor ward exercise in calculus of variation to show that the minimum "moment" corresponds to line "a," a constant value of Pi which is certainly the smoothest possible curve. If, in the smoothness index, (Eq. 14) we replace one Pi with a mono tonic function of Pi, that is ln Pi, we should ex pect similar behavior. In other words, the effect of maximizing Pi In Pi is to smooth out our distribution. The advantage of the logarithmic function is that it allows expressing S as a func tion of the probability of the microstates, and it prevents Pi from taking on negative values. Allow me to end with a speculative aside. Maximizing entropy smooths a distribution. This suggests to me that it might be possible to re state the principle in terms of geodesics. I say this because I would assume that a maximally smooth curve should have a minimum arc length. I have tried using a criterion of "minimum arc length' to find a distribution function, har boring secret hopes that the criterion would lead to Pi In Pi and even more general expressions for new entropies. I regret that I've not been suc cessful. The geodesic idea (that an unbiased dis tribution has minimum arc length) nevertheless continues to intrigue me and I would welcome thoughts of others on how to work it into a selection formalism. References 1. Andrews, F. C., "Equilibrium Statistical Mechan ics," John Wiley & Sons, Inc., 1963. 2. Denbigh, K., "The Principles of Chemical Equi librium," Cambridge University Press, 1961. 3. Tolman, R. C., "The Principles of Statistical Me chanics," Oxford University Press, 1942. Dr. M. V. Sussman is Professor of Chemical Engi neering and Department Chairman at Tufts University and is presently on leave with NSF in New Delhi working on an Indian Engineering Education program. In August he will be an NIH Fellow at the Weizmann Institute studying biological thermodynamics and mechanochemis try. Dr. Sussman has degrees from City College of New York (BChE) and Columbia University (MS and PhD). Thermodynamics is a compulsive hobby with him and some of the ideas expressed in this article will appear in a book to be published by Wiley. Join THE AMERICAN SOCIETY FOR ENGINEERING EDUCATION and Receive CHEMICAL ENGINEERING EDUCATION W. Leighton Collins, Executive Secretary The American Society for Engineering Education 2100 Pennsylvania Avenue, North West Washington, D. C. 20037 Dear Mr. Collins, Please send me an ASEE application blank I would like to join the Chemical Engineering Division. Name .. A d dress .. ...... ...............                CHEMICAL ENGINEERING EDUCATION The world of Union Oil salutes the world of chemical engineering We at Union Oil are particularly indebted to the colleges and universities which educate chemical engineers. Because their graduates are the scientists who contribute immeasurably to the position Union enjoys today: The twentysixth largest manufacturing company in the United States, with operations throughout the world. Union today explores for and produces oil and natural gas in such distant places as the Persian Gulf and Alaska's Cook Inlet. We market petroleum products and petro chemicals throughout the free world. Our research scientists are constantly discovering new ways to do things better. In fact, we have been granted more than 2,700 U.S. patents. We and our many subsidiaries are engaged in such diverse projects as developing new refining processes, developing new fertilizers to increase the food yield, and the conservation of air and water. Today, Union Oil's growth is dynamic. Tomorrow will be even more stimulating. Thanks largely to people who join us from leading institutions of learning. If you enjoy working in an atmosphere of imagination and challenge, why not look into the world of Union Oil? Growth...with innovation. Union Oil Company of California. unitn SUMMER, 1968 The New Stoichiometry* EDWARD M. ROSEN COMPUTER AIDED CHEMICAL PROCESS Monsanto Company DESIGN SYSTEM St. Louis, Missouri I PROCESS PHYSICAL MATERIAL & ERNEST J. HENLEY LANGUAGE PROPERTIES MODELS ENERGY BAL. COSTING University of Houston Houston, Texas Fig. 1.Elements in computer aided chemical process Houston, Texas design systems. In May of this year we sent a questionnaire to all AIChE accredited schools to determine the subject matter now included in stoichiometry or the equivalent first course in chemical engineer ing. The replies to this questionnaire indicate quite clearly that 1) the overwhelming majority of the courses are still in the mold cast by Hougen and Watson in the 1940's, and 2) there is a cer tain amount of experimentation, dealing mostly with the introduction of computer techniques into the curriculum. This introduction of computing techniques into material and energy balance courses must ultimately give rise to what we call 'the new stoichiometry.' The new stoichiometry, in turn, will form the foundation for the computer aided design and simulation courses which we expect will find a place in all chemical engineering cur riculums within a decade. It seems appropriate to examine first, therefore, the elements of a computer aided design system. Table I is a partial listing of computer aided chemical design systems. Of the industry pro grams, the CHEOPS is considered by many to be the grandfather because of the wide publicity it received in the early 1960's. The CHEVRON program, which is oriented towards hydrocar bons, has been made operational at the Univer sity of California, Berkeley. The PEDLAN pro gram is one of the first to be written in a problem oriented language and requires a Fortran pre compiler. The CHIPS, KELLOGG, PECOS, and UOS programs are available through service com panies, as is PACER, which was originally de veloped at Purdue and Dartmouth. The CHESS program is in operation at the University of *Presented at the Annual Meeting of ASEE, June 17 20, 1968. Houston, and its capability is now being greatly extended with help of a Themis grant, ONR Contract N001468A0151. SLED, under devel opment at Michigan, is analogous to PEDLAN in Table I. Computer Aided Chemical Process Design Systems* Industry CHEOPSChemical Engineering Optimization Sys tem, Shell Oil CHEVRONGeneral Heat and Material Balancing Program, CHEVRON Research Company PEDLANProcess Engineering Design Language, Mo bil Oil Company Service Companies CHIPSChemical Engineering Information Processing System, IBM Service Bureau KELLOGG Flexible FlowsheetM. W. Kellogg PECOSBechtel Company UOSUnit Operations Simulator, Bonner and Moore (Fluor Company) Education Institutions CHESSChemical Engineering System Simulator University of Houston MAEBEMaterial and Energy Balance Execution, University of Tennessee PACERProcess and Case Evaluator Routine, Dartmouth SLEDSimplified Language for Engineering Design, University of Michigan SPEEDUPSimulation Program for the Economic Evaluation and Design of Unsteady State Processes, Imperial College that it utilizes a problem oriented language. MAEBE is a first generation material and energy balance program, and SPEEDUP is not fully im plemented. If a stochiometry course is to serve as a pre cursor to a computer aided design course, we must analyze the design system in terms of its com *A complete tabulation and discussion of computer aided design systems is given by Evans, Stewart, and Sprague, CEP, Vol. 64, No. 4, 1968. CHEMICAL ENGINEERING JOURNAL L LEVEL 5: MASTER EXEC. CONTROL LEVEL 4: SPECIAL SUBEXEC. PROGS. LEVEL 3: UNIT OP'NS LE VEL 2: THERMO CALCS. 1 LEVEL 1: PHYSICAL S,$ PROPERTIES Fig. 2.Building blocks in a preliminary design and capital cost system for fractionating columns. ponent parts to see what fundamental principles are involved. Figure I shows the five component parts: 1. The process language which converts the language of the engineer to that of the computer 2. The physical property package which generates the necessary information regarding transport, PvT, and thermodynamic properties 3. The mathematical representation of the building blocks (transfer functions, if you will) 4. The material and energy balance 'executive program' which links the building blocks 5. Costing programs, which may include some sort of optimization program. In Figure 2 we see a more detailed breakdown of the blocks in Figure 1 as they are used in the design of a fractionation column. On the lowest level we have the physical property tables or equations. These are really a part of a system which includes subroutines to produce enthalpy values, equilibrium constants, etc. Next there is a second level of thermodynamic calculations which use the lower level physical property programs. Dew point, bubble point, and flash programs are the examples cited. On the third tier we have the transfer func tions for the building blocks; the mathematical representation of the classic unit operations. The level four function ties together the block of pro grams comprising the fractionation system, and overseeing the whole conglomeration of subpro grams which comprise the bottom four levels we have an executive control program which takes into consideration all input and output format and everything else that goes into a well formulated system. If one of the objectives of the 'new stoichio metry' is to train a student to create and use computer aided design systems, it is necessary to define the topics which must be included. In Figure 3 we define the five building blocks for the new stoichiometry. We have (1) thermodynamics and (2) classi cal stochiometry; these two blocks together form the manual method block in the 'HougenWatson mold.' The other three elements, (3) linear alge bra, (4) solution of equations, and (5) algorithm development, together with (1) and (2) are the required building blocks for machine method cal culations. The remainder of this paper details the material in building blocks (3), (4), and (5). The examples used are from our forthcoming book "Material and Energy Balance Computa tion," John Wiley (June 1968). SUMMER, 1968 Fig. 3.Elements of the new stoichiometry. Linear algebra, in the words of Rutherford Aris, "is the proper language of stoichiometry." Indeed, linear algebra is the only type of algebra digital computers can do; they cannot handle non linear problems. Consider, for example, Gibb's Rule of Stoichiometry, Figure 4. It states that the maximum number of linearly independent chemical reactions in a set of reactions is equal to the number of chemical species known (from experiment) to be present, minus the rank of the atom matrix. The atom matrix for a five com ponent mixture consisting of CO, H2, CHSOH, CO2, andHO is shown in Figure 5, where the rows are the species and the columns the atoms. The determination of the rank of this matrix is an exercise in linear algebra. A classic technique for determining the rank of a matrix is the Gram Schmidt method where we attempt to construct a set of m orthogonal vectors, Y1, Y,, .. Y, from X1, X,, . X.. If the length of a Y vector is zero, then orthogonalization is impossible, and the X vector is parallel to one of the others. The procedure is shown in Figure 6: the rank of the atom matrix in Figure 5 is three. Thus, accord ing to the Gibb's Rule of Stoichiometry, there are are two independent reactions. Taking the two reactions shown in Figure 7 as the independent reactions, we construct the reaction matrix in Figure 7. The rows are the species; the columns the stoichiometric coeffi cients for reactions (1) and (2). The matrix formulations of the material balance lead logi cally and simply to the elegant statement for the MAX. NUMBER OF \ NUMBER RANK OF THE) LINEARLY INDEPEN = OF ATOM DENT REACTIONS \SPECIES MATRIX 4 = N  Fig. 4.Gibbs rule of stoichiometry. conservation of atoms shown in Figure 8. The product of the transpose of the reaction matrix times the atom matrix must be zero. We hope that this example is a convincing demonstration of Aris' axiom. Next we consider the nature and function of block four, the solution of nonlinear equations. In the isothermal flash vaporization shown in Figure 9, fH(a) and fR(a) are two valid and identical solutions of the material balances. In these equations a = L/V and Ki yi /xi. Since zi, the feed composition is known, and K is known, ATOMS SPECIE C 0 H CO 1 1 0 H2 0 0 2 CH OH 1 1 4 CO2 1 2 0 H 20 0 1 2 Fig. 5.Atom matrix for a five component system, example 1. GIVEN: XI, X2, ... XM Y1 = X1 1 1 Y X Y1X 2 2 Y'* Y 1 I Y X YM 1 X SM MI YM_ Y " Mi ... (Y : Y Fig. 6.The GramSchmidt procedure for example 1. Rank, R = 3. CHEMICAL ENGINEERING EDUCATION REACTION SPECIE 1 2 CO 1 1 H2 2 1 CH3OH 1 CO2 1 HO 1 2 0 M= 5 3= 2 CO + 2H2 =CH3OH (1) CO2 + H2 = H20 + CO (2) Fig. 7.Reaction matrix for two linearly independent reactions. these are simply nonlinear equations in one un known, a. They can be solved readily by any number of onedimensional, nonlinear root find ing techniques. In Figure 10 we have a plot of both fB(a) and fII((a) vs. a. The root, at f.(a) = f.(a), has been successfully found and is, as it should be, identical for both equations. There are, however, major differences in the shape of the curves, and we see that the f,1 (a) function gives us two roots, REACTION MATRIX ATOM MATRIX 1 2 1 0 0 1 1 0 0 0 2 =0 1 1 0 1 1 1 1 4 1 2 0 %0 1 2! Fig. 8.The conservation of atoms. one of which is spurious. Clearly, if we are to avoid such pitfalls we can not blindly set up and solve material and energy balances and feed the resulting equations to a computer. In this 'onedimensional' example we had only one nonlinear equation to deal with. Let us now examine the multidimensional set of equations F z Fzi = Vy. + Lx. BY REARRANGEMENT: N N SV z.K. i= 1i 1 + a(K i R N N N Sx. L y = i=l i=l i=l V Yi L x I = fH( ) d1) 1. fR(a) zi(1 Ki) 1 + a(Ki 1) fR) 1 Fig. 9.Isothermal flash equations, example 2. which will arise from the flowsheet for the cata lyting dehydrogenation of propane, Figure 11. We note immediately that there are two recycle streams, S12 and S2, which preclude a straight through solution to the material and energy bal ances. f H Or fR BUBBLE POINT  () 1. DEW POINT / =_V Fig. 10.Plot of functions fH (a) and f, (a) for example 2. One method of handling problems of this type is by 'tearing' the flowsheet and estimating a composition. If, for instance, we tear stream S13 (between the stripper and absorber) and guess at the composition for S7, we are able to calculate all of the remaining process streams, S1  S13, in the sequence S8, S12, S10, S11, S2, S3, SUMMER, 1968 S4, S5, S9, S6, S13. If we have guessed the com position S7 correctly, then S13 will equal S7. If not, we have to reestimate S7 and try again. This physical situation is given a mathemati cal formulation in Figure 12. We estimate the stream vector X, calculate the process vector 0(X) and if 0(X) equals X we are finished. If not we pass through a convergence block which, hopefully, will give us a new X which is a better approximation to O(X). Since the X stands for all unknown parameters of temperature, pressure, compositions, and properties, it is apparent that the solution of problems of this type are primarily exercises in the solution of large sets of non linear equations in many unknowns. ABSORBER FRESH PROPANE FEED Sl S3 n S4 7 S5 The methods of the new stoichiometry provide the tools for the development of useful algorithms, which is building block five for the machine meth ods. By useful algorithms we mean a well defined set of statements that lead to the solution of a problem. In order to obtain the output of any building block as a function of the input to the block, and hence to set up our design system, we must have algorithms. Let us now see how we would use our knowledge of thermodynamics and nonlinear equation solving techniques to develop PRODUCT COLUMN 16 STRIPPER 13 S7 S10 ., f PRODUCT Fig. 11.Flowsheet for catalytic dehydrogenation of propane to propylene, example 3. The next block in our 'new stochiometry' is a notsonew subject, thermodynamics. The rigor ous formulation of material and energy balances requires a deeper background in thermodynamics than is now attempted in the majority of material and energy balance courses. For example, if a chemical reaction takes place thermodynamics tells us that at equilibrium the stoichiometric co efficient times the chemical potential equals zero (Figure 13). In terms of the reaction extent, e, the number of moles of component i present at any time is ni = nio + ale, where nio is the initial number of moles. The final equation from which we cal culate the composition of the reaction mix given free energy data and the initial number of moles is a nonlinear function in one unknown, 0(e) = 0. To obtain this equation we needed thermodynamics. ESTIMATED STREAM CALCULATED STREAM 0(x) FRESH PRODUCTS FEEDS AND WASTE S0 ) 0(X) X = 0; X 10 Fig. 12.The convergence block as an equation solver. an algorithm to calculate the composition of a mixture in physical and chemical equilibrium. CHEMICAL ENGINEERING EDUCATION CONDITION OF EQUILIBRIUM AT T AND P IS N Z a.i. = 0 i=l FOR IDEAL CONDITIONS i. = Pi + RT In P. 1I 1 N RT 2. In P RT 1i i 1= 1 N i= i=l 0 (iXi FOR: n. = n. + a. e 1 10 1 SOLVE: 0 (e) = 0 Fig. 13.Use of thermodynamics, example 4. In Figure 14 we have a simple system in which we have a flash vaporization plus a series of M chemical reactions (j = 1 to j = M). There are N components (i = 1 to i = N). The component balances as well as the overall balance are shown in Figure 14 and our final equation is shown in Figure 15 in terms of Ki which, as before, is yi/xi. V yi F z I If the temperature and pressure and the feed composition zi are fixed, f(a) is one equation in two unknowns, a and e. To solve the equation we propose the algorithm shown in Figure 15. We (1) estimate the e reaction extents, (2) solve for a, (3) calculate the material balances, (4) check to see if the equilibrium constant has been satisfied. If it is not, we make a new estimate of e and start again. The new estimate is usually made using a Wegstein or similar convergence forcing routine. What we have tried to demonstrate in this paper are (1) the techniques now being used by industry in the formulation of computer aided design and simulation systems and (2) how these may be incorporated into existing stochiometry courses to produce the 'new stoichiometry.' BY REARRANGEMENT M z + F (I Ki) / N M 1 a + 1ij i=1 j=1 e) + K.a 1. ESTIMATE el, e2 ... eM 2. SOLVE FOR a 3. CALCULATE x. AND y. FROM RESULTS OF STEP 2 4. EVALUATE RT n K. = j 0(y) J j = 1, 2, ...M Fig. 15.Suggested algorithm. COMPONENT BALANCE M Fz. = Vy+ Lx. a ej j=l OVERALL BALANCE N M F=V+LZ Z c.. ej i=1 j=l Fig. 14.Model of process. Professor Henley is Associate Dean and Professor of Chemical Engineering at the Cullen College of Engineer ing, University of Houston. He received his BS from the University of Delaware and an MS and Dr. Eng. Sci. from Columbia University. He served on the faculty at Columbia from 1953 to 1958, was associated with Stevens Institute of Technology from 1958 to 1964, and from 1964 to 1966 was ChiefofParty of the AID mission at the University of Brazil. He is the author of over 50 re search papers, and five books, and is the editor of the Advances in Nuclear Science and Engineering. He has done extensive consulting for government and industry and is a member of the Board of Directors of three pub liclyheld corporations. SUMMER, 1968 l laboratory Ki 4ticb * KENNETH B. BISCHOFF The University of Texast Austin, Texas The background of the current extent of chemical engineering kinetics laboratory work is briefly discussed along with some observations on laboratory operation. The statistical results of a survey on this topic are presented and indicate that although many departments have laboratory work, there are a number that do not. As an aid to the introduction of more experiments, a list of successfully used reactions is given. Finally, a detailed example of an experiment used at the University of Texas is discussed. It is realized that some type of formal chemi cal engineering kinetics course is a vital part of chemical engineering education. Utilizing the aspects of applied chemistry through reactor de sign is a unique feature which differentiates chemical engineers from other engineers. In the 1940's Hougen and Watson began to systematically treat chemical reactor design, which resulted in their wellknown textbook. Even then, it was felt that this was essentially graduate level material. It was not until the late 1950's that many chemical engineering depart ments had undergraduate courses dealing with reactor design. During the last decade this seems to have changed in that now most departments have some sort of undergraduate lecture course in this area. Although the trend had started, the Dynamic Objectives Report1 of AIChE, with its recommendation that more emphasis be placed upon the chemical content of the curriculum, un doubtedly also had an effect. In recent years with the introduction of courses on transport phenomena, process dy namics and control optimization, along with ki *Presented at the annual meeting of ASEE, June 19 22, 1967. tPresent address: Department of Chemical Engineer ing, University of Maryland, College Park, Md. Dr. Bischoff was educated at the Illinois Institute of Technology. He has written many articles in the fields of chemical reaction engineering and bioengineering and has recently written a textbook (with D. M. Himmelblau) on "Process Analysis and Simulation." netics into the curriculum, the time available for extensive laboratories has been steading decreas ing. The major aims of this paper will be to first discuss what is currently done in the chemical engineering departments of the U.S. and Canada concerning chemical engineering kinetics labora tories and to list some examples of chemical re actions which could be used by other departments to introduce kinetics experiments into their cur riculum. The final part of the paper will describe in detail an experiment used with success at the University of Texas. Survey of Chemical Engineering Kinetics Laboratory Work A survey of the North American departments was conducted to obtain data on the extent of chemical engineering kinetics laboratories. Re TABLE I Extent of Kinetics Laboratory Work* Number of Topic Departments Separate chemical engineering kinetics 8 laboratory course and/or taught in con junction with chemical engineering kinetics lecture course. Experiments in other chemical engi 41 neering laboratory courses. No chemical engineering kinetics 28 experiments. Note: 76/145 replies were received. CHEMICAL ENGINEERING EDUCATION TABLE II. Type of Chemical Reaction Number of Departments Type Homogeneous 38 Heterogeneous, noncatalytic 6 Catalytic 20 Reaction engineering/design study 16 plies were received from 76 of 145 surveys mailed. The results are shown in Table I from which it is seen that very few departments have either a separate kinetics laboratory course or have one taught in conjunction with the chemical engineer ing kinetics lecture courses. These two categories from the survey have been lumped together, since there is not a clear distinction between them. Most of the present work is designed as a part of other existing laboratory cources. In other words, the term "unit operations laboratory" quite often seems to be something of a misnomer since things other than this topic are studied. Thus, about half of the replies indicated that they had some work dealing with kinetics and, in fact, several departments had more than one experiment of this type. Perhaps the most interesting figure in Table I is the fact that 28 departments indicated that they had essentially no work at all. This seeming ly large lack does need some qualifications, since most students do get some exposure to kinetics in physical chemistry. However, it does seem that chemical engineering kinetics laboratory experi ence is lacking in a substantial fraction of chemi cal engineering departments. Several depart ments are presently in the process of adding ki netics experiments, but many are not. Table II indicates various types of reactions that have been used for the laboratories. It can be seen that the major emphasis has been with homogeneous reactions, probably because they are the easiest to perform and obtain consistent re sults. Heterogeneous catalytic reactions are also fairly extensively used, probably because of their great practical interest. Very few noncatalytic heterogeneous reactions were reported. The final category of reaction engineering design study seems to have a relatively small amount of work, but this may be somewhat ambiguous. Many of the homogeneous and heterogeneous reactions are run for "engineering" purposes and could pos TABLE III. Examples of Reactions Used for Kinetics Experiments Homogeneous 1. Ethyl acetate saponification 2. Acetic anhydride hydrolysis 3. Methyl acetate hydrolysis 4. Ethyl acetate hydrolysis 5. Acetone bromination 6. Isopropanol oxidation to acetone 7. Acetic acid + ethanol esterification 8. Benzaldehyde oxidation to benzoic acid 9. Permanganate reduction with dissolved hydrogen 10. Crystal violet hydrolysis 11. Methyl acetate saponification 12. Phthalic anhydride + butanol esterification (pilot plant scale) 13. Ethylene glycol + periodate 14. Hydrogen peroxide + iodide (iodine clock reaction) 15. Ethylenepropylene polymerization 16. Formaldehyde + methanol esterification 17. N.Ndimethylaniline + ethyl iodide (by DTA) Heterogeneous, noncatalytic 1. Coke oxidation on cracking catalyst 2. Corrosion kinetics 3. Cyclohexane hydrogenation 4. Cu++H+ ion exchange 5. Cottonseed oil hydrogenation 6. Pyrolysis of plastics Catalytic 1. Ammonia decomposition, iron oxide 2. Cumene cracking, silicaalumina 3. Ammonia oxidation, platinum gauze 4. Toluene hydrogenation, Raney nickel 5. Isopropanol (liq.) dehydrogenation, nickel 6. Propylene oxidation, copper oxide 7. Acetaldehyde decomposition, copper gauze 8. Benzene alkylation, acid catalyst 9. Propylene disproportionation to ethylene + 2butene, cobalt oxidemolybdenaalumina 10. Sulfur dioxide oxidation 11. nPropanol dehydrogenation 12. Cumene hydrogenation 13. Styrene hydrogenation 14. 1Hexanol dehydration 15. Catalytic cracking 16. Permanganate reduction with dissolved hydro gen, Ag+ sibly be included here also. Many of the depart ments out of the 16 indicated that an important part of this topic was the use of analog or digital computers to simulate chemical reactor operation. Also, the various reactions were run in a variety of reactors such as tubular, stirred tank, as well as batch. Table III presents a list of the actual chemi cal reactions used, which might serve as an aid to those who are trying to find proven reactions for their own laboratories. The saponification of ethyl acetate is the most popular reaction in use, SUMMER, 1968 probably because of its good kinetic characteris tics, the ease of measuring the results, and the experiment devised by Kendall.2 Detailed Example An example of a chemical engineering re action kinetics experiment that has worked well in our laboratories at the University of Texas is ethyl acetate saponification in a tubular reactor. Kendall2 has given a very complete discussion of the system he developed to study the effects of different flow patterns in the reactor. Our system has many features in common with his but the emphasis is somewhat different. A major aspect of our system is to measure and interpret the ef fects of nonplug flow in the liquid phase tubular reactor and to interpret these results quantita tively in terms of mathematical models. The fact that the ethyl acetate saponification is a very "clean" second order reaction with no side reactions is given to the student as basic data. The reaction is run in a Tygon tube of 0.615 cm diameter and 810 cm (35 feet) long, looped through baffles in a section of glass pipe which serves as a constant temperature water bath. Gravity feed lines from bottles of ethly acetate and sodium hydroxide are run through the con stant temperature water feed tank to attain reaction temperature and joined in a Y section at the reactor tube entrance. Analysis of product samples is by a simple titration method similar to that described by Kendall. Electrical conductivity methods were tried but did not work any better and were somewhat more complicated than sim ple titration. In order to have high conversions of 5090%o the reactor is run at a temperature of 100F, where the rate constant is 0.22 liter/gm mole second, and with the feed concentrations of both reactants Co = 0.2 gm mole/liter. Since nonplug flow is most pronounced under laminar condi tions, the flow rates range between Reynolds numbers of 100 to 3000. A comparison of the experimental data with theoretical predictions from the axial dispersion model (see Levenspiel3) is required, using the established correlations of the axial dispersion coefficients. Results of some of the recent student data are shown in Figure 1. At the turbulent end of the range, the plug flow equations give good agreement with the experimental data. At the lower flow rates, although there is quite a bit of 1.0 z IO 0 PLUG FLOW o 0 o o DISPERSION MODEL .5 obo oo 50 1000 2000 REYNOLDS NUMBER Figure 1.Student data for ethyl acetate saponification in a tubular reactor. scatter, it is seen that the plug flow predictions are not very good and the data approach the axial dispersion model line. The data actually fall most ly between the two predictions, but this may be caused by the looped Tygon tube which would lead to less effective axial dispersion than that predicted by the correlations for straight tubes. In any event, the experiment not only gives an example of tubular plug flow reactor results but also illustrates quantitatively the effects of non plug flow. Conclusions The survey of chemical engineering kinetics experiments indicated that many departments do have some work in this area, but there are a large number that do not. Very few departments have separate kinetics laboratory or one taught in conjunction with a lecture course. In addition to the statistical information, the survey produced a rather large selection of chemi cal reactions that apparently have been success fully used. These have been tabulated to help in structors find experiments that might develop their own laboratories. Finally, an example of an experiment used at the University of Texas was discussed in some detail and the types of results than can be obtained in a student labora tory were indicated. REFERENCES 1. "Dynamic Objectives for Chemical Engineering," Chem. Eng. Prog. 57, (10), 69, 1961. 2. Kendall, H. B., in "Small Scale Equipment for Chemical Engineering Laboratories," ed. R. N. Maddox, Chem. Eng. Prog. Symp. Ser. No. 70, 63, 315, 1967. 3. Levenspiel, O., "Chemical Reaction Engineering," John Wiley and Sons, Inc., New York, 1962. CHEMICAL ENGINEERING EDUCATION classroom Te'moaeSyifaics View Programmed Instruction* Wright State University Dayton, Ohio 45431 The potential of programmed instruc tion as an educational device is demonstra ted by its present use in the classroom, in dustrial training programs, the continuing education program of the medical profes .sion, and by the recent interest of several large corporations who have entered the education business with systems based on programmed instruction. This paper de scribes a set of thermodynamics programs developed at Purdue University and ex amines their potential from the viewpoint of the student who used them, the teacher, and the psychologist. Various aspects of the design of these programs are examined including linear versus branched style, step size, concrete illustrations of abstract concepts and perceptual organizers. The programs and the textbook are compared in terms of their ability to transmit in formation to the student. The program is described as psychologically superior be cause it shapes behavior from the simple to the complex and guides the student so he avoids misconceptions which must be un learned. Finally, the value of the programs in freeing class time for more valuable ac tivities is described. If you asked Harvard psychologist B. F. Skinner' what programmed instruction can do for education he would reply, "What is now taught by teacher, textbook, lecture, or film can be taught in half the time ... by a teaching machine" using programmed instruction. Before you dismiss Skinner's claim you should carefully consider the fact that RCA, IBM, GE, Westinghouse and several other large corporations have recently *Presented at the Annual Meeting of ASEE, June 1922, 1967. staked a claim in the education business with sys tems that involve programmed instruction ma terials. In addition, many industrial firms al ready use programmed instruction to teach basic skills to their employees. And the medical pro fession is using programmed instruction in a pro gram of continuing education. While Skinner's claim of a 50% gain may be a little unrealistic, it should be clear that programmed instruction has definite potential as an educational device. In the discussion that follows I will examine this po tential from three view points: that of the educa tional psychologist who applies the theories of psychology to the classroom; my own viewpoint as a teacher who has written, experimented with and used programs in my teaching over a period of five years; and the viewpoint of the student who has studied from my programs. WHAT IS PROGRAMMED INSTRUCTION? The concept of programmed instruction was introduced by Skinner in 1954. Since that time three methods of presentation and two different styles have been developed. The three methods are: 1. Computer assisted instruction: the student operates a typewriter linked to the com puter which contains the programmed ma terial. 2. Teaching machines, any device which me chanically controls the presentation of the program to the student. 3. Programmed texts, which place the mater ial in the hands of the student. Each method has its advantages, but the pro grammed text is basic to the other two. There fore, this discussion will be limited to that meth od. SUMMER, 1968 The Student The Teacher The Psychologist CHARLES E. WALES The two program styles are called linear and branched. Table I shows an example of a simple linear program, a series of questions and answers. To use this program the student covers the an swer with a sheet of paper, reads the question and thinks or writes his answer. He then un covers the program answer and checks his work. Table II shows a branched program. In this case the student reads the question, selects one of the given answers, and then checks his choice against the answer given in the program. When he se lects the correct answer he proceeds to the next question. Table I. Simple Linear Program. Consider the open system, steady state process shown below, mixing operation with salt and water. TABLE II. Physical Material Balance Calculations Two or more process units may be included in the system chosen for a material balance calculation. For example, Figure 8 shows two driers used in series to remove water from salt. In this problem it is pos sible to write material balances not only for each unit but also for the pair of units combined Figure 8 SH20 20 A  E 98% salt 18% H20 10% H20 82% salt 90Z salt Section 1 Q. 1220 lbs/hr of wet salt (A) are supplied to the two stage drier system shown in Figure 8. Assume steady state operation. How many unknown flow rates are there in this system: Your A. 5 unknowns 5Q. How many flow rate unknows are there? 5A. Three flow rate unknowns: A, B, C. 6Q. How many composition unknowns? 6A. Six composition unknowns, two in each stream. The total number of flow rate and composition unknowns is 9. 7Q. What is the total number of material balance equa tions that can be written? 7A. Three material balance equations can be written: salt balance water balance stream balance 8Q. How many of these material balance equations are independent? 8A. Two material balance equations are independent. Program Versus Text If you have had no previous personal contact with programs your first question will probably be, why a program instead of a text? The answer to this question is provided by the psychologist Ausubel2 who identifies the most crucial condition affecting the acquisition and transfer of knowl Section 2 A. 6 equations. No. You counted material balances around unit 1 and unit 2. What about balances around both units ? Go to section 7. Section 3 A. 4 independent equations. Correct. All the other equa tions are dependent, they can be derived by adding or subtracting the four independent equations. Is it possible to solve a salt and a stream balance around unit one, a stream balance around unit two, and a stream balance around both units? Your A. Yes No See section 6 Section 4 A. 5 unknowns. Check the problem again, you probably counted the flow rate of stream A as an unknown. The flow rate of this stream is given and should be used as the "basis" for your calculations. Section 5 A. 9 equations. Correct. You can write a stream, salt, and water balance around each unit and around both units combined. Now, how many of these equations are independent? Your A. 4 equations 6 See section 3 8 CHEMICAL ENGINEERING EDUCATION See section 4 7 9 Table II. (Continued) Section 6 A. Your answer is yes. The correct answer is no. It is impossible to get an answer if you use three equations of the same kind (i.e., stream balances). Try it if you have doubts. Go to section 3. Section 7 A. 4 unknowns. Correct. The unknowns are stream flow rates B, C, D, and E. Streams B and D are pure water so there are no composition unknowns in this problem. Next, what is the total number of equations that re late these 4 unknown variables? Your A. 4 equations See section 10 Section 8 A. 6 independent equations. No. You have correctly reasoned that not all three equations in one set (i.e., unit one) may be used. But it is also impossible to use all three equations of one kind( i.e., salt balances). Go to section 5. Section 9 A. 8 unknowns. No. You have counted 4 composition unknowns for the water streams which are pure water. Go to section 1. Section 10 A. 4 equations. No. You didn't read the question care fully. What is the total number of equations you can write for this system that involve the stream flow rate unknowns? Go to section 7. edge as the internal logic and the organization of the material. The usual text is logically sound but psychologically incongruous because it segre gates material by topic, does not clarify the re lationship between topics, and presents material at a uniform level of abstraction instead of build ing from the simple to complex. As a result the student treats meaningful material as if it were rote in character. He memorizes formulas, learns type problems, performs mechanical manipula tions and both learning and retention are reduced. By contrast, Ausbel identifies the program as a psychologically correct device because it is con structed around the basic organizing concepts of the discipline and ideas are arranged sequentially to build the hierarchial structure that matches the way in which psychologists believe knowledge is organized and stored in the human nervous system. The method used to construct a program illustrates Ausubel's point. First, the basic con cepts of the course must be identified and or ganized into a logical pattern. Second, a detailed set of performance objectives such as those shown in Table III are prepared for each concept. Then the teacher begins the final step, the writing of the questions and answers that will lead the stu dent from the objectives he learned in the prev ious program to the objectives of the new pro gram. It is the combination of all these steps that gives the program its great strength. Table III. First Law of ThermodynamicsSummary* A. State Properties (Q 13) 1. Define a state property: a property that depends only on a point's location, not on the path used to get there. 2. Name 5 state properties: P,T,V,U,H. B. Path Properties (Q 412) 1. Define a path property: A property that depends on the path used. Q and W are path properties. 2. Use a PV diagram to prove that W depends on the path used. C. First Law of Thermodynamics for a Closed System (Q 1332) 1. State the first law of thermodynamics for a closed system: Q W, = U2 U, = AU 2. Define internal energy a. Q W = AU for any closed system, any ma terial. b. AU = C,(T, T1) for any ideal gas process and for an isometric process for any material which has a constant C,. c. Units, BTU/lb mole or BTU/lb d. Zero point, arbitrary 3. Apply the First Law to a Closed System Ideal Gas Real Material a. Closed Isothermal Process Q W, = U, U Q W, = U, U, = C,(T, T,) Q W = 0 U = (P,T) Q=W, b. Closed Adiabatic Process Q W, = AU = CAT Q W, = AU W, = C,AT, for Q = 0. R +W, + , 1 (TI T2) U = 0 (P,T) + PV  P2V2 Y1 *Part of the Performance Objectives for the program on the first law. SUMMER, 1968 By its Socratic form the program provides the student with many of the best features of fine tutorial instruction. The program shapes the stu dent's understanding by establishing simple be haviors which are gradually combined and modi fied until they lead to the final performance ob jectives which include both abstract concepts and concrete applications. Programs were the primary vehicle for trans mitting information in the thermodynamics course I taught at Purdue last semester. The stu dents also had the regular text and they were told which sections of the text they should study. At the end of the semester they were given a ques tionnaire which asked, "If you had to choose between good programs or a good text as the basis for study in a class, which would prefer? Some of their anonymous replies were: "The program, you can understand it rather than memorize it." "In a program a person can usually tell which points he did not understand, whereas in a text he may not understand the whole material." "The program, it forces you to stop and think and not just read, I tend to read over things in a text." As you can see, the students identified many of the factors predicted by the psychologists. In all, twentyfive students preferred the program while three preferred the text. One of those who picked the text gave the following reason. "I would probably choose a good text because that is more familiar, but I never read a text that left me with as clear an understanding of the subject as the programs did." Because the material in the programs is not exactly the same as that in the text I asked the students the additional ques tion, Would you have preferred to have the ma terial in the programs written in text form with out the questions and answers?" Twentysix re plied no; two were undecided. Linear or Branched Programs As he creates the program, the teacher must make many decisions. First he must choose the style of the program, either linear or branched. The linear style was chosen for my thermody namics material because it provides the most di rect control of the shaping process. In addition, the linear program makes the student a more ac tive learner. To answer each question he must reformulate the material in terms of his own vo cabulary, background and structure of ideas. Ac Table IV. First Law of ThermodynamicsSelf Quiz* 7. The flow work terms do not appear in the equation Q Wo = AH, the first law of thermodynamics for an open system. Does one of the terms in this equa tion include the flow work energy? If so which one? a. Q b. W, c. AH d. none of the above 7a. The term Q accounts for the energy transferred to or from the system as heat. Flow work is not included in this term. Return to question No. 7. 7b. The term W. accounts for the energy transferred to or from the system as shaft work. Flow work occurs when a stream crosses the boundary of a system. Some of the flow work energy may be converted to shaft work in a given process but the two types of work energy are not directly related. Reread the pro gram from just after A31 to Q33, then return to question No. 7. 7c. This answer is correct. The flow work is accounted for by the enthalpy H = U + PV. The terms U and PV are added because U represents the energy car ried by a stream that enters (or leaves) and PV represents the flow work done at the boundary when that stream enters (or leaves) the system. 7d. This answer is not correct. In an open system, flow work occurs whenever a stream enters or leaves the system. One of the terms in the first law must ac count for this energy. Reread the program from just after A31 to Q33, then return to question No. 7. *Sample SelfQuiz question for the program on the first law. cording to the psychologists these acts are cru cial to the learning process. In a sense the linear program is an experience in guided discovery. The student participates in the development of the first law and in the application of the law to different reversible and irreversible processes. The students find this participation stimulating. In response to the question, "What is the great est strength of the programs? they replied: "Hav ing the student answer the questions to work out the principles for himself." "I got into the act of actually developing equations." In a branched program the student does not construct answers to the questions. Instead, he demonstrates that he has learned something by choosing the correct answer from a set of given answers. This behavior is most appropriate for a testing situation and that is exactly how the branched program has been used here. Table IV CHEMICAL ENGINEERING EDUCATION is part of the branched program used as the Self Quiz at the end of the program on the first law. A branched program requires that each question have one correct answer and two or three rea sonable alternates or distractors. Since each incorrect answer must provide some feedback in formation to the student, more effort is required to construct a branched program. In some types of material there are no logical alternates and the branched program cannot be used. However, when these alternates exist, the branched pro gram can be very effective in teaching the stu dent to discriminate between similar ideas. Step Size The second decision the teacher must make is one of step size. Skinner's original concept of a linear program involved a short, one or two sen tence question properly cued or prompted to in sure the correct answer would be forthcoming. Recently, several, psychologists have questioned the wisdom of the small step. For example, Resnick3 has said "good students become bored with too many small steps and come to resent the time spent on such programs." Ausubel also sup ports this conclusion with the thought that small steps often artificially and unnecessarily "frag ment ideas so that their interrelationships are ob scured and their logical structure destroyed." By a trial and error process I came to the same con clusion, the small step does not suit the ability of the engineering student. Using feedback from my students I finally evolved the program style shown in Table V. These programs involve rela tively large steps, meaningful, unprompted ques tions combined with uninterrupted sections of explanatory material. This style integrates the best features of a textbook, the lecture that fills in the gaps left by the text, and the recitation or discussion that supplements both. Guiding the Student Some of you may question the idea of care fully guiding the student through derivations, proofs and sample problems. In fact you may pre fer the incomplete ideas presented in textbooks because you want the student to provide the neces sary clarification for himself. I agree that the student should learn to think for himself but I would argue that this struggle should not take place when the student is learning basic concepts. This reasoning is supported by Ausubel who says, "Excessively difficult material makes for an un Table V.Sample Page from the first law programs Since we can always use a path such as (1a2) between any two points, this equation can be used to evaluate AH for any ideal gas process. This is an im portant characteristic of a state property, any path be tween two points can be used to evaluate the change in a state property. 37Q. An ideal gas is compressed adiabatically in an open system process, can the work for this process be evaluated with the following equation? W= AH CdT C ,T C(T,, T) 37A. Yes, the AH of an ideal gas always equals C,(To Ti). 38Q. If a real material is compressed adiabatically in an open system process, can the work for this process be evaluated with the equation Wo =AH = COdT 38A. No. The equation Wo = AH is valid for any ma terial, but AH = CdT is valid only for an iso barbic process for all real materials. The enthalpy of an ideal gas is a function of only the temperature. The definition AH = Cp(To Ti) proves that when T. = Ti, AH = 0. Pressure has no effect on the enthalpy of an ideal gas. We can reach the same con clusion by noting that both U and the (PV) product (note PV = RT) are functions of only the temperature. Since H U + PV U+RT the enthalpy of an ideal gas must also be a function of only the temperature. 2. Isothermal Process 39Q. Write the first law for an open system, combine it with the definition of AH for an ideal gas and prove that Q Wo for an isothermal process involving an ideal gas. 39A. Q Wo = Ho Hi = C,,(To T,) Since T. = Ti Q W, = 0 Q =W, desirably large number of initial errors and mis conceptions that have to be unlearned." This in terferes with further learning, it lowers the stu dent's self confidence and motivation, and pro motes task avoidance. It is not that the student doesn't want to learn on his own, but rather that he lacks the necessary selfcritical ability. The student usually finds it easy enough to manipulate words so as to create an appearance of knowledge and thereby to delude himself and others that he really understands. Does that sound like some SUMMER, 1968 of your students? By contrast, consider the fol lowing reactions of my students to the programs: "They don't let you get a misconception." "We could go back over a question to clarify points." "Being able to correct ideas before going on to new material." "You can't go on unless what came before is understood." Other Factors We have considered several of the factors the psychologist considers crucial to effective learn ing. They are: organization around the broadest principles, systematic sequential organization which shapes the students behavior, and an ac tive learner who reformulates ideas in his own words. There are two additional factors to be considered. First the psychologists say that new, abstract subject matter should include concreteempiri cal illustrations and analogies to clarify mean ings. For this reason, my programs include both theory and example problems. The student's re action to this combination is very positive. Their response to the question, "What is the greatest strength of the programs?," was: "Working with the material as it is intro duced." "Seeing how each concept can be related to a problem right after the concept is presented." The second factor to be considered is what the psychologist would call an integrative perceptual organizer, a device which helps the student relate similar concepts and discriminate between over lapping ideas. In my thermodynamics programs this organization is accomplished by relating each concept and calculation to an appropriate phase diagram. As each subject is introduced it is re lated to a process line on a projection of the three dimensional surface for an ideal gas. For ex ample, the concept of reversible shaft work is re lated to the area under a process curve drawn on a PV diagram. The concept of reversible heat transfer is related to the area under a process curve drawn on a TS diagram. When real ma terials are introduced the appropriate threedi mensional models and projections of the models are used to relate the process conditions to the change in a state property. The students response to the question, "Did you find the emphasis on the graphical representation of each process helpful in understanding the material?" varied from "definitely"; and "very helpful"; to "yes, I can picture what is happening"; "yes, it was some thing basic to refer to"; and 'yes, I need a physi cal feeling for something to really understand it." In all, twentysix students found this graphical approach helpful, two others liked the approach but were confused by the great number of graphs presented. Programs Free the Teacher Designed as carefully as they are, you would expect programs to teach a subject and teach it well. The response of my students to the question "Do you think the programs helped you learn more than you usually do?", bears this out. The students' reply was a unanimous yes. When asked if the programs helped them un derstand more than usual, twentyseven students said yes; one was undecided. Part of the students' reactions can probably be attributed to the Haw thorne effect, but I'm not willing to admit that this is a major factor. I don't think engineering students are that naive. The fact that graduate students ask me for copies of my programs to study for their qualifying exams is further sup port for the value of the programs. Hopefully, by now I have convinced you that programs can be of significant value in an engi neering course. If not, let me tempt you with one final attribute of programmed instruction. Dur ing the past semester I taught an entire course in thermodynamics using the set of programs I have developed. Each program and its accompanying problem set were assigned as homework. There were no lectures in this course, class time was completely free for other activities. In a typical class meeting I spent from five to twenty minutes answering the students' questions about the ma terial in the program and discussing the home work problems. During the rest of the period we did a variety of things; we probed the concept to greater depth, we extended the concept to new situations and we applied the concept to indus trial type problems. Those of you who would like to find time to put some engineering in the engi neering curriculum should be especially eager to try programs. By increasing the efficiency of the transmission of knowledge, the programs can give you the time you need for other activities. This, I might point out, is exactly the role the psychologists predict for programmed instruc tion. Ernest Hilgard, a former chemical engi neer, head of the Department of Psychology and CHEMICAL ENGINEERING EDUCATION dean of the Graduate Division at Stanford put it this way4. ". . the program does not replace the teacher but can hopefully free the teacher from routine exposition, and give time for doing the things that only the teacher can do," teaching students to think for themselves. Programmed instruction can help you give your students a better education; I hope the in formation I have presented here will encourage you to try programs in your classroom. References 1. Skinner, B. F., Harvard Educational Review, 31, (4), 1961. 2. Ausubel, D. P., The Psychology of Meaningful Verbal Learning, Grune & Stratton, New York, 1963, (pp. 213, 208, 212). 3. Resnick, L. B., Harvard Educational Review, 33, (4), 1963. 4. Hilgard, E. R., Stanford Today, Series 1, (6), Sept. 1963. Dr. Charles E. Wales is an associate professor of engi neering and the President's assistant for educational re search and development at Wright State University. His present assignment includes organizing and presenting a series of seminars on effective teaching techniques for the Wright State faculty. He was educated at Wayne State (BSChE), University of Michigan (MSChE), and Purdue University (PhD). Professor Wales has written programmed instruction material in the areas of material balance calculations and basic thermodynamics. His programs have been or are being used on an experimental basis at Purdue, Kansas State, West Virginia, Ohio, and Wright State universities, at the Universities of Texas and Missouri (Columbia), and at Ohio College of Applied Science. 3 book reviews Engineering Thermodynamics M. W. Zemansky and H. C. Van Ness, McGrawHill (1966). Professors Zemansky and Van Ness have writ ten a text on thermodynamics with the "common core" course in mind. As such, the text repre sents a combination of and selection from the ma terial offered in the conventional beginning cour ses in thermodynamics in the chemical and me chanical engineering curricula. In following this path, the authors had to judge that certain topics included in these portions of the typical chemical engineering program would either be deleted, or discussed in other courses. A similar statement, but with different topics in mind, applies equally well to the typical mechanical engineering pro gram. Viewed against the background of the typical chemical engineering program, there are certain features which make this book different. First, there are a number of applications discussed in the text which are not presently included in this part, if indeed in any part, of the chemical engi neering program. In this category are such top ics as "bars in tension and compression" (chap. 2), "work in straining a bar" (chap. 3), "work in changing the polarization of a dielectric in a parallel plate capacitor" (chap. 3) "work in changing the magnetization of a magnetic solid" (chap. 3) and some of those discussed in "ap plications" (chap. 14). Secondly, a number of the classical experi ments are discussed. This includes the determina tion of "J" factor mechanical equivalent of heat (chap. 4), determination of (3U/3P)T of a gas (chap. 5), reversible change of volume of a gas (chap. 7), and the measurement of latent heat of vaporization (chap. 11) to cite a few. By the discussion of experimental methods and the in clusion of experimental data in some figures, I believe the authors are attempting to impress on the student the physical significance of the quan tities which are later used in the solution of prob lems. This is a part of education which is ap parently being phased out in the fundamental sciences and mathematics. Looking at the other side of the coin, the missing material, the chemical engineer will note that fugacityy" is not mentioned. The theorem of correspondence states is introduced and used only in one problem11.1. Also, only mixtures of ideal gases are considered. Nothing is in cluded on heats of solution, or properties of real mixtures, and very little on thermochemistry. Also, the development and use of the humidity SUMMER, 1968 TL l COLUMBUS WATERED HERE In August 1492, the crews of Columbus' expeditionary ships Santa Maria, Pinta and Nifia took enough water from this well in Palos, Spain to last until they reached the New World. Now, 475 years later, the well is still in use, but as a tourist attraction. Several Fluor employees and their families toured this part of Spain during 1967. Why not? They were living there as part of the team building a refinery for Rio Gulf de Petroleos at La Rabida, the site from which Columbus actually sailed. The Rio Gulf project is just one of some thirty foreign jobs currently under way by Fluor. Fluor's principal engineering centers are located in the United States and Europe. Almost every plant Fluor builds is engineered in one of four support facilities... Los Angeles, Hous ton, London or Haarlem, Holland. But an en gineer who starts at one of these offices may eventually end up at a foreign jobsite (if he chooses to do so). Right now there are openings in Los Angeles and Houston for Chemical Engineers with a B.S. degree or higher. Areas of specialty include process design, process development, computer and project engineering. Why not join a company with an international flavor and with international opportunities? For more details write our college recruiters, Frank Leach in Los Angeles or Ed Hines in Houston. THE FLUOR CORPORATION, LTD. ENGINEERS & CONSTRUCTORS 2500 South Atlantic Boulevard, Los Angeles, California 90022 3137 Old Spanish Trail, Houston, Texas 77021 AN EQUAL OPPORTUNITY EMPLOYER CHEMICAL ENGINEERING EDUCATION chart and calculation of dewpoints and bubble points using Raoult's lawtopics common to practically all initial chemical engineering cour sesare not considered. Undoubtedly, many mechanical engineers re viewing this book would find that some of their favorite topics have been omitted or treated with brevity and, conversely, some topics have been covered more extensively than is usually the case. The book is well written and the level of mathematicssome partial differential equations are usedsuch that the second year, or certainly the first semester third year, student should have no trouble. If a student cannot learn the the principles of thermodynamics from this book, it should certainly not be due to the mathematics used. Each chapter is concluded with a number of problems which appear to offer the user a rea esonable choice; i.e. some difficult ones and some not so difficult. Apparently, the problems were selected so a slide rule is the only type of com puter necessary. The usage of this book by chemical engineers depends upon how our programs develop over the next few years. If we move to more common core coursesand thermodynamics is one of the prime areas where such movement is possiblethis book "Engineering Thermodynamics," should be seriously considered for use. James H. Weber University of Nebraska IM problems for teachers The following solutions to thermody namics problems published in CEE Spring quarter, pp. 9596, 1968, were prepared by Professors R. K. Irey and J. H. Pohl at the University of Florida. We continue to so licit questions on subjects of general en gineering or scientific interest to be pre sented in this department. 1. (a) Consider u as u(s,xi), du = \ds + :f d , 7asj I ' By analogy with du = Tds di j T and =M w Fl ,(N+l eqs.) (b) The Maxwelf relations are aTN a /at, aF) (c) i) N+l, for a total of 4(N+1) eqs. 3N(N+l) ii)  , for a total of 2N(N+1) eqs. iii) Take the derivative of 4 q and sub stitute du into the equation d q = sdT  Consider the total derivative of 'q = q(T,x.), i= 1, ,N. d +q ( dT + t' thus, T s and . Since 2 we have 5 1' _1) JJ T/) \aT ig,! ta2RT, 2. (a) Consider s = s(T,5L) and s = s(T,FI). Then A( ads = dT d +j (i) and ( / and ds = dT + 'I (ii) = = T 1 and S = = T (iii) Use the Maxwell relations, and the relations (iii) in (i) and (ii). Then set the right of (ii) equal to the right of (i). If F is constant, ^. T4 ;x ,, If xZ is constant, the result is the same. (b) From (i) above dJ= i dT ( Ell .ti From the exactness of this equation Hold T constant in this equation and integrate with respect to all 5%. The lower limit is a reference value, Ci. The upper limit is variable. SUMMER, 1968 would you like to write "The Formation of Perhydrophenalenes and Polyalkyladamantanes by Isomerization of Tricyclic Perhydroaromatics?" How's that again? Well, never mind Bob Warren, Ed Janoski, and Abe Schneider already wrote it. They're chemists in Sun Oil Company's Re search and Development Department. Their paper is just one of many re sulting from imaginative and origi nal basic research conducted at Sun Oil. Maybe basic research and technical papers aren't your cup of tea. But isn't the kind of company that in vests in and encourages such projects the kind of company you'd like to work for? Especially when the company does things like pioneer the $235 million 138 Athabasca oil sands project in North ern Alberta to multiply the world's petroleum resources; plan a new $125 million processing facility in Puerto Rico; expand the Toledo Refinery to the tune of $50 million; sponsor the "Sunoco Special" and the racing team of Roger Penske and Mark Donohue in big league sports car racing to competitionprove and improve Sun oco products for the public; pursue a continuing program for air and water pollution control; beautify Sunoco service stations everywhere. Sunoco is geared for growth. We need men and women to grow with us and build a future. We have open ings in Exploration, Production, Manufacturing, Research, Engineer ing, Sales, Accounting, Economics, and Computer Operation. Locations Philadelphia, Toledo and Dallas areas. You may write us for an appoint ment, write for our book "Sunoco Career Opportunities Guide," or con tact your College Placement Director to see Sun's representative when on campus. SUN OIL COMPANY, Indus trial Relations Dept. CED, 1608 Wal nut Street, Philadelphia, Pa. 19103 or P. O. Box 2880, Dallas, Texas 75221. An Equal Opportunity Employer M/F CHEMICAL ENGINEERING EDUCATION views and opinions I THERMODYNAMICS: DEATH AND TRANSFIGURATION JAMES L. THRONE* Ohio University Athens, Ohio 45701 In a recent article1 I criticized vehemently present approaches to the teaching of thermo dynamics. In particular, I argued that thermo dynamics at present is based on mysticism and magic when dealing with the fundamental con cepts such as temperature, energy, and entropy. I argued that what was needed was a rational approach to the development of concepts and their application to chemical engineering and that, for the nonthermodynamicist, in particular, thermodynamics should be viewed as a hand maiden to the major chemical engineering areas such as kinetics, process design and control, and transport mechanics. In this paper, then, I offer a program which attempts to prepare the graduate engineer for a career in which thermodynamics plays an im portant, but not dominant, role. While this pro gram also has limitation, I should hasten to point out that it has been used successfully at Ohio University on a firstsemester graduate level for some time. Statistical or Mechanical Approach? As I pointed out in the earlier paper, I con sider that the fundamental concepts of thermo dynamics are three in number: 1. The concept of temperature 2. The concept of energy 3. The concept of entropy Traditionally, there are two major ways of intro ducing these concepts: 1. The intuitive approach, sometimes referred to as a phenomenological approach, in which, for example, the concept of temperature is regarded as a primitive con cept, like force and displacement, and therefore, not re quiring definition, merely illustration. 2. The statistical approach, in which it is necessary to identify a constraint in the system of describing equations *A biography of Dr. Throne is available in CEE 2, 92, 1968. with one of the concepts. The describing equations may deal with energy in kinetic form (classical approach), or quantum form, or even level of information form (Tribus). As I stated earlier, probably the only time the statistical approach is applied in traditional grad uate level chemical engineering first courses is in shoring up otherwise weak and faltering develop ments of the concept of entropy. It is apparent that if the proper approach to the development of the concept of entropy is employed, no shoring up is needed and, hence introduction of statistical concepts into a first course is not needed! Traditionally, the intuitive approach to chemi cal engineering thermodynamics has been "mole culeless mechanical thermodynamics," with em phasis on steadystate operations of system con taining continue of material. To say that this ap proach represents a crazyquilt of sterile applica tions of sound principles of mathematics and clas sical physics and empirical rulesofthumb so typical of chemical engineering in the thirties would undoubtedly insult many socalled chemical engineering thermodynamicists. In this program, I attempt to establish a firm, rational basis for the determination of a working program (no pun intended). I emphasize establishment of rigorous axioms on which we can evaluate the empirical concepts presently in vogue in the literature.2 Undoubtedly, I cannot hope to pre scribe a single remedy that will cure the multiple ills plaguing authors of articles and textbooks in one, introductory course. It is my primary goal to make the average graduate student aware of the maladies, so that he can intelligently evaluate work in his chosen field of endeavor. Our Program: Goals and Gaols* We begin the course by reviewing the funda mental laws of thermodynamics as primitive con cepts, requiring no definition. We then construct concepts total and path differentiation from a mathematical viewpoint. Concepts such as work *The texts we have been using, along with the support ing reference material, are listed in Table 1. SUMMER, 1968 I~ihE'k _....... __._.    introduced in metric form as being the result of relationships between generalized forces and differential displacements.** The close relation ship between fluid mechanical systems and ther modynamic systems is then discussed, and the generalized concepts of enthalpy and heat capa cities (in terms of generalized forces and dis placements) are developed, with specific examples in linear extension, surface extension, and pres surevolume. The theorems of Caratheodory, Pfaff, inaccessible states, and mathematical de velopment of constitutive equations for entropy, reversible heat and temperature are developed. Shaw's method of Jacobian of Transformation5 and the development of Maxwell's equations are presented, with extension of Shaw's method to multicomponent systems. These equations are then applied to the generation of equation such as the GibbsDuhem Equation. Partial molar properties, multicomponent sys tems, and the natural appearance of the chemical potential are presented. With special emphasis on gases, rules for the development and evaluation of constituitive equations are presented, along with fugacity and perfect mixtures of perfect and nonideal gases. It is emphasized that fugacity is the true thermodynamic pressure. The role and limitation of chemical potential, the phase rule, and degrees of freedom are then developed. We then consider first and higher order phase transitions, developments of Clapeyron and Er henfest equations from direct integration of Max well's equations and from L'Hopital's rule, and their physical implications in single component and multicomponent systems. We then expend considerable effort in apply ing the GibbsDuhem equation to the selection of constitutive relationships between partial pres sure, composition and temperature, emphasizing Raoult's law of ideal systems, Henry's law of equations. It is important to note here that we emphasize the approximate empirical nature of these constitutive equations; we do not let these equations live by themselves, as it were. Application of constitutive equations to engi neering systems such as heat of mixing and volume change, depression of freezing point, os **It is important to note that standard approaches to work utilize affine coordinates. While developments of concepts in affine coordinates are satisfactory for explicit problemsolving, development of general concepts, par ticularly when thermodynamics is used in transport me chanics, must be made in metric coordinates.3,4 TABLE I. Books Used in First Course in Graduate Thermodynamics Required Texts: 1. Denbigh, K. G. The Principles of Chemical Equi librium, 2nd Ed., Cambridge 1966. 2. Tribus, M., Thermostatics and Thermodynamics, D. Van Nostrand, Co., 1961. Recommended Reading Reference: 1. Zemansky, M.W., Heat and Thermodynamics, 4th Ed., McGrawHill, 1957. 2. Guggenheim, E. A., Thermodynamics, 3rd Ed., North Holland Publishing, 1957. 3. Dodge, B. F., Chemical Engineering Thermodynam ics, McGrawHill, 1944. 4. Smith, J. M., Introduction to Chemical Engineering Thermodynamics, McGrawHill, 1949. 5. Coull, J., and Stuart, E. B., Equilibrium Thermo dynamics, Wiley, 1964. 6. Lewis, G. N. and Randall, M., Pitzer, K. S. and Brewer, L., Thermodynamics, 2nd Ed., McGraw Hill, 1961. 7. Bosnjakovic, F., Technical Thermodynamics, Holt, Rinehart and Winston, 1965. 8. Gibbs, J. W., The Scientific Papers of., Volume 1, Thermodynamics, Dover, 1961. 9. Weber, H. C., and Meissner, H. P., Thermodynamics for Chemical Engineers, 2nd Ed., Wiley, 1957. 10. Van Wylen, G. J., Thermodynamics, Wiley, 1959. 11. Fong, P., Foundations of Thermodynamics, Oxford, 1961. 12. Bridgman, P. W. The Nature of Thermodynamics, Harper, 1961. 13. Fermi, E., Thermodynamics, Dover, 1956. motic pressure, and such, follow. Thermodynamic consistency tests and their relative reliability are stressed. Finally, we introduce concepts of thermo dynamics of the steady state, dealing with the concept of entropy production and the phenome nological coupling tensor between fluxes and forces. We discuss "Curie's theorem" and its logical basis as a fundamental theorem of tensor calculus,6 and the faults of the present state of irreversible thermodynamics (linear "Onsager ist" approach) and its future role in thermody namics. We conclude by examining real engi neering examples of steadystate thermodynamics in coupled systems such as heatmass transfer, kineticsfluid flow, and fuel cell technology. To implement the development of the course, I present, in flow diagram form, apparent inter actions in the major areas of thermodynamics. This diagram is shown below. While I do not pretend to imply that this flow diagram is wholly correct or complete, it does serve graphically to illustrate chemical engineering thermodynamics. CHEMICAL ENGINEERING EDUCATION THERMODYNAMICS Thermodynamics: Who Cares? First, it is important that the above program makes no mention of cycles, refrigerators, en gines, TS diagrams, Mollier Charts, compressi bility curves, etc. This is done deliberately. Em phasis is placed on understanding of underlying mathematical, mechanical, chemical, and physical principles. Interrelationships between thermo dynamics, kinetics, and mechanics are continu ally emphasized and illustrated through engineer ing examples. Why? It is my belief that rational understanding of the role of thermodynamics in the overall concept of chemical engineering comes, not from the ability of the student to calculate coefficients in equations of stategiven critical properties, but from his ability to understand the usefulness and limitations of the present concepts of thermodynamics. It is his ability to intelli gently and rationally question existing practices, not blindly calculate and manipulate empirical equations, that will make him a valuable member of the chemical engineering community. Conclusion Classical thermodynamicists with their minds intently focused on new PVT correlations or nth degree refinement in the current Mollier dia gram for steam or ammonia, are being bypassed and circumvented by people who need to answer thermodynamic questions dealing with biological metabolism, kindey or fuel cell operation, kinetic fluid flow interaction, cyclic operation of non ideal transport systems, thermomechanical foun dations of nonlinear visocelastic media, nonFick ian diffusion, sewage disposal and antipollution systems. We cannot afford to ignore the challenge of modern chemical engineering by offering ma terial that was designed to support chemical en gineering Edisonianism of the 30's. It is my opinion, then, that Dr. Bates' ap proach ("First Aid to Ailing Thermodynamics") will eventually lead to the death of thermody namics as it is traditionally taught. To this, I say, good riddance. For, like the Phoenix of Egyptian mythology, from its ashes shall rise anew a thermodynamics founded on the rational principles of Gibbsian mechanics. REFERENCES 1. Throne, J. L., Chem. Eng. Ed. 1 7071, (1966). 2. Giles, R., "Mathematical Foundations of Thermo dynamics," The Macmillan Co., New York, 1964. 3. Throne, J. L., "Applications of Tensor Calculus in Chemical Engineering," McGrawHill Book Co., New York, to be published. 4. Brillouin, L., "Tensors in Mechanics and Elastic ity," Academic Press, New York, 1964. 5. Tribus, M., "Thermostatics and Thermodynamics," D. Van Nostrand Co., Inc., New York. 6. Fitts, D. D., "Nonequilibrium Thermodynamics: A Phenomenological Theory of Irreversible Processes in Fluid Systems," McGrawHill Book Co., New York, 1962. SUMMER, 1968 WHERE ARE THE ENGINEERS?* T. B. METCALFE University of Southwestern Louisiana Lafayette, La. In spite of our usual confident reliance upon the balance between supply and demand, the re lationship between the output of our engineering colleges and the need for practicing engineers does not seem to be following the rule. All of the factors which we would expect to contribute to a great demand for engineers seem to be present. Engineering employment has reached new highs and graduating students of engineering colleges are offered a half dozen or more jobs upon gradu ation. There are complaints from many potential employers that they are unable to fill their quotas. Indeed, the meteoric rise in the employment of technicians in the engineering field, while largely due to a heretofore unfilled need for this kind of service, is also greatly influenced by the unavail ability of young engineers. Incentives are certainly present in the current situation. The satisfaction to the individual of making a contribution to technical advancement has never been greater and recognition on the part of the general public of the contribution of engineers is well established. Salaries and other remuneration for engineers are at new peaks, higher than those for most other career profes sionals, at least in the years immediately follow ing graduation. Engineering starting salaries are increasing and at a rate higher than the rate of increase for other professionals. Thus, the high and unsatisfied demand seems to have created the expected result of increased incentives for the study of engineering. Why then, should there be any shortage of engineers? Many contend that there is no shortage, or rather, they cite statistics to show that there is a consis tent increase in the number who choose to study engineering. They conclude that we should not fear a shortage as long as the trends continue. A comprehensive study published in the Janu ary, 1966 Journal of the American Society for En gineering Education, by the ECAC (committee for analysis of engineering enrollment) presented data in total engineering enrollments between 1949 and 1962. They note the large contribution of veterans under the government educational *Presented to the Spring Meeting of the GulfSouth west Section ASEE, College Station, Texas, 21 March 1968. Dr. T. B. Metcalfe is Head of the Department of Chemical Engineering at the University of Southwestern Louisiana. His background and experience includes de grees from Georgia Institute of Technology and the University of Texas; faculty positions at West Virginia Institute of Technology and the University of Houston; and professional experience with Shell Oil Company, U. S. Naval Reserve (WW II) and Dow Chemical Com pany. programs who swelled the enrollment in the years immediately following World War II and also during 195456 subsequent to the Korean military involvement. This analysis illustrated that if the enrollment of veterans was not included in the totals, the fluctuations in enrollment of engineer ing students are much reduced and a definite and consistent trend was evident. It was concluded that the apparent appreciation in engineering enrollments of about 13,500 each year ( during the entire thirteenyear period covered) might be con fidently extrapolated for another few years. It becomes the responsibility of engineering educators to perceive the changes in trends, and to exert the necessary influence to reverse unde sirable ones. Two conditions which contribute markedly to the rate of output of engineers are (1) the number of entering college students choosing engineering as a career and (2) the re tention of those students through graduation from engineering college. The desirability of, and the incentive to, study engineering must be com municated to the high school and junior high school public (student, parent, and counselor). Depending upon the success of this contact, more (or fewer) students may choose the profession of engineering. The statistics upon which Figure 1 is based illustrate that in the years 1949 to 1952 there was indeed a marked decrease in the total enrollment in universities in our country. This was undoubtedly due both to the then declining number of World War II veterans enrolling and the decrease in the enrollment of younger men CHEMICAL ENGINEERING EDUCATION FIRE I Tal Enrollments By Year T Total College Enrollmnt E Total Engierng Enrollment 1950 52 54 56 58 60 62 64 66 FGURE 2 Englenring Prcealagr of Taal Collea Enollmnat by year O0 \ \ S .... EnrolluntTrend (ae Fipre 1) 195 52 54 56 58 60 62 6 66 674 5323C mo n5 Is 5e6Iw I Es OL 60 6_ 6156 .9. 6 b6 7\ 1067 1 x 1956 5o 56 56 60 62 , / ^ students due to the Korean involvement. Subse quent to that period, however, from 1952 to the present no disregard of veterans or any other group is necessary to allow the recognition of a consistent, rapidly upward trend in the total en rollment of college men students in our colleges and universities. Comparison of trends in the total college enrollment and in engineering enroll ments show the same fluctuations, with variations in the trend for the most part occurring at the same times. However, the variations are greater in the case of the engineering enrollment and the ECAC prediction of an appreciation of 13,500 each year has been exceeded considerably each of the last 4 years, with an ever increasing rate. A significant difference in total enrollment and engi neering enrollment is the occurrence of a peak in engineering enrollment in 1957 and a subse quent fouryear decline in that enrollment, during which four years, the rise in total college enroll ment slowed only slightly. In 1961, while total college enrollments con tinued to climb (due, no doubt, to the coming of college age of the unusually large number of post war babies), engineering enrollments began again to rise. Each year since, the rise has been at a larger rate. Since our analysis of incentives has been dis cussed earlier in terms of comparison to other professions and careers, it is logical to evaluate the trends in engineering enrollments in terms of comparison to the overall enrollment. The sig nificance of the 1957 reversal in the upward trend of engineering enrollments is clarified by the curve of Figure 2 which represents the fraction SUMMER, 1968 of total enrollment represented by engineers. The percentage of engineers in the total college popu lation reached a peak in 1957 after having risen consistently during the postKorean period. Sub sequent to 1957, this percentage has persistently dropped, until at the present time, it is little more than half of the 1957 value of nearly 15 per cent. This is taken to be a clear indication of a ser ious and dangerous lack of rapport with the po tential college student on the part of engineering educators. There is small comfort in the existence of an upward trend in engineering enrollments in view of the fact that the shortage of engineers is not being relieved and the increase in engineering enrollments falls so far short of the increase in total college enrollment. To be most meaningful the statistics must be expressed in terms of the various disciplines. The classical disciplines of Chemical, Civil, Electrical, and Mechanical Engineering account for about half of all engineering students. Industrial and Petroleum Engineering are the only other disci plines with appreciable fractions of total engi neering enrollments. In 1952, there were in ECPD accredited departments 3,822 entering freshmen students who wished to study Chemical Engineering, and in 1962, at the end of the re porting by ASEE, there were 3,862, an only slightly larger number (see Figure 3). Reflecting the difference in total engineering enrollments at the start and at the end of this period, the nearly equal numbers of students in Chemical Engineer ing represented 8 per cent (of total engineering enrollment) in 1952 and hardly more than 7 per cent in 1962. Thus, while maintaining the num ber of its students, Chemical Engineering has de clined slightly in public acceptance as an engi neering discipline. By comparison, and considering the absolute numbers for the beginning and end of the ten year span as well as the trends, it is evident from the curves (Figure 3) that enrollments in Civil Engineering have dropped slightly, while their percentage has dropped from 111/2 to 91/2 per cent. There has been a more marked drop in the number of Mechanical Engineers and their percentage is down from 17 to 12 per cent of the total. Both Industrial and Petroleum Engi neering disciplines have shown large decreases in the number of students and in their fraction of the total engineering enrollment during this per iod. Only Electrical Engineering has shown a marked increase in number of students. This has resulted in an increase in its fraction of the total from 16 to 20 per cent. It becomes evident that the classical disci plines are not generally increasing in spite of the marked increase in total engineering enrollments. The increase is distributed among the newer dis ciplines, each representing smaller numbers of engineering students. These newer disciplines, while offshoots of the classical disciplines, have completely divorced themselves from the parent departments except in the case of Electrical Engi neering. The growth of the Electrical Engineer ing discipline can be attributed to their absorp tion of a number of new interests such as Elec tronics and Communications. This action on the part of Electrical Engineers to retain within a single discipline the widely varied interests which represent different appli cations of the same engineering principles is con sidered a wise one and one which should be emu lated by other disciplines. New branches of engi neering often are created because of the recog nition on the part of their practitioners that their interests stem from more than one of the classical disciplines, and therefore, they consider them selves separate from both. Preferable to this proliferation of engineering disciplines would be an interdisciplinary interest on the part of the parent disciplines. This would tend to unify and strengthen engineering instead of weakening it as does the current practice of splintering. Having determined the total enrollments as the potential with which we have to work, it is now interesting to observe the retention of this group of students. Over a tenyear period, the average retention for Chemical Engineering 144  EUR4 T6DE Ti AniE I0  (Figure 4) shows that after the first year the number of students enrolled for their second year is only 90 per cent, and those persisting to the third year only 73 per cent of the entering fresh men. Sixtyseven per cent persisted to their fourth year, and finally 61 per cent were gradu ated with the B.S. degree after four years. In Civil Engineering, 5 per cent were lost in the first year, with 95 per cent remaining; 90 per cent remained for their third year and a slight ap preciation then resulted in the fourth year class of 92 per cent of their entering freshmen. At the end of four years, 80 per cent of the entering Civil Engineering classes were graduated. Mechanical and Electrical Engineering appreciated 6 and 7 per cent, respectively, in the second year after which their number declined so than Mechanical Engineering Departments graduated 85 per cent of their entering freshmen and Electrical Engi neering, 83 per cent. Thus, among these disci plines only Chemical Engineering shows no in crease at any level during the college career. Rather, the number dropping out of Chemical En gineering during each year is significant. We can conclude that engineering educators must face up to the fact of a declining acceptance of engineering as a course of study by college students. Instead of fatalistic acceptance, we must strive to reverse this trend and provide greater numbers of graduated professionals by stronger recruitment of high school and junior college graduates and by greater retention of entering students who choose an engineering course of study. CHEMICAL ENGINEERING EDUCATION MARATHON: DYNAMIC PROGRESS ;r**r31i ~n*rri*1 L vII"WE L"YL1" ~** ""~i L~ U r'E.  Marathon Oil Company was founded in Find lay, Ohio in 1887; however its ultramodern Denver Research Center is located at the foot hills of the Rockies. The company is a producer, transporter, refiner and marketer of crude oil and petroleum products on five continents throughout the world. The Denver Research Center was established to make discovery of new petroleum reserves more economical, to help recover a larger percentage of oil in present fields, to develop more profitable refining and chemical processes, and to develop new products. Marathon employs more than 8,000 persons at its offices around the world including its head quarters in Findlay. There are over 300 em ployees at the Denver Research Center of which more than half are scientists and engineers. CHEMICAL ENGINEERING AT MARATHON Using engineering research to determine ways to recover more of the oil from known deposits is an important part of the work at the Research Center. It includes projects aimed at stimulating wells so they will produce more oil; in situ com bustion; and fluid injection processes, such as miscible displacement, which are more efficient than conventional techniques where gas or water are used to drive oil to a production well. Reservoir mechanics comprise another signifi cant part of the engineering work at the Denver Research Center. The transient behavior of oil reservoirs and the flow of fluids through porous media are important phases of this work. Mathe matical models, which simulate reservoir behav ior, provide insight into future behavior of oil bearing reservoirs. Chemical engineers are also engaged in the pilot plant study of existing refinery and chemical processes as well as in the evaluation and devel opment of new processes and new chemicals. Projects are underway, for example, on petro chemical processes to make monomers and other basic components for polymers. At Marathon's Research Center, qualified en gineers are provided with both the challenge and incentive in supplying answers to these problems. Your further inquiry is invited. Mr. L. Miles Personnel Supervisor Dept. CE1, P. O. Box 269 Littleton, Colorado 80120 AN EQUAL OPPORTUNITY EMPLOYER MARATHON MARATHON OIL COMPANY DENVER RESEARCH CENTER LITTLETON. COLORADO ..1 '5,: 4;, f* * i If i'.~ Professor, What Do You Think? Process Design Oilfield Production Technical Sales Plant Design Refinery Engineering Development Research Technical Service With all the opportunities available today you probably often hear this question from your students. You can be a major factor in his career. If you find yourself in this situation why not consider an industry that can offer a full range of Chemical Engineering assignments and advancement opportunities? Standard Oil Company of California has challenging assignments in just about any area that would interest Chemical Engineers. These initial assignments will test their ability and can lead to advancement in many areas. Should you or any of your students wish additional information on our industry or Company write to: Mr. Robert E. Rodman Coordinator, Professional Employment Standard Oil Company of California 225 Bush Street San Francisco, California 94120 Standard Oil Company of California An Equal Opportunity Employer 
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