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Dinesh Shah of Florida ( PDF )
University of Kentucky ( PDF ) Symposium on undergraduate thermodynamics: Introduction ( PDF ) Use of slides and selfstudy examples ( PDF ) An integrated approach ( PDF ) Thermodynamics with design problems ( PDF ) Computergenerated phase diagrams for binary mixtures ( PDF ) Supplemental TV taped problems ( PDF ) Fundamental property relation ( PDF ) Residual functions and fugacity ( PDF ) A graphic look at availability functions ( PDF ) Putting problem solving to use in the classroom ( PDF ) Book reviews ( PDF ) 
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5: i ' w ?~"f U' 8 ItwP; &CC SUN COMPANY, INC. CHEMICAL ENGINEERING EDUCATION &wAidA a dSiiaei of jauneds. EDITORIAL AND BUSINESS ADDRESS Department of Chemical Engineering University of Florida Gainesville, Florida 32611 Editor: Ray Fahien (904) 3920857 Consulting Editor: Mack Tyner Managing Editor: Carole C. Yocum (904) 3920861 Publications Board and Regional Advertising Representatives: Chairman: Lee C. Eagleton Pennsylvania State University Past Chairman: Klaus D. Timmerhaus University of Colorado SOUTH: Homer F. Johnson University of Tennessee Jack R. Hopper Lamar University James Fair University of Texas Gary Poehlezn Georgia Tech CENTRAL: Robert F. Anderson UOP Process Division Lowell B. Koppel Purdue University WEST: William B. Krantz University of Colorado C. Judson King University of California Berkeley NORTHEAST: Angelo J. Perna New Jersey Institute of Technology Stuart W. Churchill University of Pennsylvania Raymond Baddour M.I.T. A. TV. Westerberg CarnegieMellon University NORTHWEST: Charles Sleicher University of Washington CANADA: Leslie W. Shemilt McMaster University LIBRARY REPRESENTATIVE Thomas W. Weber State University of New York Chemical Engineering Education VOLUME XVII NUMBER 3 SUMMER 1983 The Educator 94 Dinesh Shah of Florida, Dick Dale and John O'Connell Department of Chemical Engineering 98 University of Kentucky, William L. Conger Symposium: Undergraduate Thermodynamics 104 Introduction, R, G. Squires, Symposium Editor 105 Use of Slides and SelfStudy Examples, Alan J. Brainard 108 An Integrated Approach, Thomas E. Daubert 110 Thermodynamics With Design Problems, E. V. Cilento and J. T. Sears 112 ComputerGenerated Phase Diagrams for Binary Mixtures, Kenneth R. Jolls, John Burnet, Jeffrey T. Haseman 117 Supplemental TV Taped Problems, Robert G. Squires and David V. Frank 119 The Fundamental Property Relation, Joseph J. Martin 124 Residual Functions and Fugacity, K. R. Hall, P. T. Eubank, J. C. Holste 128 A Graphic Look at Availability Functions, Martin V. Sussman Classroom 134 Putting Problem Solving to Use in the Classroom, Richard D. Noble Features 97 Division Activities 103 Letters to the Editor 137, 138, 139 Book Reviews 97 Stirred Pots CHEMICAL ENGINEERING EDUCATION is published quarterly by Chemical Engineering Division, American Society for Engineering Education. The publication is edited at the Chemical Engineering Department, University of Florida. Secondclass postage is paid at Gainesville, Florida, and at DeLeon Springs, Florida. Correspondence regarding editorial matter, circulation and changes of address should be addressed to the Editor at Gainesville, Florida 32611. Advertising rates and information are available from the advertising representatives. Plates and other advertising material may be sent directly to the printer: E. O. Painter Printing Co., P. O. Box 877, DeLeon Springs, Florida 32028. Subscription rate U.S., Canada, and Mexico is $15 per year, $10 per year mailed to members of AIChE and of the ChE Division of ASEE. Bulk subscription rates to ChE faculty on request. Write for prices on individual back copies. Copyright 1983 Chemical Engineering Division of American Society for Engineering Education. The statements and opinions expressed in this periodical are those of the writers and not necessarily those of the ChE Division of the ASEE which body assumes no responsibility for them. Defective copies replaced if notified within 120 days. The International Organization for Standardization has assigned the code US ISSN 00092479 for the identification of this periodical. SUMMER 1983 Educator eof Florida of Florida O'CONNELL DINESH SHAH IS A rebel, a philosopher, an in vestigator of science, a poet and a man of two worlds. His heritage is deep in 5,000 years of East Indian culture and his devotion is to a fledgling nation of only two centuries. "I was rebellious in many respects," he says. "I didn't like some of the traditional values. I was greatly influenced by Mahatma Gandhi and his writings. Before Gandhi we were a society of many castes where only people of low caste did manual labor. Gandhi said manual labor was good for everyone. "We had a low caste guy who cleaned our high school and I guess he just quit or something. The school was dirty so I told the principal that I would clean it if he gave me the money they paid before. He didn't see anything wrong with such an ar rangement but it sent a shockwave through the school. "I was known as a nonconformist! But no one had the nerve to question me. I was the top stu dent. I took that job in the eighth grade and kept it for four years. My brother continued doing it." Life for the Shah family wasn't easy. The breadwinner was ill for a long time prior to his death. Money was short and sacrifices had to be made. Tradition gave way to survival. "We had our own home so we didn't have a rent problem. And, in India, the relatives pitch in and help. I know my mother felt bad. If you bought Besides being a keynote speaker on several occasions, he has won two outstanding paper awards at international meetings. Among his one hundred publications are two books he edited on enhanced oil recovery. Copyright ChE Division, ASEE, 1983 something in the market, it was proper to engage a low caste to carry it to your home. I couldn't afford a porter. "My mother said to come home by way of the back streets where no one would see me. I walked through the main street with my bundles on my shoulder." College for the young Shah was, in his words, something of a miracle. With meager savings, help from relatives and acquaintances, and money from academic awards earned in high school, he went to the University of Bombay. "There was a special boarding house there. Heavily subsidized. No frills but adequate and at about half the usual cost. Even with that, in six months my money was gone. "I walked on the beach one day, trying to find a way to solve my problem. As I walked, I looked at the fine houses along the shore and, without know ing why, I moved closer and studied the names. These were homes of doctors, lawyers and profes sional people. I saw a name! An attorney who had been prominent in our preindependence move ment. And I pushed the bell." The young man asked to speak to someone in the family and was ushered to an audience with the matriarch, a daughterinlaw of the late fam ous barrister. CHEMICAL ENGINEERING EDUCATION DICK DALE AND JOHN University of Florida Gainesville, FL 32611 "She listened while I told my story. That I needed work. Washing clothes, dishes, tutoring children. There were no children of the immediate family but there were children of the staff. The servants." "Come every evening," she said, "and tutor the children. We will not pay you a salary but when you need money for anything just ask." "I was overwhelmed! They were very wealthy, indeed. And they supported me all through my undergraduate studies. It was a miracle! "In college there were two ways I might have gone. Engineering or medicine. Cutting up frogs or other "living" things was opposed by religious sentiments and engineering appeared uninterest ing. I settled for physics. "But as time went on there was nothing exotic or mystical about physics and I became fascinated with a new area called biophysics. Physics applied to biological systems and processes. I thought that would be really good. "That year the university started a graduate program in biophysics. I was in the first batch of four students who were selected and I spent two years at the Indian Cancer Research Center doing course work. "When I moved to graduate study I expressed my thanks to my patron and said I could carry on alone. I had expanded my tutoring to college stu dents and increased my earnings. My benefactor was delighted with my independence. We remained close friends. "But in 1960 I applied for a doctoral fellowship at Columbia, in the United States, and was ac cepted. To go to America meant that someone must post a financial bond. A substantial figure. And, without hesitation, she accepted responsibility for my move to America. Much later, when I had earned my degree, I received a lovely letter of congratulations. "When I first came to Columbia I was going to work in radiation biophysics. My first summer job, however, was with Professor J. H. Schulman in the school of mines. He was a pioneer in surface and colloid sciences. And I got hooked! "This is a terrific thing! You can handle the molecule! You can measure the molecule! And you can feel them! You can see the effect of molecular film on the surface tension of water. I was really hooked! "Fortunately, the professor was also on the advisory committee of the biophysics program. I took him as my supervisor for doctoral research. "I was exposed to many things in his labora tory that have enabled me to work broadly on such things as oil recovery, coal dispersions, pharma ceutical microemulsions, contact lens solutions, membranes and anesthesiology. Working with such a man was my second miracle!" Subsequently, Dinesh held a NRCNASA Resi dent Research Associateship to conduct research on chemical evolution and the origin of life at the NASA Ames Research Laboratory. Later, he moved to the Biological Oceanography Division of Columbia University and investigated the disper sion of oilspills, retardation of evaporation and :I Shah receives Outstanding Service Award from Wayne Chen, Dean of Engineering. Front row: John Biery, ChE Department Chairman (deceased), Shah, Dean Chen, K. S. Chan. Second row: Joseph Noronha, Wenching Hsieh, Michael Chiang, ShihYung Shiao. wave damping by thin films of surface active agents. In 1970, he joined the University of Florida as an Assistant Professor and was promoted to Pro fessor of Chemical Engineering, Anesthesiology and Biophysics in 1975. He has continued his re search love of the areas of monomolecular films, foams, wettability and contact angle, microemul sions, liquid crystals, improved oil recovery, com bustion of coal dispersions in oil and aqueous media, surfactantpolymer interaction, boundary lubrication and surface phenomena in magnetic media, membranes, lungs, vision and anesthesia. The initiation of a multidisciplinary research program on enhanced oil recovery jointly with other colleagues in the department was a major milestone in his research career. The international SUMMER 1983 recognition accorded to this program is a reflec tion of his relentless efforts and dedication. In the summer of 1983, Dinesh was invited to present a threeday short course on enhanced oil recovery at the Imperial College, London. With frequent over seas visitors and students from various parts of the world, his research group exudes a spirit of international cooperation and harmony. Dinesh introduced one undergraduate and two graduate courses on interfacial phenomena to chemical engineering curriculum which continue to attract not only students from chemical engi neering but also from other engineering and basic science departments. He has offered special topic courses on membrane biophysics, biochemical en gineering and enhanced oil recovery processes. A treat to listen to, Dinesh has presented about one hundred papers at scientific meetings and two hundred seminars at academic institutions and in dustrial laboratories. The first slide of his numer ous seminars (shown below) illustrates his ap proach to science and life. Besides being a keynote speaker on several occasions, he has won two out standing paper awards at international meetings. Among his one hundred publications are two books he edited on enhanced oil recovery. Dinesh's breadth of quality contributions is remarkable. The University of Florida has hon ored him with its highest awards in each area of teaching, research, and service, and the Federation of Asian Indians in North America has given him its "Outstanding Achievement Award". "I am going to be an academic for my lifetime. I could do other things but I wouldn't enjoy it. I like the freedom. And I like the personal inter action with the students. You feel you are shaping their careers. Essentially, you are expanding your : IN '4. Tradional opening slide of Shah's speeches. family. It's a great satisfaction". The common bond of love, affection and mutual respect between him and his students is maintained long after the students leave his laboratory. Perhaps Dinesh's approach to teaching, re search and education in general can be summar ized by the last sentence of his seminars, a quota tion from a poem by Tagore, which says "My J J .. ... Shah and his family on a recent visit to India and the Tai Majal. friend, drink my wine in my own cup to appreciate its sparkling bubbles." And Dinesh understands the meaning of fam ily and appreciates the support he receives from the family in all his endeavors. His wife Suvarna and two children are frequently seen at the chem ical engineering department. Guests at their home often meet other relatives. And a delight for many visitors is seeing the costumed children dancing to drums tapped by their father. Finally, there is always a verse. Deep thoughts written mostly in Gujarati. Poetic philosophy drafted en route in airplanes and in infrequent quiet moments. Some to be published soon in two languages that all in his two worlds may enjoy. Of his adopted country he speaks positively. "I like the general philosophy here in terms of the appreciation of a person for his accomplish ments. That you are judged without consideration of origin, race or creed. "We see an occasional exception but by and large this is so. You are allowed to become what you want to become. You are the architect of your life. There are no traditions or laws to follow and obey! "Wonderful!" E CHEMICAL ENGINEERING EDUCATION CHEMICAL ENGINEERING DIVISION ACTIVITIES TWENTYFIRST ANNUAL LECTURESHIP AWARD TO WARREN E. STEWART The 1983 ASEE Chemical Engineering Di vision Lecturer was Warren Earl Stewart of the University of Wisconsin. The purpose of this award lecture is to recognize and encourage out standing achievement in an important field of fundamental chemical engineering theory or practice. The 3M Company provides the financial support for this annual lecture award. Bestowed annually upon a distinguished engi neering educator who delivers the Annual Lec ture of the Chemical Engineering Division, the award consists of $1,000 and an engraved certifi cate. These were presented to this year's Lecturer at the Annual Chemical Engineering Division banquet, held at the Rochester Institute of Tech nology in Rochester, NY, on June 20. Professor Stewart's lecture was entitled "Simulation and Estimation by Orthogonal Collocation." NOMINATIONS FOR 1983 AWARD SOLICITED The award is made on an annual basis with nominations being received through February 1, 1984. The full details for the award preparation are contained in the Awards Brochure published by ASEE. Your nominations for the 1984 lecture ship are invited. They should be sent to Warren D. Seider, Chairman, 3M Award Committee, ChE Department, University of Pennsylvania, Phila delphia, PA 19104. ChE's RECEIVE HONORS A number of ChE's were honored with awards at the ASEE meeting. The Chester F. Carlson Award was given to Charles E. Wales (West Vir ginia University), and James E. Bailey (California Institute of Technology) was the recipient of the Curtis W. McGraw Award for Research. The Western Electric Fund Awards, given on a sec tional basis, were: Middle Atlantic, Robert Kabel (Penn State); Pacific Northwest, Louis Edwards (University of Idaho; Rocky Mountain, E. Dendy Sloan (Colorado School of Mines), Southeastern, John Gainer (University of Virginia); St. Law rence, Arland H. Johannes (Rensselaer Poly technic). NEW DIVISION OFFICERS ELECTED The newly elected ChE Division officers are: Dee Barker, Chairman; Angelo Perna, Past Chair man; Deran Hanesian, Chairman Elect; Bill Beck with, SecretaryTreasurer; Richard Noble, Pro gram Chairman; and H. S. Kemp, Robert Squires, and H. Burpo, Members at Large. 1 stirred pots LACEY LECTURER IS LUSS Editor's Note: Some years ago a new tradition was established at CalTech when Professor R. A. Aris wrote a poem to honor the current lecturer in the CalTech lecture series named in honor of William N. Lacey. These poems, or songs, are now performed at a banquet honoring the lecturer each year and constitute a colorful and humorous col lection of tributes. The 1983 Lacey Lecturer was Dan Luss of the University of Houston, who was recognized with the following poem. Oh Danny Boy, the cusps, the cusps are calling From tank to tank they make their winged way. Uniqueness' gone, complexities appalling Have risen up and, seemingly, to stay. But came ye here with simple bifurcations, Contact transforms and singularities, You dazed us all with farfetched explanations And, Danny Boy, with such becoming ease. From far ye came, in fact ye came from Houston, To bring these marvels of reaction rate. "Tex" Luss they call ye, so good are you at boostin' The best department of the Lone Star state. Ye also came to tell of strange perversions Of hotspots waxing when we thought they'd wane, Of better feeds that yield worse conversions. Oh, Danny Boy, you give us all a pain. But are ye sure these stories all so racy Lie well within the engineering ken Or have you strayed, in these our lectures Lacey Oh, Danny Boy, off into math again. SUMMER 1983 Central Campus mp department UNIVERSITY OF KENTUCKY WILLIAM L. CONGER University of Kentucky Lexington, KY 40506 THE COLLEGE OF ENGINEERING at the University of Kentucky had its beginning in an act of the Kentucky legislature on February 22, 1865. The act accepted the provisions of the Morrill Land Grant College Act and established the Agricultural and Mechanical College of Kentucky, to be located in Fayette County near the city of Lexington. Six days later Governor Thomas E. Bramlette signed into law another statute, which provided for the consolidation of Transylvania University and Kentucky University (a denominational school in Harrodsburg). Transylvania, the oldest college west of the Appalachian Mountains, had fallen on lean years and the buildings of Kentucky Uni versity had burned the year before. The new A & M College was made a college of the new con solidated Kentucky University. All did not go well for the A & M College and Kentucky University. The connection of the state supported A & M College with a private denomina tional school brought about dissension. As the situ ation grew worse the legislature began to look into a solution and on March 13, 1878 passed an act re pealing the legislation that authorized the union of the A & M College with Kentucky University and providing that the Agricultural and Mechan ical College would forever remain a state institu tion free of all ecclesiastical entanglements and control. Later Kentucky University changed its name back to Transylvania University. Problems were not yet solved for the fledgling A & M College for the courts held that it had lost all its land and buildings acquired while it was a part of Kentucky University. A search for a new CHEMICAL ENGINEERING EDUCATION Copyright ChE Division, ASEE, 1983 home began and an offer from the city of Lexing ton to give the College fiftytwo acres of the old fair grounds was accepted. Thus the A & M College was located on the site of the present University of Kentucky by an act of the Kentucky legislature in February, 1880. In 1908 the name of the Agricultural and Me chanical College of Kentucky was changed to "State University, Lexington, Kentucky" and finally in 1916 the name was officially changed to its present "University of Kentucky." ChE AT KENTUCKY Although a department of chemical engineer ing did not formally exist until 1956, when it was created at the request of the Chemistry Depart ment to replace an industrial chemistry program, many prominent chemical engineers graduated from the university prior to that date. Among them are William H. McAdams, who was later awarded an honorary D.Sc. degree, and E. V. Murphree. Just as the early years of the university did not always go smoothly, the early years of the depart ment also encountered difficulties. The program was formally initiated when Sam Hite (now at RoseHulman) registered 16 freshman and 5 sophomores for the spring of 1957. The depart ment was housed in space made available in the Mining Laboratory. It was not until 1966 that Anderson Hall was completed and chemical engi neering was moved into the first floor of this build ing. In the fall of 1958 Stan Heath and George Crewe joined Sam. Stan remained for two years while he finished a Divinity Degree at nearby Asbury College. Sam and George held the fort to gether until Noel Moore (now at RoseHulman) and Ed Litkenhouse came in the spring of 1964. Ed taught one semester and then departed. The early 1960's marked a major change in the University of Kentucky. Previously the university had emphasized undergraduate programs with little regard to graduate education and research. Under President John Oswald a major emphasis was placed on the development of these areas. The new orientation of the university translated into major change for the department of chemical engi neering. Sam Hite left during the summer of 1966 and Bill Conger (now Head of Department at VPI) and Tom Schrodt were hired as new as sistant professors in November 1966. Bob Grieves (now Dean of Engineering, Uni versity of Texas at El Paso) joined the faculty as Professor and Chairman in July 1967, soon fol lowed by Dick Kermode. With the resumes of Bob and Dick attached, the department received ap proval for a Master's program in April 1967, thus instituting its graduate program. The PhD pro gram was instituted in 1969 after the addition of Charlie Hamrin (1968), Bob Brett (1968now Some of the ChE faculty in Memorial Coliseum, "The House that Rupp Built." Left to right: front row, Asit Ray, Bill Conger, Tom Schrodt; Center row, Dick Ker mode, Len Peters, Charlie Hamrin, Jonathan Berman; Rear row, Dibakar Bhattacharyya. with a consulting firm), Ed Moorhead (1969), and Peter Skelland (1969now at Georgia Tech). The faculty has continued to grow with the addition of Len Peters (1974), John Yamanis (1975now with Allied Chemical), Dibakar Bhattacharyya (1979), Asit Ray (1980), and Jonathan Berman (1982). The latest phase in the development and growth of the department began in 1979 when Bob Grieves moved to a position as Associate Dean of the College of Engineering and Len Peters took over the Chairmanship. The first four BSChE degrees were awarded in August 1959, the first MSChE degree in 1968, and the first PhD degree in 1969. As of the 1982 winter semester the department has awarded 559 Bach elors, 126 Masters, and 21 PhD degrees. As a point of comparison, through 1964 the College of Engi neering had only awarded 576 Master of Science SUMMER 1983 In recent years a number of chemists and mathematicians have entered the graduate program. We have developed a package which includes, in addition to the regular requirements, a core of chemical engineering undergraduate courses . requiring) 3 to 3 1/2 years to finish. and professional degrees and 6 Doctor's Degrees. Many of chemical engineering's PhD graduates have chosen teaching as a profession and are now faculty members at Rensselaer, Auburn, Vander bilt, VPI, Iowa, and Cleveland State. Much of the department's early development under Bob Grieves was a result of his efforts in obtaining Air and Water Pollution Traineeship Grants and the Water Resources Institute. More recently we have emphasized energy and especially coal and oil shale. The proximity of the Kentucky Center for Energy Research Laboratory of the Commonwealth of Kentucky has helped in these areas. The present faculty of the department includes Leonard K. Peters, Jonathan Berman, Dibakar Bhattacharyya, George F. Crewe, Charles E. Ham rin, Richard I. Kermode, Edward D. Moorhead, Asit K. Ray, and J. Thomas Schrodt. UK AND THE BLUEGRASS The university is located in the heart of the Kentucky bluegrass region, well known for its' "beautiful horses and fast women." Lexington is at one corner of an almost equilateral triangle with Louisville and Cincinnati at the other two corners. 164, a main eastwest artery, and 175, a main northsouth artery, intersect at Lexingtonallow ing easy highway access to most of the eastern U.S. The bluegrass region features a rolling grass covered terrain dotted with horse farms. Most of the major racing stables maintain farms in this region. The topography of Kentucky is highly varied, with the foothills of the Appalachians within an hours drive to the east and the flat lands of Kentucky several hours to the west. Kentucky is noted for its extensive state park system and many manmade lakes. Fishing for bass, crappie, trout, muskie, and all kinds of panfish is available, and all forms of boating are possible on the state's lakes and rivers, including some good whitewater for the canoeing, kayaking, or rafting enthusiast. Just an hour to the east of Lexington lies the Daniel Boone National Forest where one may hike, climb, canoe, and camp. Within the forest is the Red River Gorge with its natural sandstone arches and sculptured cliffs. 100 For the history buff there is much of interest within the state. Lincoln's birthplace outside Hodgensville is a state shrine, Stephen Foster's "My Old Kentucky Home" is nearby, and there are several battlefields of the Civil War. Daniel Boone opened up Kentucky by leading settlers through the Cumberland Gap; his grave can be found at Frankfort and a replica of the fort he built is at Boonesborough, just a half hour from Lexington. The recreational assets of the state include the cave country, where it is possible to explore hun dreds of limestone caves including Mammoth Cave. Basketball must be mentioned when you speak of Kentucky. It is more a religion than a sport there is even a rumor that Kentucky children are born bouncing a ball. UNDERGRADUATE PROGRAM The College of Engineering has a policy of re stricted entrance. This policy is in the process of being revised, and if the revisions make it through our university approval system, a new policy should be in place by the fall of 1984. Chemical engineering has proposed standards that will be more restrictive than those proposed by the college. Action on our restricted entrance policy has been delayed pending action on the new college policy. Our goal for an entrance policy in chemical engineering is stated below. High school applicants or transfer applicants with less than 30 college semester credit hours must meet all the following minimum admission criteria: (1) an ACT composite score at or above the 75th percentile on national (college bound) norms, and (2) an ACT mathematics score at or above the 80th percentile on national (college bound) norms. All transfer students with at least 30 college semester credit hours must meet the following minimum admission criteria: students from UK Community Colleges, other UK pro grams, 32 programs with other universities, and all other colleges and universities must have a cumulative GPA of 2.7 or greater and not less than 2.5 in each area of chemistry, mathematics, physics, and engineering. Chemical engineering appears to get a dispro portionate share of the better students entering the College of Engineering. Our students, on the CHEMICAL ENGINEERING EDUCATION average, rank among the best in the college and among the very best in the university. While our program is just a little over 20 years old, it has gone through many reorganizations and modifications. In the 60's the College of Engineer ing went to core fluid mechanics, heat transfer, and thermodynamics courses. Our students take the first two, but we have successfully resisted the core thermodynamics. We have maintained that phase and chemical equilibria are so important to our program that we must teach our own thermo. In addition to the above courses we have 4 credit hours of stoichiometry, 5 hours of mass transfer, and required courses in reactor design and process control. The university requires 18 hours of general studies, and 6 hours of unre stricted electives. We have one further elective that must be taken in the department. Finally, we have the usual chemistry through Pchem, calculus, physics, English and engineering science courses. The result is a 4 year, 132 semester credit hour curriculum leading to a BS in chemical engineer ing. In addition we have optional programs for premed and predent students, a 5 year coop program (just initiated), and an accelerated 4 1/2 year program resulting in a BS and MS. For the fall of 1982, 325 undergraduates officially enrolled in our department, and we graduated about 53 during 198283. Kentucky has a community college system, and a large number of students are transfers after 2 years of study. Considering this fact, for fall 1982 there were 400 undergraduates seeking a chemical engineering degree in the University of Kentucky system. Over 20 % of these were female. We have active student chapters of Tau Beta Pi, Omega Chi Epsilon, Society of Women Engi neers, Society of Black Engineers, and the AIChE. GRADUATE PROGRAM We offer the MS in chemical engineering and the PhD. The MS degree requires 24 semester hours of course work, a thesis, and an oral exam. There is an option to receive a MS on course work only, but this is only used by special permission of the faculty. In general it takes 16 to 18 months to complete the program. The requirements for the PhD are less specific. There is no official course requirement, but in gen eral we require 30 semester hours past the MS. The student must pass a 2 to 2 1/2 day qualifying examination once his or her course work has been completed, complete a dissertation on an original research project, and successfully defend the work in a final oral examination. Generally 2 to 2 1/2 years are required beyond the MS to complete the PhD. A few students elect to bypass the MS and work directly on the PhD. In recent years a number of chemists and mathematicians have entered the graduate pro gram. We have developed a package which in cludes, in addition to the regular requirements, a core of chemical engineering undergraduate courses. This program usually requires 3 to 3 1/3 years to finish. Graduate offerings are listed in Table 1. Those marked with an asterisk are required of all PhD TABLE 1 Graduate Offerings Analysis of Chemical Engineering Problems* Air Pollution Control Transport I* Chemical Reactor Design Polymeric Materials Advanced Chemical Engineering Process Design Energy Engineering NonNewtonian Flow and Heat Transfer Chemical Separation and Measurement for Chemical Engi neers Design of Rate and Equilibrium Processes for Water Pollu tion Control Advanced Air Pollution Control Air Sampling and Analysis Equilibrium Thermodynamics* Nonequilibrium Thermodynamics Properties of Gases and Liquids Transport II Diffusional Mass Transfer Operations Staged Mass Transfer Operations Transport Phenomena in Packed and Fluidized Beds Advanced Process Control I Advanced Chemical Reactor Design* Equilibrium and Rate Processes of Coal Conversion Basic Electrode Processes in Electrochemical Engineering Biochemical Engineering Residence Credit for the Master's Degree Residence Credit for the Doctor's Degree Seminar Special Problems in Chemical Engineering *Indicates core course in Masters Program students. The reader will note there is an emphasis on pollution and energy courses in the available offerings. This relates to past and present research interests of many of the faculty. A full time graduate load is 9 hours, with many students taking 12 hours. Most graduate students are on 12 month appointments and are supported by fellowships or research assistantships. The SUMMER 1983 Anderson Hall: The College of Engineering current stipend is $8400/year plus tuition. A few PhD students may teach regular department courses with permission of the faculty and may receive additional compensation for this service. RESEARCH PROGRAMS The graduate programs at Kentucky were initially based upon air pollution and water pollu tion traineeship grants and the associated re search. While this is still a strong area of interest in our faculty, most of our present emphasis is in energy. In particular, we have faculty working in shale oil, coal conversion, and hydrogen produc tion. The Kentucky Center for Energy Research Laboratory of the Commonwealth of Kentucky, which receives state and federal funding, is run by the University of Kentucky and is located within 10 miles of the campus. Cooperation with this fa cility strengthens our energy programs. A recent grant in this area is from Phillips Petroleum to study eastern oil shale retorting. Len Peters is in atmospheric transport and chemistry on regional and global scales, and physicochemical behavior of aerosol systems. He is studying the chemistry and transport of CH4 and CO in the global troposphere as a principal subset of the carbon cycle. These theoretical stud ies are being compared against observations of the CO concentration from 40S latitude to 40N lati tude obtained by an infrared radiometer which was flown on one of the space shuttle flights. He is a coinvestigator on that experiment. He is also investigating the regional scale transport, deposition, and chemistry of SO2, NOx, and sulfates in the eastern United States. These studies are aimed at understanding the formation and distribution of sulfate aerosol and acid rain. This and the previous study solve the threedimen sional, timedependent species continuity equa tions, including the nonlinear chemistry, and are solved on vector computers. Asit Ray and Len are collaborating on studying the physical and chemical processes of tobacco smoke aerosol. Individual projects involve studies on coagulation, growth in humid atmospheres, physical and chemical characteristics of the aero sol, phoretic phenomena, the aerosol formation processes, and deposition in the lung. Dibakar Bhattacharyya has done extensive work involving the development of novel separa tion processes with special emphasis in the area of water pollution control. He has also worked on a joint research project with Boliden Metal Corpo ration, Sweden, involving the study of sulfide pre cipitation systems for selective separation of toxic metals and arsenic. His research interests are: novel lowpressure membrane (charged and com posite membranes) processes for selective solute removal and water reuse, recovery of metals by sulfide precipitation, coal conversion wastewaters and water recycle models, and eastern oil shale retorting studies dealing with porosity change and metal leachability. Charlie Hamrin has four areas of active re search: determination of oxygen and nitrogen in coal using instrumental neutron activation analysis (joint with Chemistry Department), hy droliquefaction of oil shale, modeling of a catalytic, crossflow reactor, and solution of ordinary and partial differential equations using computer codes. In the first project he has measured oxygen before and after drying by several techniques and finds that only by assuming volatiles in addition to water can the data be explained. The oil shale CHEMICAL ENGINEERING EDUCATION project is an application of the tubing bomb re actor extensively used in coal research to study kinetics of eastern oil shale hydroliquefaction. Modeling of a crossflow reactor is part of an over all program of a gasliquidsolid reactor study in cluding the HCoal ebullatedbed reactor. The solu tion of equations using computer codes has been applied to the Graetz problem for circular tubes and parallel plates. He has generated dimension less temperatures and Nusselt numbers in agree ment with the extensive tubulations of Shah and London. Many problems involving transport phe nomena will be amenable to solution by computer codes. The main emphasis of Ed Moorhead's research deals with electrochemical studies of oxidation and reduction at conducting and semiconducting elec trode surfaces, and includes: investigating the kinetic effects of surface and solution catalysis (and photocatalysis), studies of mass transport to various electrode geometries, development of new or improved electronic measuring techniques (in cluding relaxation methods), measurement of ppb level trace metals, and application of inlab mini/ micro computers for data acquisition and analysis. He has recently developed (with NSF support) the electromagnetically driven transverse oscillat ing resonant electrode ("TORE") wire for elec trode process studies. The vibrating wire (50 micron dia.) presents some challenging problems in cylindrical diffusion which are presently being addressed using finite element analysis. Bill Conger's main interest in recent years has been the use of the second law of thermodynamics to analyze the energy inefficiencies in chemical process flow sheets. In addition he is interested in process simulations. He has combined these inter ests to analyze proposed hydrogen production schemes and coal gasification processes. Presently he is interested in using the second law analysis in determining design alternatives. Jonathan Berman has several areas of interest. Among them are studies on diffusive and reactive transport of oxygen in red blood cells and on membrane blood oxygenators. He is presently working on theoretical and experimental studies to investigate the assumption normally made that the internal contents of the red blood cell are in in stantaneous equilibrium with the local plasma sur roundings. His work on membrane oxygenators centers around efforts to enhance the relatively inefficient mass transfer process which results from the separation of the two phases involved. He is working on theoretical solutions consisting of coupled asymptotic and numerical analyses and on experimental verification of these solutions for particular oxygenator configurations. The above are examples of the interests of some of our faculty showing the strong emphasis of the department in the pollution and energy areas. FUTURE DIRECTIONS We are faced with many of the same problems that confront other departments across the coun try. Our undergraduate population is growing rapidly, it is difficult to convince U.S. citizens to continue in graduate school, and financial support from the university is not what we would have it to be, to name just three. In spite of these prob lems we feel we are a dynamic growing depart ment and our faculty is looking forward to what the next five years and beyond will bring. Being a very young department, we are experiencing grow ing pains; but maturing into a department that is recognized and respected by others in our profes sion has made it all worthwhile. E letters S ALTERNATIVE APPROACH TO SELECTION OF REFERENCE STATES Dear Sir: The possibilities for selection of reference states for several thermodynamic functions are discussed in the article "Reference States and Relative Value of Internal Energy, Enthalpy, and Entropy" in the Spring, 1983 issue of Chemical Engineering Education by Professor A. G. Fredrickson. This letter is intended to suggest an alterna tive approach to that used in the article and some possible reinterpretation and extension. My points are: 1. The results of the article can be derived more satisfactorily from a starting point of simple closed system equations rather than the model used, which is applicable to complex open systems. 2. In discussion of an open system problem from Modell and Reid's classic text, unwarranted physical meaning is implied for the quantity total internal energy. 3. The discussion of reference states can be usefully expanded to include Gibbs and Helmholtz free energy, which are state functions of significantly different charac ter from those treated in the article. The article starts with mathematical statements of mass balance, first law, and second law applicable to ". open, moving and deforming, and unsteady state Continued on page 132. SUMMER 1983 I~sc SYMPOSIUM ON UNDERGRADUATE ChE THERMODYNAMICS INSTRUCTION SYMPOSIUM EDITOR R. G. SQUIRES Purdue University West Lafayette, IN 47907 The eight papers which follow were all pre sented at the 90th Annual Meeting of the Amer ican Society for Engineering Education at Texas A&M on June 22,1982. The Chemical Engineering Division of ASEE sponsored a daylong series of sessions on undergraduate thermodynamic in struction. The Annual Tutorial Lecture, by Pro fessor Joseph J. Martin, opened the day, followed in the afternoon by a twosession symposium of seven shorter papers. These papers fall into two groups: the first group presents teaching methods that, although they are presented in the context of undergraduate chemical engineering thermodynamics courses, have much broader application and would be use ful methods in many other courses. The second group of three papers presents application of re lationships that are specific to thermodynamics. The authors in these papers emphasize the im portance of these specific relations in undergradu ate instruction. In the first paper in the teaching methods group, Prof. Alan Brainard describes how, at the University of Pittsburgh, a series of over three hundred 35mm slides, in conjunction with an "ActiveInvolvement book" are used to increase information transfer and student motivation. Prof. Tom Daubert then describes how, at Penn State, rather than teach a separate course in thermodynamics, the material is integrated in the overall curriculum. A similar idea is presented by Profs. E. V. Cilento and J. T. Sears, who, at W. Virginia U., after presenting the thermodynamic fundamental concepts through standard lectures, integrate these basic concepts with a design prob lem. The next two papers discuss supplemental ma terials to be used in conjunction with a conven tional course. Prof. Jolls describes the use of com These papers fall into two groups: the first group presents teaching methods that... have... broad application and would be useful methods in many other courses. The second group of three papers presents application of relationships that are specific to thermodynamics. puter generated two and three dimensional phase diagrams that have recently been developed at Iowa State. He believes that thermodynamics pre sents unique teaching difficulties due to its level of abstraction and that computer generated phase diagrams greatly aid in student understanding of phase equilibrium. Finally, at Purdue University, Professor Squires and D. V. Frank have developed a series of twenty videotaped supplemental ther modynamic problems, covering topics from the first law to phase and chemical equilibrium. Stu dent use of these problems outside of class time has increased both the flexibility and efficiency of the course. In the second group of papers, Prof. Joseph J. Martin, the University of Michigan, contends that the Fundamental Property Relation is one of the four basic equations of thermodynamics. Consider ing its importance, it is surprising to find that the generalization of the fundamental property rela tion to include effects other than thermal, com pression and mass change has led to considerable confusion which this paper attempts to remedy. Anyone who has taught chemical engineering thermodynamics realizes the difficulty in present ing the concepts underlying phase equilibrium. Professors Hall, Eubank, and Holste, of Texas A&M, present an approach which uses the residual functions to provide a starting point to derive the fugacity equations. In the last paper, Prof. Martin Sussman, Tufts University, contends that greater thermodynamic insights may be gained by considering a graphical representation of the availability function. He then applies this method to steady flow and chemically reactive systems. O CHEMICAL ENGINEERING EDUCATION leachsin? 2/1de,49'adA4ad T,..mrvltnMawar... USE OF SLIDES AND SELF STUDY EXAMPLES ALAN J. BRAINARD University of Pittsburgh Pittsburgh, PA 15261 BEFORE LAUNCHING INTO a description of the STATE1 . Methods that I utilize in my teaching, I feel that definitions of the following terms are re quired: LEARNING may be conceived of as a change, due to experience, in the students ways of thinking, feeling, and acting. The effectiveness of the learning process may be thought of in terms of (1) the magnitude of the  changes taking place in the individual student or (2) . the proportion of students who have changed signifi  cantly in one or more characteristics relevant to the ." learning process. Thus conceived, education may be re garded as a system of learning experiences which brings :7 ' about certain desirable changes in students. [1] MOTIVATION, in the scientific sense, may be defined as the measure of the direction and intensity of the expenditure of animal energy. . Human institutions may be said to be formed primarily to motivate men .... Educational systems are designed to motivate human beings to accept a cultural heritage. [2] FIGURE 1. The objective of my teaching can now be intro ducedI seek ways of maximizing the learning of K Alan J. Brainard is an Associate Professor of Chemical and Petro leum Engineering at the University of Pittsburgh. His M.S. and Ph.D. degrees are from the University of Michigan. He worked for Exxon for two years before joining Pitt. He was the recipient of the Western Electric Award for Excellence in Engineering Education in 1976. He is a past vicechairman for programs of the Educational Research and Methods Division of ASEE and continues to participate actively at both the regional and national levels of that oragnization. a given subject matter by providing conditions which are motivational for my students. To be more specific, this paper will discuss methods used in teaching thermodynamics to students at the University of Pittsburgh. The details of this ap proach have been described elsewhere [3,4] and accordingly only the salient features will be intro duced here. Three hundred and thirty nine 35 mm slides were developed. The slides were prepared by using pressure sensitive black letters and symbols (Tac type) on white cards. These cards include the necessary definitions, postulates, laws, equations and a limited number of applications of the sub ject matter. These individual cards were then superimposed on colorful backgrounds and colored slides were prepared from this combination. The backgrounds include popart posters, colorful wrapping papers and examples of contemporary modern art. Figs. 1 and 2 present black and white versions of two of the slides used in the thermo Copyright ChE Division, ASEE, 1983 SUMMER 1983 dynamics course. Each of the cards used to prepare slides was photographed and made into an ActiveInvolve ment book [5] for classroom use. Additional space is provided on each page in this book for student note taking. In use, the student can add relevant material introduced by the lecturer directly in his or her ActiveInvolvement book as the slides are being shown. It has been my experience that I communicate more information that serves to tie the slides together and elaborate their meaning with my continued use of them. Now I must admit that when I first developed my slides and their companion, the ActiveInvolve ment book, I thought that I would see immediate, significant improvement in the ability of my stu dents to do problems in thermodynamics. After all, hadn't these materials provided the motivation namics problems; they must recognize that they have to learn how to solve them also. Before turn ing to a discussion of my recent experiences con cerning my materials, I feel it appropriate to spend time discussing educational objectives as I feel they are an important element in self study examples. Mager [7] was an early advocate of the use of instructional (educational) objectives. Ac cording to Mager, a properly written instructional objective must: 1. Describe what the learner will be doing when demon strating that he has satisfied the objective; 2. Describe the important conditions under which the learner will demonstrate his competence; 3. Indicate how the learner will be evaluated, or what constitutes acceptable performance. The book by Mager [7] and a paper by Stice [8] provide a good discussion on the preparation of in The objective of my teaching can now be introducedI seek ways of maximizing the learning of a given subject matter by providing conditions which are motivational for my students. To be more specific, this paper will discuss methods used in teaching thermodynamics... necessary to greatly enhance student learning? For some students the answer was yes, but, un fortunately, for most the answer was no. I began to see that the slides presented the theory but the students needed additional help in applying the theory to solve problems. If I wanted the students to demonstrate problemsolving skills I had to pro vide them with lots of practice of those skills and/or lots of examples of solved problems. The book by Abbott and Van Ness [6] in Schaum's Out line series was not available so I elected to prepare materials of my own. I generated a series of self study examples that serve as a major input for student learning outside the classroom. These self study examples now number in excess of 100, with examples both in the "British" system and SI sys tem of units. The examples are of two types: 1. Those having a problem statement followed by a list ing of the educational objectives which are appropri ate for the solution of the problem followed by a detailed solution to the problem; 2. Ones similar to those described above but which leave some of the steps of the solution up to the individual student to complete. The later category is necessary. Without it, too many students just sit back and do not "dig" hard enough with those self study examples that are solved completely. It is not enough for them to recognize that I know how to solve thermody structional objectives. Two aspects concerning the use of instructional objectives discussed in Stice's paper deserve our attention. First, several objec tions to the use of instructional objectives are raised and shown to be without merit. Second, Stice comments on the fact that others are too rigid in their choice of words used to write acceptable objectives. In particular, Walbesser et al [9] sug gests that only the following nine action verbs are to be employed: to name, identify, describe, con struct, distinguish, demonstrate, order, state a rule, and apply a rule. Stice suggests that words like "derive", "explain", "calculate", and "esti mate" are sufficiently unambiguous to be added to the above set. I, too, find these words convenient and well understood when used to prepare objec tives for students. Certainly just which words can be considered to be acceptable will depend upon the subject matter of concern. Objectives 1, 2, and 3 shown below are specific examples of educational objectives used in my course. Example 1. The student must be able to utilize the relationship h u + pv to convert the specific internal energy into the spe cific enthalpy and viceversa. CHEMICAL ENGINEERING EDUCATION FIGURE 2. Example 2. The student must utilize the fact that two inde pendent intensive properties are sufficient to set the intensive state of a simple comprehensive fluid. Example 3. Given a table of thermodynamic properties of a fluid, a steam table for example, the student must be able to correctly locate a given equilibrium state once the conditions described in Example 2 have been met. I am convinced of the merit of using educa tional objectives and encourage you to prepare them for your students. I have found, however, that students are largely unfamiliar with them and some class time must be devoted to explaining their importance and their use. Now we get to the "bottom line"do my ma terials work? I think they do and I base this judge ment on two sources of information: My own experiences in testing students with and with out the materials. Student reactions described in course evaluations. While both of these sources are subjective, I feel that they do provide evidence of an enhanced learning experience for my students. Students do demonstrate considerably more organization in the solution of thermodynamics problems. Their ap proach is more direct and largely avoids many of the errors in applying the basic principles of the subject matter. I feel that the self study examples are largely responsible for this. What are the students' reactions? The follow ing is a summary of student response gathered from an anonymous survey taken near the end of the course. The instructor was considered an interesting and dedi cated teacher who cared about his students. The course was well structured and the instructor used new teach ing techniques successfully. The work book (Active Involvement book) was excellent. The following represents individual student com ments. I came into this course with apprehension. I was told that thermo was the hardest and dullest course of all the engineering courses I was ever to take. However, Dr. Brainard has made this the most interesting as well as informative course I have ever taken. His zeal for the subject is extremely apparent and he communicates this well to the class. It is encouraging to see someone take as much time in preparing a course as Dr. Brainard has. Dr. Brainard is unbelievably dedicated and concerned about the student. His self study examples are very helpful. I feel these comments speak for themselves. Will my material work as successfully for others? I don't know. I have found that faculty tend to develop an inertial effect in their teaching methods. (I am no doubt guilty of this also.) Cer tainly individual faculty members will and should develop their own style and that style must be one that they believe in and are comfortable with. E BIBLIOGRAPHY 1. Bloom, B. S., "Testing Cognitive Ability and Achieve ment" in Handbook of Research on Teaching, ed. by N. L. Gage, Rand McNally & Co., Chicago, 386 (1968). 2. Anon., Kaiser Aluminum News, 26, No. 2, 3 (1968). 3. Brainard, A. J., and H. T. Cullinan, Jr., "New Instruc tional Media for Teaching Large Classes," Engineering Education, 62, No. 8, 930 (May, 1972). 4. Brainard, A. J., "Preparing Effective Slides for Class room Use," Engineering Education, 66, No. 5, 412414 (1976). 5. Brainard, A. J., A Course In Thermodynamics, Mono Book Corp., Baltimore, Maryland (1970). 6. Abbott, M. M., and H. C. Van Ness, Thermodynamics, Schaum's Outline Series, McGraw Hill Book Co., New York, NY (1972). 7. Mager, R. F., Preparing Instructional Objectives, Fearon Publishers, Belmont, California (1962). 8. Stice, J., "A First Step Toward Improved Teaching," Engineering Education, 66, No. 5, 394398 (1976). 9. Walbesser, H. H., E. B. Kurtz, L. D. Goss, and R. M. Robl, Constructing Instruction Based on Behavioral Ob jectives, Engineering Publications, Oklahoma State University, (1971), p. 14. SUMMER 1983 AN INTEGRATED APPROACH THOMAS E. DAUBERT Pennsylvania State University University Park, PA 16802 SINCE 1972 THE CHEMICAL Engineering Depart ment at Penn State has attempted to eliminate compartmentalization of basic course material by providing a presentation which attempts to show students the relationships between the various parts of the sophomore and junior level required courses. Thermodynamics has been the integrating factor in many respects. In brief the following in tegration has taken place. The first law of thermodynamics is combined with the material balance and industrial chemical processes as has been the case at most universities for many years. After this point, the study of the second law and its applications is carried out con currently with the study of fluid mechanics and heat transfer such that some of the applications can be seen immediately. Phase equilibria is studied in the same course with mass transfer, while chemical equilibria is covered in the basic course in chemical kinetics and reactor design. Table 1 notes a brief outline of the material in these courses. As Penn State moves to a semester system in 1983, we intend to continue this ap proach with the exception that the first law will have to be separated from the stoichiometry and coupled with the second law. Thomas E. Daubert, Professor of Chemical Engineering at Pennsyl vania State University, has been at Penn State since 1961. His teaching and research interests are in the area of physical, thermodynamic, and transport properties. In addition to the text described in this paper he has coauthored two other books. TABLE 1 Curriculum Content PRINCIPLES OF CHEMICAL ENGINEERING I, II, III Chemical Process Industries and Stoichiometry First Law of Thermodynamics and Applications Organic and Inorganic Chemical Processes in Brief Material Balances Fluid Mechanics including mass, energy, and momentum balances and compressible flow. Heat Tranfer including basic modes of conduction, con vection, and radiation and design of systems Equations of State Thermodynamic Properties of Real Fluids Entropy and the Second Law of Thermodynamics Rela tions among Properties and Diagrams Engines, Compressors, Refrigeration, Liquefaction Chemical Process Thermodynamics MASS TRANSFER AND PHYSICAL EQUILIBRIA Homogeneous fluid mixture properties: Fugacity and Activity Phase Equilibria and Diagrams Equilibrium Stage Separations: Single and Multiple GasLiquid (Absorption, Distillation) LiquidLiquid (Extraction) FluidSolid (Leachng, Adsorption) Interphase Mass TransferDiffusion Differential Continuous Contacting Equipment Dimensions Simultaneous Heat and Mass Transfer CHEMICAL EQUILIBRIA, KINETICS, AND REACTOR DESIGN Chemical Reaction Equilibria in chemical process sys tems for homogeneous and heterogeneous systems and single and multiple reactions Chemical Kinetics and Equilibriumbasic principles and relationships Chemical Reactors and Systems Homogeneous Reactions in ideal batch, continuous stirred tank, and tubular reactors including design of reactors Introduction to heterogeneous (catalytic) reactions, models, and reactor designs Does such an approach have merit? Our experi ence shows that two of the perennial student im pressions are alleviated, i.e., "Thermodynamics is not relevent to actual situations" and "I've never seen that equation or method before." Whether such a method better promotes a fundamental understanding of thermodynamics in the long run cannot be proven except that feedback indicates Copyright ChE Division, ASEE, 1983 CHEMICAL ENGINEERING EDUCATION the student acceptance of thermodynamics of equilibria are much improved by the inclusion of this material together with mass transfer and kinetics. Following up the integrated approach is a seniorlevel elective in thermodynamics which stresses and reenforces broader applications of the basic principles as well as giving a deeper treat ment of equations of state and more sophisticated calculational methods. Included is the use of both a physical and thermodynamic property data base package and subroutines for solving various equa tions of state for various thermodynamic param eters with main programs supplied by the students. BASIC TEXTBOOK ON THERMODYNAMICS "Introductory Thermodynamics for Chemical Engineers" is a first level textbook which attempts to summarize the aspects of thermodynamics nec essary to formulate, design, operate, and control chemical processes of the 1980's. Continuous ad vancement of thermodynamics has occurred at such an increasingly rapid pace that no textbook can attempt to cover the entire field. The book de veloped is a textbook, not a research monograph, and does not advance new theories; it does attempt to summarize the salient features of current re search which will be helpful in using the thermo dynamic methods which are currently most ac curate and convenient. The book begins with an introductory chapter which provides necessary background and defini tions of common terms and quantities of thermo dynamics. The first major chapter treats equations of state (both analytical and corresponding states approaches) in some detail, emphasizing the meth ods which are now used by industry rather than the historical perspective offered by most texts. This allows immediate use of any equation of state in subsequent chapters on the first and second laws of thermodynamics, phase equilibria, and chemical equilibria. This approach is unusual in that most texts relegate equations of state to a later chapter following the first and second law treatment. The latter treatment requires that all topics must again be considered as only the ideal gas law is available for the first pass. A unique feature of the book is the chapter on estimation of auxiliary physical properties neces sary for thermodynamic calculations. Most equa tions of state and other thermodynamic methods require critical properties and third parameters. Densities, molecular weights, normal boiling ... feedback indicates the student acceptance of thermodynamics of equilibria are much improved by the inclusion of this material together with mass transfer and kinetics. points, and vapor pressures are often also re quired. Treatment of mixtures is quite necessary in processing calculations. Quite often these data are not readily available and sometimes experi mental values do not exist. Thus, drawing on work as coauthor of the Technical Data BookPetro leum Refining for the petroleum industry through the American Petroleum Institute and background for the Data Prediction Manual for the chemical industry through the AIChE Design Institute for Physical Property Data, the author has included in a separate chapter in the text, the most upto date generalized prediction methods for each of these properties. The text is arranged in nine chapters. Treat ments tend to be brief so that students do not get lost in the prose. Line drawings, diagrams, and plots are included throughout. Exercises for the student are liberally located throughout the text following the appropriate subsections. Such ex ercises allow a student to more clearly determine his or her understanding of the material and are valuable for both normal classroom instruction or selfstudy of the material. Lists of problems fol low each chapter and references to topics discussed and bibliographies of the most important current literature, reviews, and compendia are included in each chapter. Appendices listing pure component physical properties of common compounds, selected thermodynamic properties of model compounds, thermodynamic properties of steam, and conver TABLE 2 Skeleton Table of Contents I. Purpose, Usefulness, and Definitions of Thermody namics II. PVT Properties of FluidsEquations of State III. Conservation of EnergyFirst Law of Thermody namics IV. The Second Law of Thermodynamics and its Appli cations V. Relationships Among Thermodynamic Properties Graphical Representation of Properties and Pro cesses VI. Estimation of Auxiliary Physical Properties of Mixtures VII. Solution Properties and Physical Equilibria VIII. Physical Equilibria Among Phases IX. Chemical Equilibria SUMMER 1983 sions among different systems of units are in cluded. Table 2 gives as skeleton table of contents including only chapter titles. A complete table of contents is available from the author. The text is designed for a first course in chem ical engineering theromodynamics at the late sophomore or junior college level. No previous thermodynamic study is required. The goal is a balanced treatment between essential thermody namic principles and the methods actually used in current practice to calculate thermodynamic prop erties and to use modern equations of state. THOUGHTS My philosophy is clear. Beginning chemical en gineering thermodynamics should be vital, upto date, and presented in as simple a form as prac ticable to solve problems of industrial importance, while not compromising the underlying principles. Since thermodynamics pervades almost all areas of practice and many students never receive any additional formal study in the field, it is incum bent upon professors to make certain that the beginning courses in the field provide the back ground for students to function as working chem ical engineers. The mode of presentation of the material is variable; it may be integrated with other subjects or presented by itself, or may be offered tradition ally by lecturerecitation or with modern teaching aids or selfstudy. The most important feature, however, is the content, assuring that our students can effectively practice their profession. O THERMODYNAMICS WITH DESIGN PROBLEMS E. V. CILENTO AND J. T. SEARSt West Virginia University Morgantown, WV 26506 THERMODYNAMICS IS AN abstract subject, which students have more difficulty in relating to their more concrete career objectives than studies in subjects like unit operations. As most students will utilize thermodynamics in the future in a support ing calculation mode, it was thought desirable to emphasize the important connection of thermo dynamics to design concepts in a direct way. Thus the general goals of thermodynamics course work can be stated such that at the conclusion of their studies the students should learn the important fundamental concepts of thermo dynamics, and be able to utilize the concepts of engineering calcula tion problems (including design). Time was made available in the course for both goals. FUNDAMENTALS The first goal was covered through standard lectures, using overheads etc., with the accompany ing text written by S. I. Sandler, "Chemical and Engineering Thermodynamics." A synopsis of the syllabus covered includes the common concepts: First Law Second Law Real Substances Multicomponent Mixtures Gibbs Free Energy Phase Equilibrium Chemical Equilibrium The text served the course well and has many good features. It has an excellent presentation of FIGURE 1. DESIGN I TO: Design Group FROM: L. Brightman, Director Design Services Goal, Inc. SUBJECT: Recirculating Solids Boiler Concept Please analyze the recirculating solids boiler concept, outlined on the attached sheet, as compared to a conven tional industrialheat boiler. Dr. R. C. Bailie, consultant, will present complete details at a meeting tomorrow. List advantages and disadvantages of this system for use in generating steam from coal, oil or waste from our LP7 plants. The results of your study and recommenda tions will serve as a basis to determine if further develop ment work is justified. Include in your analysis the net steam efficiency as a function of fuel feed, the efficiency potential for electrical production of the steam as a function of fuel load, and operational characteristics as a function of fuel capacity. Your report is due five (5) weeks from Thursday, on December 5th. SPresently at Montana State University Copyright ChE Division, ASEE, 1983 CHEMICAL ENGINEERING EDUCATION phase and chemical equilibrium. It has a new ap proach to the development of the second law by using a pseudoconservation equation, in parallel to the energy balance for the first law. This perhaps causes the instructor some difficulty, but less to the student. As with many instructors, we desire more example and illustrative problems. DESIGN Throughout their school years, most students have learned to examine a problem by searching for the appropriate equation(s) needed to solve the problem. Conceptualizing the control volume and stating reference conditions, are new modes of problem solving. The students are often con fused by errors such as thinking all liquids are saturated liquids, not understanding the meaning of a sign on an answer, or misinterpreting the steps of a flow process on a pH diagram. To help alleviate these types of errors, to inter relate thermodynamics with other engineering course material, and to motivate the students, we try to integrate basic concepts with a design prob lem. Often the problem may be multifaceted and the same design may be studied from a different point of view in a companion course. Designs we have used have focused on chemical equilibrium limits in reactors, physical properties of materials for portable heat paks, calculation of ionic acitiv ity coefficients for solubility limits, and process efficiencies. . , . Eugene V. Cilento is an Assistant Professor at West Virginia Uni versity. He did his undergraduate work at Pratt Institute, receiving his BChE in 1973. His graduate studies were performed at the University of Cincinnati, where he received his M.S. in 1976 and PhD in 1978. His research interests are in biomedical engineering and include projects in biological transport phenomena using whole organ per fusions and in vivo microscopy. (L) John Sears, Professor and Head of Chemical Engineering at Montana State University, has been active in educational innovation for over a decade. He helped organize the PRIDE program at West Virginia Uni versity upon which this paper is based. (R) .. we try to integrate basic concepts with a design problem. Often the problem may be multifaceted and the same design may be studied from a different point of view in a companion course. lIn NOIJSniw03 V IYAO5Ha 1V3H *u 3 SB a nd s'L ~ OPERATION: AirConstant FuelVariable BedB1Modal Size Distribution Large Particles for Large Uif Small Particles for Elutriation and Sensible Heat Transfer Combustion without Internals Disturbance CycloneReturn Small Particles to Bed Heat RemovalSteam Generation hair/entrained particles >1 hair FIGURE 2 Schematic: Recirculating Solids Boiler Figs. 1 and 2 illustrate a recirculating solids boiler design concept we analyzed three years ago. This project was analyzed by the students in con junction with a unit operations course. The stu dents were broken into small groups to analyze and discuss the advantages or demerits of a re circulating waste boiler as compared to a conven tional fluidized bed boiler. Discussion of the fluid flow through a packed/fluidized bed, cyclone, and heat transfer could be emphasized by the unit SUMMER 1983 operations course. Process efficiency and Rankine cycle efficiency as a function of turndown ratio can be discussed from a thermodynamic viewpoint. The advantages of a 6:1 turndown ratio with good operability, lack of heatexchange tube burnout and reduced startup can be discussed in terms of process efficiency. The problem is openended, lim ited by student time and knowledge. The project was extremely wellreceived by the students, who became very interested in the design. ADVANTAGESDISADVANTAGES Major advantages of the integrated design in clude student motivationmaking the subject more con crete, rather than an abstract subject emphasis on interrelation of variables (such as ef ficiency) with process design operability concepts reinforcement of particular thermodynamic concepts by use in the design analysis. An ultimate test is whether the students feel more comfortable and able using thermodynamics in subsequent work. In one case of design problem subsequently on separations, the students used DebyeHuckel theory to calculate mixedsalt ionic activity coefficients to find solubility limits in a crystallization problem. Disadvantages are mostly time commitments. Design takes class time, and the philosophical de cision on such time must be made as to the worth of design integration at that point in a curriculum. If the design is done in conjunction with a second course, then some planning and integration be tween faculty instructors is necessary. If an indi vidual instructor decides to add this design ele ment to his course independently, then a full un derstanding should be present that this component replaces some more details on particular topics. We are convinced that this approach is a worth while concept. O COMPUTERGENERATED PHASE DIAGRAMS FOR BINARY MIXTURES KENNETH R. JOLLS,1 JOHN BURNET, AND JEFFREY T. HASEMAN2 Iowa State University Ames, IA 50011 PREVIOUS PUBLICATIONS [1,2,3,4,5] have described programs that generate projections of thermo dynamic phase surfaces through computer graph ics. Using these techniques, we have produced diagrams representing the properties of water and steam and the pressurevolumetemperature be havior of most of the common equations of state. These programs have been used successfully with a variety of output devices, such as CalComp and Versatec plotters, Tektronix storage terminals, and an Evans and Sutherland MultiPicture Sys tem. In addition to making possible phase dia grams that have previously been unattainable, our programs also offer several options that enable the user to emphasize thermodynamic features of spe cial interest. 0On leave 198182 at the University of California at Berkeley. 2Currently with Eli Lilly and Company, Lafay ette, Indiana. ATIDN OF STATE "GA .Bb ETHYLENE 'ErS V Cr T C. +" ~"."" " (RT A T/T 2) R Tb . S.  .2 pla T s0 9.6 wR I CopyTight, ChE Di vilo, A 198 4 T '^    NEAR S0EAL IN PRESSURE AID VOL2R1 I .. IL I ' : '_ '._I. . . FIGURE 1. BenedictWebbRubin equation of state for ethylene. Fig. 1 presents a PVT diagram drawn with this technique. The surface is generated by the BenedictWebbRubin equation as applied to ethy lene. A twophase region consistent with that equa Copyright ChE Division. ASEE, 1983 CHEMICAL ENGINEERING EDUCATION tion has been superimposed on the surface through use of an algorithm due to Balzhiser et al [6]. The principal use for these diagrams has been in teaching. Thermodynamics, because of its level of abstraction, has gained a longstanding unpopu larity among students. Even the best teaching ef forts have often been ineffective because of the gap in understanding between instructor and stu dent. The reason for this has often been that words, symbols, and equations have not been ade quate to present abstract ideas to students with any assurance of their being grasped. Something more tangible has been needed to catalyze compre hension until more of the subtleties of thermody namics are understood and the enormous value of the subject appreciated. Phase diagrams offer a vehicle for doing this. By utilizing the geometrical interpretation of property relationships, they provide a more con crete model of physical behavior than do the theoretical statements from which they are de rived. While the experienced thermodynamicist sees instinctively how properties influence pro cessesinversion in a JouleThomson expansion, for examplestudents may not understand this and may require more explanation. On a model of the enthalpypressuretemperature surface, the JouleThomson inversion curve stands out as a distinct topographic feature. If presented with such a model, students will see this and expect a system to behave differently on opposite sides of the curve as experiments show. Kenneth Jolls earned his BSChE at North Carolina State University and his graduate degrees at the University of Illinois, where he worked for T. J. Hanratty. After five years at the Polytechnic Institute of Brooklyn, he moved to Iowa State University where he is pres ently on the faculty. His chemical engineering interests are in thermo dynamics and applied electronics, and he has held several NSF grants related to teaching improvements in both areas. The last of these are supporting his current sabbatical year at Berkeley. Outside of engineering, Dr. Jolls has a strong interest in music. He has a degree in music from Duke University and is a regularly performing jazz player. (L) John Burnet studied computer science at Iowa State University and obtained experience there in applications programming related to thermodynamic property diagrams. He is currently a freelance pro grammer in Berkeley, CA, and continues to develop graphics software Phase diagrams... provide a more concrete model of physical behavior than do the theoretical statements from which they are derived. If problems with conceptualization exist in pure systems, they are even more prevalent in mixtures. Since the properties of multicomponent systems depend on more than two independent variables, complete phase diagrams in such cases are beyond construction through conventional graphics. One or more variables must be elimi nated and our attention restricted to subsets of the data possessing threedimensional character. The loci of saturatedliquid and saturated vapor states in a system of two components com prise such subsets. These surfaces (called bubble point and dewpoint) may be plotted in pressure temperaturecomposition (PTx,y) space to give an envelope portraying all states that coexist in liquidvapor equilibrium. Such information is im portant in separation processes and also reveals the macroscopic behavior resulting from a given solution model. Some notable attempts have been made to con struct these figures by hand [7,8], but only a small number are available, and even these are often limited in detail. Even through computer graphics, solution diagrams require more effort than those for pure components. In the latter case the gen erating equations are straightforward, and we are for use in teaching. (C) Jeffrey T. Haseman is a process engineer at the Tippecanoe Labora tories of Eli Lilly and Company in Lafayette, IN. For the past year he has been associated with antibiotic synthesis and production. He graduated from Carthage College in Kenosha, WI, with a BA in chem istry and is currently completing the thesis requirements for his MS in chemical engineering from Iowa State University. (R) SUMMER 1983 able to compute and plot simultaneously. Con structing PTx,y diagrams, however, requires far more effort, both for the acquisition and for the management of data. Determining the gamut of vaporliquid equilibrium states for any binary sys tem would be too costly, and some type of com promise is necessary. THERMODYNAMIC DATA BASE For the work reported here, the program of M. S. Han and K. E. Starling [9] was used as a data base for mixtures. This program is based on the modification of the BWR equation described by Cox et al [10]. Extension to mixtureproperty prediction is through mixing rules analogous to those developed by Bishnoi and Robinson [11] and by means of a generalized correlation of the prop erties of pure fluids [12]. Predictions of density and enthalpy departure with this program com pare favorably with experimental data, and vapor pressures are also accurately determined. An interaction parameter k1j accounts for devi ations from ideal solution behavior for each pair of components accessible to this program. Since kij strongly influences vaporliquid equilibrium cal culations, its values are based on VLE data. Ref erence [13] presents a tabulation of k, values along with phaseequilibrium predictions that justify their use in this method. As obtained from the authors, the HanStarling (HS) program operated in batch mode and pro duced output summarizing the properties of a pure component or mixture either in a specified state or in a final state resulting from a specified process. For this project, the HS routines were fixed within an executive program that directed computation along paths of constant temperature, pressure, and composition in the bubble and dew point surfaces. A bicubic spline program deter mined a "best surface" through the true points, and the projections of the smoothed isotherms, isobars, and isopleths were produced in the same manner as for the purecomponent diagrams [14]. DETAILS OF CONSTRUCTION Fig. 2 shows the PTx,y diagram for the sys tem normal butanenormal heptane. Four complete isothermal sections and four complete isobaric sections are drawn. Tie lines which mark the inter sections between isobars and isotherms have been added by hand to connect coexisting liquid and vapor states. The initial estimates required by the TIE LINES ARE DOTTED FIGURE 2. PTx,y diagram for heptane. normal butanenormal COMPUTER GENERATED HS subprograms that perform bubblepoint and dewpoint calculations were derived geometrically. Computational difficulties with the Han Starling program prevented us from obtaining convergence in the vicinity of the critical locus. It was, therefore, not possible to construct the pre cise critical curves that match the PTx,y dia grams shown in this paper. The dashed curves that are shown were obtained by using the method of Prausnitz and Chueh [15], first to estimate critical temperatures and volumes, and then to compute the critical pressures from a modified Redlich Kwong equation. Construction of isotherms and isobars between the purecomponent critical was begun in the usual way, but when a composition was reached where convergence could no longer be obtained, the section was left open at that point. The final step in each drawing involved the construction of dewpoint and bubblepoint iso pleths. Data for these curves were accumulated in earlier steps, then arranged into bubblepoint and dewpoint arrays, and finally fitted to smooth iso pleths using a 2D spline. CHEMICAL ENGINEERING EDUCATION s s o ..2 .0 1 E FIGURE 3. PTx,y diagram predicted by Raoult's Law. Vaporpressure curves are for nC4 and nC,. PTx, 4 DIAGRAMS CO2 CRIICL POINT FIGURE 4. PTx,y diagram for COzethane. These procedures yielded a wireframe model of the bubble and dewpoint surfaces with border regions and tic marks added for completeness. Embellishments beyond the basic structure have been added by hand to give the result shown in Fig. 2. COMPARISON WITH OTHER PTx,y DIAGRAMS Because of their chemical similarity, butane and heptane form nearly ideal solutions which, at low pressures, conform closely to the model pre dicted by Raoult's law. This is illustrated by com parison to Fig. 3 where the PTx,y diagram pre dicted by Raoult's law has been constructed for a mixture of pure components with vaporpressure curves identical to butane and heptane.* Having no critical region, Fig. 3 has been left open at the top with unterminated isopleths to signify con tinuing ideality. The surfaces in Fig. 2 do develop a negative deviation at higher pressures as shown by the bubblepoint isotherm at 2900 F. More pronounced nonideality is seen in Fig. 4 where, for the carbon dioxideethane system, the HanStarling program predicts a minimumboiling azeotrope over the entire range for which constant property sections were determined. This is in good agreement with data reported by Gugnoni et al [16] and by Khazanova et al [17]. Although Fig. 4 was constructed in the same manner as the diagrams representing nonazeotropic systems, computa tional procedures were sufficiently different to necessitate a separate version of the program. GRAPHICAL OPTIONS Constructing phase diagrams through com puter graphics gives one control over various artistic effects. These effects can often enhance a diagram and emphasize topographic features of thermodynamic interest. Nonlinear scaling and automatic smoothing are examples of this and were both used in the construction of Fig. 1. Vari able orientation, adjustable perspective, variable line structure, and the drawing of superimposed views and stereo pairs are further options. Controlling the degree of perspective in the . drawings gives a depth effect to the threedimen sional figures. While this is desirable in a pictorial view, it would not be so in the side or top view one *Fig. 3 was drawn with a Versatec electrostatic plotter and uses heavier lines for bubblepoint curves than for dew point curves. SUMMER 1983   ~v In' I A 52 = .N F 1 I P, z 396.H K r S  flII O 1 s1 F i p1    if FIGURE 5. Pressurecomposition projection of Fig. 2. obtains by setting the orientation angles at 0, 90, etc. As an example of this, Fig. 5 shows the "flat" view of the butaneheptane diagram that com ii CHEMICAL ENGINEERING EDUCATION FOLE FrACTION ETHANFo FIGURE 6. Temperaturecomposition projection of Fig. 4. prises the pressurecomposition plot. Similarly, Fig. 6 shows the Tx,y projection for the CO2 ethane system. CLOSURE Modern computer graphics provides the means for constructing thermodynamic phase diagrams in number and variety never before possible. Individually or in groups, these diagrams have the ability to convey information about properties and processes that would otherwise require tedious and often confusingexplanation. The dia grams described in this paper, or any of their variants, can be compressed, expanded, molded, or altered in any way that makes thermodynamic subtleties easier for students to understand. Coupled with an approach that attempts to explain physical property behavior in terms of funda mental concepts, phase diagrams can complete the picture the teacher wishes to draw. Such ideas were not overlooked by Gibbs [18] as he began his first paper on graphical methods in 1873: Although geometrical representations of propositions in the thermodynamics of fluids are in general use, and have done good service in disseminating clear notions in this science, yet they have by no means received the extension in respect to variety and generality of which they are capable. ACKNOWLEDGMENTS Major support for this work was provided by the Iowa State University Engineering Research Institute and by the Local Course Improvement Program of the National Science Foundation. [ REFERENCES 1. Jolls, K. R., G. P. Willers, and L. D. Jensen, Trans. Am. Soc. Eng. Educ., Comput. Educ. Div., 8, 10 (1976). 2. Jolls, K. R., G. P. Willers, and L. D. Jensen, Educom, 12(4), 19 (1977). 3. Jolls, K. R. and G. P. Willers, Cryogenics, 18, 329 (1978). 4. Willers, G. P., "The Construction of Thermodynamic Phase Diagrams Through Computer Graphics," M.S. thesis, Department of Chemical Engineering, Iowa State University, Ames (1978). 5. Jolls, K. R., "Research as an Influence on Teaching," accepted for publication in J. Chem. Educ. (1983). 6. Balzhiser, R. E., M. R. Samuels, and J. D. Eliassen, "Chemical Engineering Thermodynamics: The Study of Energy, Entropy and Equilibrium," PrenticeHall, Inc., Englewood Cliffs, N.J. (1972). 7. Dickerson, Richard E., "Molecular Thermodynamics," W. A. Benjamin, Inc., Menlo Park (1969). 8. Wales, C. E., Chem. Eng. (1963), May 27, p. 120; 3lu June 24, p. 111; July 22, p. 141; Aug. 19, p. 167; and Sept. 16, p. 187. 9. Starling, K. E., "Fluid Thermodynamic Properties for Light Petroleum Systems," Gulf Publishing Co., Houston (1978). 10. Cox, K. W., J. L. Bono, Y. C. Kwok, and K. E. Star ling, Ind. Eng. Chem. Fundam., 10(2), 245 (1971). 11. Bishnoi, P. R. and D. B. Robinson, Can. J. Chem. Eng., 50, February, p. 101 (1972). 12. Starling, K. E. and M. S. Han, Hydrocarbon Process., 51(5),129 (1972). 13. Starling, K. E. and M. S. Han, Hydrocarbon Process., 51(6), 107 (1972). 14. Jolls, K. R., and W. C. Dowling, "ComputerGenerated Phase Diagrams for Use in Teaching Thermodynam ics," final report, Local Course Improvement Program, National Science Foundation (Grant SER 7800298), ISUERIAmes 81246, 1981. 15. Chueh, P. L. and J. M. Prausnitz, AIChE J., 13, 1107 (1967). 16. Gugnoni, R. J., J. W. Eldridge, V. C. Okay, and T. J. Lee, AIChE J., 20(2), 357 (1974). 17. Khazanova, N. E. and L. A. Lesnevskaya, "Phase and Volume Relations in the System EthaneCarbon Di oxide," Russ. J. Phys. Chem., 41, 1279 (1967). 18. Gibbs, J. W., Trans. Conn. Acad., II 309 (1873). SUPPLEMENTAL TV TAPED PROBLEMS ROBERT G. SQUIRES AND DAVID V. FRANK Purdue University West Lafayette, IN 47907 TOPIC SARGE INCREASES IN engineering enrollments in recent years have caused instructional prob lems in many departments. For example, since 1974 chemical engineering enrollment at Purdue has increased from 243 to 558 while the faculty has gone from 19 to 21. This has resulted in an increase in class sizethe fall chemical engineer ing thermodynamics (Ch 311) enrollment has in creased from 50 to 135. This class size increase presents particular instructional difficulties in a problemoriented engineering course such as ChE 311. The purpose of this project was to develop a series of sample TV taped chemical engineering problems which could be used by the student, out side of class at his or her own pace, to supplement the course material. COURSE DESCRIPTION ChE 311 is a semester course with 45 classes of fifty minutes each. The 15 week course is divided into five major sections (see Table 1). In order to rapidly introduce the first and second law in the beginning of the course, we use steam as the work ing fluid in the first two sections of the course. In section three, additional first and second law prob The purpose of this project was to develop a series of sample TV taped chemical engineering problems which could be used by the student, outside of class at his or her own pace, to supplement the course material. Copyright ChE Division, ASEE. 1983 TABLE 1 Course Outline NO. OF NO. OF COPIES TAPES IN LIBRARY First Law First & Second Law Equations of State Phase Equilibrium Chemical Equilibrium lems are presented using other equations of state including the generalized charts, other tabular and analytical expressions. The last two sections cover applications of interest to chemical engineers phase and chemical equilibrium. The lecture material for each topic area is covered in lectures at the beginning of the section. In the remaining periods, a series of practical problems of increasing complexity are discussed. The problems are presented in three parallel methods: Discussed by the professor and students in class A photocopied solution handed out to each student A video taped discussion of supplemental problems are on file in the library and available at the student's request. At the end of each section, all students simul taneously take a common exam. This method has the following advantages: The better students may work ahead at their own pace, checking out the video taped problem solution from the library. They need not attend classes in which material they already understand is being dis cussed. Inasmuch as these students do not attend the problem discussion classes, the class size is reduced and more individual attention can be given to the remaining students. Students attending class but still having difficulty SUMMER 1983 with the material may also check out the video taped problem solutions. In their case, the video tapes would be used not to work ahead, but to reinforce the dis cussion of similar problems. They could, in effect, repeat the problem discussion, via video tape, as often as they wish. By thus spending extra time, they could also slow down their pace through each section. Since all students are required to take the same exam at the end of each section, the procrastination prob lem so often present in selfpaced courses would not occur. All students would be required to be at the same point five times during the semesterat each exam. TV TAPED SUPPLEMENTAL PROBLEMS The thermodynamics videotapes were prepared during a 16month period from September 1980 to December 1981. The twenty videotapes are divided into five groups, as shown in Table 1. Each tape discusses the solution to a problem similar to the homework problems. As each new topic is begun, students are given typed problem statements for that topic. The solutions are available on the video tapes only. Table 2 shows the topic of each prob lem. Each taped problem is approximately twenty minutes long. The tapes were prepared in a Purdue TV studio using two color TV cameras; one an overhead showing the material being written on a pad by the lecturer, and the other facing the lec Robert G. Squires is a Professor of Chemical Engineering at Purdue University. His Bachelor's degree is from Rensselaer and his Master's and Doctorate from U. of Michigan. He has received the Amoco Foundation Outstanding Teaching Award and the Western Electric Fund Award for Excellence in Engineering Instruction. He is past chairman of the I&EC Division of ACS and was the 1982 Program Chairman for the Chemical Engineering Division of ASEE. In his spare time he is a jogger, a pilot and a skier. David V. Frank is currently a graduate student in chemical educa tion at Purdue University. He received his BA degree from Macalester College in 1976 and his MS degree from Purdue in 1980. His doctoral research will be conducted in the area of problem solving in chemistry. COURSE SECTION 1. First Law 2. First Law 3. First Law 4. 1st & 2nd Law 5. 1st & 2nd Law 6. 1st & 2nd Law 7. Equation of State 8. Equation of State 9. Equation of State 10. Equation of State 11. Phase Equilibrium 12. Phase Equilibrium 13. Phase Equilibrium 14. Phase Equilibrium 15. Phase Equilibrium 16. Chemical Equilibrium 17. Chemical Equilibrium 18. Chemical Equilibrium 19. Chemical Equilibrium 20. Chemical Equilibrium turer to give a more ments. TOPIC Pressure Cooker Throttling Calorimeter Triple Point Inventor's Process Actual vs Ideal Compressor Reversible Isothermal Process Trial & Error Throttling Process Throttling Process Diesel Compression Diesel Compression Data vs Nomograph vs Raoult's Law Dew and Bubble Point Flash Calculation Activity Coefficient GibbsDuhem Equation Wilson Equation Standard Heat of Reaction vs Actual Q of a Reactor NH3 Formation, Effect of T, P, Composition Multiple Reactions Multiple Reactions with Liquid Condensing Multiple Reactions with Solid Phase Reactant and Product personal touch to his com A preliminary practice tape was first made and reviewed by a panel of undergraduate students. The changes suggested by the panel were incorpo rated into the final tape. The tapes are kept in the engineering library and may be checked out for viewing at the stu dent's convenience. It should be pointed out that the TV problems are extra problems not required of the students, not turned in, and not discussed in class. They are, therefore, used as supplemental material strictly for the student's benefit. Sufficient copies of each tape are kept in the library so that students did not queue (see Table 1). EVALUATION OF EFFECTIVENESS The tapes were first made available to students during the spring and fall semesters of 1981. We were interested in the answers to the following three questions: 1. Will implementation of the tapes result in an increase in the students' test perform ance? 2. How often will students use the tapes? CHEMICAL ENGINEERING EDUCATION TABLE 2 Supplemental TV Taped Problems 3. What are the students' perceptions of the quality of the tapes? An experimental design was employed to answer the first question. The students were ran domly assigned to two groups. Group I was allowed to use the tapes for only the first and third topics and Group II was allowed to use the tapes during the second and fourth topics. (The fifth set of tapes had not yet been made.) The exam scores for both groups were compared following each test to see if normal use of the tapes had a significant effect on the student's achievement. There were 39 students in both groups who took all four exams. Each exam consisted of two or three problems. The average test score of a student throughout the semester was 75.6 when he was using the video tapes and 74.4 when he did not have access to the tapes. However, a ttest shows that the difference between these two numbers is not significant. A survey was made of the spring '81 ChE 311 class. There were 84 students in the class and 63 responded to the anonymous questionnaire. At the time of the questionnaire 19 tapes were in use. A summary shows that 43% of the responders saw all 19 tapes, 81% saw more than 11 tapes, and 10% saw no tapes. Comments from the questionnaire indicated that most students believe that using the tapes en abled them to learn the material more quickly. Many students viewed the tapes more than once. Typically they might view a tape once when the material was first discussed, and then view the same tape as a review just before the exam. CONCLUSIONS The fact that no significant improvement in test performance attributable to the tapes was ob served is not surprising. The tapes are but a small part of the course and similar problems are re quired of all students. We were encouraged that many students indicated that the tapes allowed them to understand the material more quickly. That 43% of the class saw all of the tapes and 81% saw more than half of the tapes is our best indication that the students believed the tapes were worthwhile. (Remember that the tapes were not required and were not discussed in class.) At twenty minutes per tape, this level of viewing rep resents a significant amount of voluntarily com mitted time. We conclude that the tapes are a use ful addition to the course and we plan to continue their use. If any other professors would like to use any or all of these tapes, copies can be obtained from Prof. Squires. ACKNOWLEGMENTS We would like to thank the National Science Foundation (Local Course Improvement Grant) and Purdue's Schools of Engineering for their financial support; Purdue's TV studio personnel (in particular Robert C. Sanders and Richard D. Light) for their help; Prof. John Lindenlaub of Purdue's Center for Instructional Development in Engineering for many constructive suggestions; and the many undergraduate students who served on reviewing panels or who participated in class during the development of these tapes. O THE FUNDAMENTAL PROPERTY RELATION* THE FUNDAMENTAL PROPERTY RELATION* JOSEPH J. MARTIN* University of Michigan Ann Arbor, MI 48109 SUPPOSE ONE WERE TO try to describe the field of thermodynamics in as simple a manner as pos sible. It is likely he would start with the concise definition that thermodynamics is the science of energy as displayed in all of its forms, transfers, and transformations. He would probably then *This paper was presented at the symposium prior to Professor Martins death on Dec. 13, 1982 (see CEE Vol. XVII, No. 2, pg. 73 for Memoriam). invoke the famous "three laws" that are the result of observation and some intuition, and discuss how these lead to the field which is agreed to be the one in question, as judged from a study of the multitude of books that have been written on the subject. An alternative approach would be to assume from prior knowledge the four basic equations of thermodynamics, thereby utilizing from the very start the powerful shorthand language of mathe matics. This would be followed by an interpreta tion and explanation of each basic equation. Copyright ChE Division, ASEE, 1983 SUMMER 1983 r I Following the latter approach, the first and most used basic equation is the fundamental prop erty relation, dU = T dS P dV + idmi (1) i (See Nomenclature for definition of all symbols.) The second and more easily understood equation is the energy balance, 2 mu d(U + u + mgz) 2 2 sys 2 6Q 6W + J (H + + gz) 6m = dEsys (2) The third equation is a little more sophisticated and is known as the entropy balance, dss = i ( + 6LW+ Sj6m (3) Sys i i 0 j J " while the fourth equation is the simplest of all and is the mass balance*, dm = 6m (4) sys j It is the objective in this discourse to focus attention primarily on the fundamental property relation because of its great utility in problems of thermodynamic properties and physical and chem ical equilibrium. As it stands in its simplest form, *The Einstein relation, m = E/c2 implies a transfer of mass associated with work and heat; however, except in nuclear reactions, the mass equivalent of energy is so minute due to the vast magnitude of the velocity of light that separate energy and mass balances are satisfactory. An alternative approach would be to assume from prior knowledge the four basic equations of thermodynamics, thereby utilizing from the very start the powerful shorthand language of mathematics. Eq. (1) considers only thermal, compression, and mass change effects in any finite collection of mat ter or substance whose temperature, pressure, and chemical potentials are uniform throughout. Es sentially, Eq. (1) says that thermodynamic prop erties of matter are not independent; that they are interrelated and locked together by a differential relationship such that if any property is changed, at least one other property must change to pre serve the equality of the equation. The generalization of Eq. (1) to include effects other than thermal, compression, and mass change has caused considerable confusion and difficulty, even though all writers agree on the implications of Eq. (1) in its simplest form. To understand the source of confusion, let us examine first the treat ment of the gravitational effect in the pioneering work of Lewis and Randall as revised by Pitzer and Brewer [4]. They state without proof that the reversible lifting of a weight increases its free energy per molal mass M by an amount, dG = gMdz P,T,... = gM It is interesting to note here they are implying there is a better or greater understanding of a quantity called free energy than there is of just energy. It is not meant that energy is a simple concept, but it is certainly simpler than free energy. Preceding Eq. (6) it is emphasized that al though potential energy and internal energy may be separated, their energycontent function E is to include gravitational energy.* From their defini tion and later discussion the Gibbs free energy is defined as Joseph J. Martin (deceased) was past president of ASEE, of AIChE and of Engineers Joint Council, and professor and acting director of the Institute of Science and Technology at the University of Michigan. He was graduated from Iowa State University (BS), University of Rochester (MS) and CarnegieMellon University (DSc). His main area of interest was thermodynamics. G = E + PV TS *This is the opposite approach from Gibbs [2] who wrote, "The energy of mass will now consist of two parts, one of which depends upon its intrinsic nature and state, and the other upon its position in space." CHEMICAL ENGINEERING EDUCATION Their free energy relation when gravity is not of importance is dG = S dT + V dP + P .dmi (8) i which follows directly from Eq. (1) with G = U + PV TS and the partial free energy Gi identical to the chemical potential pi. Now if any mass m = nM is lifted, Eq. (6) may be written aJ = m or dG = gmdz (9) P,T,.... and this may be added to Eq. (8) to give dG = S dT + V dP + Iidmi + gmdz (10) If Eq. (7) is differentiated and combined with Eq. (10), we get dE = T dS P dV + V P dm. + gmdz (11) i In generalizing on the terms in Eq. (11), they pre sent dE = i X dxi 3. (12) where Xi is an intensive variable or force and xi is its associated variable. A table of Xi's and xi's is given so that one may readily construct the rela tion comparable to Eq. (11) as dE = T dS P dV + P Lidmi + gzdm (13) i It is obvious there is a contradiction between Eq. (11) and Eq. (13) because the former contains gmdz while the latter contains gzdm. Thus, there is an outright error in their treatment of the gravi tational effect. As a second example of difficulty the book by Aston and Fritz [1] is considered. For a reversible process involving a closed system (the authors em phasize this restriction of a closed system) the generalized equation dE = T dS P dV l X.dx. i (14) is given with the Xi's and x,'s being respectively the intensive and extensive variables other than the usual ones associated with thermal and com pression effects. In considering the gravitational effect they identify the intensive variable as Xi = gz (15) and the associated extensive variable as xi = m (16) When these are iserted in Eq. (14), the result is dE = T dS P dV gzdm (17) Now here is an obvious contradiction because the application is to a closed system where m cannot change. Furthermore, because of the minus sign, the equation implies that the energy somehow de creases if the mass is increased in a gravitational field, a result which can be considered absurd if they mean total energy and incorrect if they mean internal energy which is independent of gravity. As a last example of difficulties with the treat ment of effects other than thermal or compression, let us look at the highly regarded textbook by Guggenheim [3]. He considers the work done in transferring dni moles of i from phase a to phase /3, each with its own gravitational potential, W = (0 $a )Midn (18) From this he deduces that terms of the form, M i dni a i i must be added to the property relation (1) in terms of moles for each phase a (and chemical potential in place of partial free energy), so that dUa = TadSe PedVa + (po + M )dn (19) i Guggenheim does not explicitly say whether his U is internal or the sum of internal and gravitational energy. However, in view of the way he treats electrical effects, it will first be assumed that he means all of the energy, which is the sum E of in ternal and potential energy. Consequently, Eq. (19) is rewritten as dEa = T dS PadVa + (PT + Mia)Ddn i (20) Since the total energy is the internal plus the po tential energy, E = U + me = U + M M n i i and Eq. (20) may be written dEa = d(Ua + M M ini t i STadSa padVa + I (a + Ma)dna This reduces to (21) (22) dUa = TdSO PadVa + p dn iM n M de (23) i i Here is an equation, obtained simply by substitut ing the sum of internal and potential energy for the total energy, which must be flatly incorrect, SUMMER 1983 for it says that the internal energy of matter changes with the potential energy which is not in accord with observation. Of course, one might interpret Guggenheim's U" in Eq. (19) to be strictly internal energy. In that event dE' = d(Ua + Mi na) i 1 1 = T dS P dVa + + Mi )dn + M.tadna + I M.nda (24) i i 1 This may be rearranged to dE = T'dS' PdV + Mn d i i + 2 (pa + 2Mi~ )dni. i (25) This equation with its double potential energy term must be just as incorrect as Eq. (23), so that either interpretation of Guggenheim's energy term leads to ridiculous results. It is the objective in this discourse to focus attention primarily on the fundamental property relation because of its great utility in problems of thermodynamic properties and physical and chemical equilibrium. Now that erroneous treatments have been shown in three wellknown textbooks, let us ex plore a logical approach to the development of the fundamental property relation where effects other than thermal, compression, and exchange of mat ter with the surroundings are considered. Consider as a system a uniform collection of ponderable matter, where uniformity implies the same chemical composition, temperature, pressure, and any other intensive properties throughout all regions. Let the total energy (sum of intrinsic energy, potential energy due to position in any kind of force field, and energy due to massive macroscopic motion such as kinetic) be denoted by E as in Eq. (2). This total energy may be changed in three ways: (1) The mass of ponderable matter may exchange heat with its surrounding environment. (2) It may transfer work with its surroundings. (3) It may exchange matter with its surroundings. The energy balance for these energy and mass transfers may be written dE = 6Q 6W + C E.dm. (26) i which is just an equivalent of Eq. (2). The energy of each component added per unit mass of that component is Ei which is the partial total energy of the component. The accompanying entropy balance for the energy and mass transfer is the equivalent of Eq. (3) for a single heat transfer and Si the partial entropy per unit mass of each component added, or dS = + T + Sdm (27) This equation simply means that the entropy change of a collection of matter is the sum of the heat transfer divided by the temperature, the lost work LW divided by the temperature, and the entropy carried in with any entering matter. Let us now make all the energy and mass trans fer processes occur in such a way that the prop erties of the system of matter are at all times uni form throughout and the properties of any enter ing matter are identical to those of the system of matter under observation. This means that if the temperature of the matter is to rise, it rises uni formly throughout the whole mass of matter, if the pressure is to rise, it does so uniformly throughout, and if the concentration (and its asso ciated chemical potential) changes, it does so uni formly everywhere, and if a component is added, it is at the same temperature, pressure, and chem ical potential as in the system of matter. Such a requirement makes any process reversible because at no point is there allowed a finite difference in any potential driving force (i.e., all driving forces are infinitesimal in magnitude). For such a re versible process there will be no lost work so that Eq. (27) becomes in a rearranged form, 6Q = T dS T S.dm. 1 1 (28) Elimination of 6Q between Eq. (26) and Eq. (28) gives dE = T dS T S dmi W + E dmi i i (29) The total energy E is the sum of the internal energy, the kinetic energy, and any potential energy due to position in force fields such as gravi tational, electrical, and magnetic, E = U + mu2/2 + m$ EP HM (30) Here by way of explanation e is the electric po tential or field and P is the electric polarization while H is the magnetic field and M is the magnetic polarization. Eq. (30) may be differentiated to give CHEMICAL ENGINEERING EDUCATION ... these extended equations account for other effects such as surface tension, tensile stress, electric polarization, and magnetic polarization. 2 dE = dU + mudu + dm + md4 + Odm 2 edP PdE HdM MdH (31) It may also be differentiated partially with respect to the mass of one component at constant values of all the intensive properties that determine the state of matter, so that 2 2 Ei = Ui + U2/2 + EP HMi (32) Now the work transferred between the system of matter and the surroundings is the sum of all pos sible ways of doing work, 6W = P dV P Vidmi yda + Y admi i i Fdk + F T idmi md$ mudu i + PdE + MdH (33) Here the first term is the work done on the sur roundings if the system expands. The second term is work done by the surroundings to force dm, of matter into the system. The yda term gives the work to overcome surface tension in creating new area while y a idmi i is the work to force dmi into the system of matter when there is surface tension. The Fdl term is the work to elongate the matter in tension while the F iidmi i is the tensile work delivered to the surroundings when dm, is admitted to a system of matter under tension. An alternative more general approach here is to set up a strain tensor that gives the change in dimensions of an elastic material re sulting from all components of stress. Such a tensor would account for tension, compression, ex pansion and the normal and shear components and would give terms of the same form as that for simple tension. The term mdD accounts for the work to move the mass in a gravitational or centri fugal field. The term mudu accounts for the work to increase the kinetic energy of the whole mass of matter. The Pde is the work involved in moving polarizable matter in an electric field and the MdH is the same thing for motion in a magnetic field. Now if Eqs. (30), (31), (32), and (33) are in serted into Eq. (29), and use is made of dm = d dm. the complete property relation is obtained, dU = T dS P dV + yda + Fdk + EdP .+dM .+ (i + P TSi 3. i *" y Fi. eP. Hti)dmi (34) It is worth noting that kinetic and gravitational energy terms do not appear in Eq. (34) so that internal energy is completely independent of these effects, as it should be. If Gibbs free energy is defined as G = U + PV TS ye FA EP HM (35) it may be differentiated at constant T, P, y, F, E, H and mi to give the partial extensive quantity, Gi = Ui + PV TS y  F EPi HM. (36) If Eq. (36) is inserted into Eq. (34), dU = TdS PdV + yda + Fdk + edP + HdM + G.dm. (37) i where the partial free energy G is the previously used chemical potential pi. Since Eq. (37) is homogeneous in mass (i.e., doubling the mass at constant state of fixed T, P, y, F, E, H, and Gi doubles U, S, V, d, 1, P, M, and m), it may be integrated from zero to finite mass, U = TS PV + ya + Fk + EP + HMi + Gimi (38) i and G = i G.m. (39) i If Eg. (35) is differentiated and compared with Eq. (37) an alternate form of the funda mental property relation is obtained, dG = S dT + V dP ady dF PdE MdH + Gidm (40) i If Eq. (38) is differentiated and compared with Eq. (37), the result is SdT VdP + cdy + RdF + Pde + MdH + m.dGi = 0 (41) i In summary Eqs. (34), (35), (36), (37), (38), SUMMER 1983 (40), and (41) are similar to the usual wellknown equations when only thermal, compression, and mass transfer effects are involved, but these ex tended equations account for other effects such as surface tension, tensile stress, electric polarization, and magnetic polarization. The proper way to handle gravitation and other field effects has been shown and contrasted with the erroneous methods in three wellknown books. For a more complete discussion of this subject the reader is referred to the previous extensive treatment of The Symmetrical Fundamental Prop erty Relation of Thermodynamics [5]. O REFERENCES 1. Aston, J. G., and J. J. Fritz, Thermodynamics and Sta tistical Mechanics, John Wiley & Sons, New York (1959). 2. Gibbs, J. W., Collected Works, Vol. I, Longmans, Green, and Sons, New York (1928). 3. Guggenheim, E. A., ThermodynamicsAn Advanced Treatment for Chemists and Physicists, Interscience Publishers, Inc., New York (1950). 4. Lewis, G. N., M. Randall, K. S. Pitzer, and L. Brewer, Thermodynamics, 2nd Ed., McGrawHill Book Co., New York (1961). 5. Martin, J. J., The Symmetrical Fundamental Property Relation of Thermodynamics, Chemie Ingenieur Tech nik, 249, Vol. 5 (1972). NOMENCLATURE C Velocity of light E Total energy (internal + kinetic + poten tial of all kinds) e Electrical potential or field F Force G Gibbs free energy, U + PV TS, or G = U + PV TS ya F P HM g Acceleration due to gravity H Enthalpy, U + PV H Magnetic potential or field 1 Length LW Lost work irreversibilityy) M Molecular weight M Magnetic polarization m Mass n Number of moles P Pressure P Electrical polarization Q Heat flow S Entropy T Temperature (absolute) U Internal (intrinsic) energy of matter u Velocity V Volume W Work flow Z Height above a reference point a Surface area 8 Quantity transferred (as heat 8Q and work 8W) S Surface tension S Potential energy (gz in gravitational field) 1 Chemical or mass potential (i = Gi) Superscript Denotes partial extensive property a"P Points in gravitation field Subscripts Denotes different chemical species Denotes all chemical species except partic ular one i being examined. RESIDUAL FUNCTIONS AND FUGACITY K. R. HALL, P. T. EUBANK, AND J. C. HOLSTE Texas A & M University College Station, TX 77843 rpWO PROPERTIES WHICH generate considerable confusion in thermodynamics courses are re sidual functions and fugacity. They are, in fact, closely related concepts and, in this paper, we have developed them in a consistent manner. In this 0 Copyright ChE Division, ASEE, 1983 way, the composition dependence of the fugacity coefficient of a component in a mixture appears in an unambiguous manner. PROPERTY CHANGES The property changes which we shall develop in this paper are all of the form: real fluid prop erty less perfect gas property. The difference is either at the same temperature and pressure or at the same temperature and density. The definitions are (using M to denote U, H, A, G, S, V). CHEMICAL ENGINEERING EDUCATION M E M(T,p) M (T,p) MR E M(T,P) M (T,P) () M M = M(T,P) M (T,Po) = M(T,p). M (T,P /RT) (3) o M M = M(T,P) M (T ,P ) = M(T,p) M (T,P/RTo) (4) We choose to develop these expressions in the Tp plane because the results are then most con venient for computer computation. The path is M(T,p) M (T,0) M (T,p) where the real fluid and perfect gas planes inter sect at zero density. The most useful working equations for this de velopment are fap dU = c dT + T V P dV = cVdT + R( dp (5) dA = S dT P dV = S dT + RTZ d (6) P We have introduced the compressibility factor to facilitate equation of state use. Integrating these expressions along the chosen paths provides Kenneth R. Hall received his BSChE from the University of Tulsa, his MS from the University of Cali fornia (Berkeley) and his PhD from the University of Oklahoma. He has been at Texas A & M since 1974. He became Professor of Chemical Engineering in 1978 and Director of the Thermodynamics Research Center in 1979. He has approxi mately 60 publications, principally in thermodynamics. (L) Philip T. Eubank has, over the past twenty years, conducted re search in the theory, correlation, and measurement of thermophysical properties of fluids, resulting in about 60 refereed publications. He received the BSChE degree from RoseHulman Institute of Technology and the PhD degree from Northwestern University. He is presently Chairman of the AIChE Committee on Thermodynamics and Transport Properties (Area 1A). (C) U(T,p) U (T,p) p =U(T,p) U (T,o) R p 0 P(/T) p U* + U (T,0) U (T,p) 0 A(T,p) A (T,p) p = A(T,p) A (T,0) + RT Z *0 * + A (T,0) A (T,p)  RT 10 Thus, the residual functions, in form, are Ur = 1 3 RT T 0 (1T) p Ar i[ RT [Z 1] d RT P 0 dimensionless (7) (8) Of course, the other residual functions are com binations of these two Hr Ur PV PV U + +Z 1 RT RT RT RT Sr Ur Ar R RT RT Gr r r G Ar PV PV Ar RT +  RT RT RT RT (9) (10) (11) James C. Holste is an Associate Professor in the Chemical Engi neering Department at Texas A & M. He received his PhD in physics from Iowa State University in 1973 and spent two years at the National Bureau of Standards (Boulder) before joining Texas A & M in 1975. He has approximately 20 publications describing thermodynamic properties of fluids and solids. (R). SUMMER 1983 C A consistent development of residual functions, property changes and fugacity reveals close relationships among the various properties. By definition, V' is zero so (12) rT PVRT RT To convert these results to residual functions in the TP plane requires only adjustment of the perfect gas values M(T,P) M (T,P) * * = M(T,p) M (T,p) + M (T,p) M (T,P/RT) (13) where the required terms are M(T,p) M (T,p) = Mr M*(T,p) M (T,P/RT) = (0 if M is U,H An Z if M is A,G,S This step is equivalent to rederiving the expres sions in a TP plane. The other types of property change (Eqs. 3 and 4) also require only adjustments of the perfect gas values. For Eq. 3, the adjustment is M M = M(T,p) M (T,p) + M (T,p) M (T,P /RT) (3) 0 where M(T,p) M*(T,p) = M 0 oif M is U,H M (T,p) M (T,Po/RT) = + 0n Z + kn L P if M is A,G,S Eq. 4 bases the property change upon the standard state and the adjustment is M M = M(T,p) M (T,p) o * + M (T,p) M (T,P /RT) + M (T,Po/RT) M (To,Po/RT) + M (ToP/RT) M (To,P /RTo) (4) In this case, it is most convenient to establish UUo* and SSo* and then calculate the others from these two. Utilizing Eq. 4, the changes are UU UU 1j o r 1 v d U r + dT RT RT T R T O * S S S S o r n T Zn R R T o * CV dT R T and the other functions become H H U U PV RT U U T o o o o + Z (18) RT T + RT RT T * AA UU TSTS o 0 oo RT RT RT * U U T[S S] S [T To] 0o o o0 RT RT RT U U SS S T 0 o i 0 (19) RT R R * GG HH S S S T 1 (20) RT RT RT R It is also very important to note that throughout these equations the only integrals required are 1 (@Z I dp  T P(1/T) p RT 0 (z ] d= A p RT fT C 0 R * dT V dT T o The first two integrals are relatively simple appli cations of the equation of state, and the latter two integrals involve only perfect gas specific heat. One last point to note is the TP plane deriva tion of GR/RT. Again following a constant tem CHEMICAL ENGINEERING EDUCATION perature path from P O0 > P produces G(T,P) G*(T,P) =G(T,P) G (T,0) + G*(T,O) G*(T,P) but the fundamental equation for G is and the value for GR becomes P dP G(T,P) G (T,P) = RT Z RT r0 P Therefore, the final expression is dP 0 G dP Al' S [Z 1 + Z In Z RT 0 RT 25 and 26. Evaluation of Eq. 27 requires closer examination * G. G. G. G. G. G. 1 1 1 + (28) RT RT RT Evaluation of Eq. 28 requires the following analy V T, Z S[Gi Gi]  P T,z RT P=0 o (22) FUGACITY The usual definition for fugacity (of a pure component) is, in differential form dG. = RT d Zn f. @ constant T 1 1 lim = 1.0 P+0 (23) G. G lim urn0R RT P+0 * * G. G. 1 1 RT G Gi RT in z. RT I =V V. i v i dP RT = An z. (ideal solution) 1 SV V + 1 1 dP (2! Io 9) Upon integration, this expression becomes Zn f. dG. = RT Un P d nn f. I Gi G [ SRT= [Z i 0  ] i dP (22) lp R 1' f, =GR (24) Gi(T,P) Gi(T,P) = RT en = G (24) 1 1 P Eq. 24 has an obvious relationship with Eq. 22. In fact, we might as well have defined fugacity with these two expressions and have extended the defi nition to mixtures and components in mixtures: f G (T,P) G.(T,P) G kn 1  P RT RT f G (T,P) G*(TP) G mn _ g__ M. M P RT RT f. Gi(T,P) G.(T,P) Pn R P RTI Eq. 27 thus becomes f. Vi Vi ZdP an = An zi + dP  o0 P V. RT P]d o'f f F . An P= 1idP (30) Furthermore, utilizing previous relationships Furthermore, utilizing previous relationships * G. G RT (26) (27) Eq. 22 reveals the calculation procedure for Eqs. R * * S G GC G G i 1 1 R i RT RT RT Zn z.P 1 (31) SUMMER 1983 It is also true that R r G. G. 1 1 T = RT n Z RT RT m = (nAr/RT) Si T,nV,nj#i = (nZ )M nV { ni JT,nV,nj#i Sd(nV) nV CONCLUSIONS A consistent development of residual functions, property changes and fugacity reveals close rela tionships among the various properties. The com position dependence of the fugacity coefficient of a component in a solution is unambiguous. All prop erties result from integrals which are easy to de rive from good equations of state. D NOMENCLATURE A Helmholz function Cv* perfect gas specific heat (constant volume) fi fugacity of pure i fm fugacity of a mixture A GRAPHIC LOOK AT AVAILABILITY FUNCTIONS MARTIN V. SUSSMAN Tufts University Medford, MA 02155 THE THERMODYNAMIC availability functions can Sbe viewed graphically, and this view provides valuable unexpected insights into the nature and meaning of the functions. To demonstrate, consider the question, "What is the maximum work a system can perform in moving into equilibrium with the temperature and pressure of its environment?" The answer is given graphically in Fig. 1. Max imum work is the work performed when moving reversibly along paths (12) and (2e), from an arbitrary initial state (1) to a final state (e) in equilibrium with the environment.  fugacity of component i in a mixture  Gibbs function  enthailpy general property symbol number of moles pressure gas constant entropy  temperature internal energy molar volume total volume  compressibility factor mole fraction density Superscripts  Tp residual S TP residual * perfect gas partial molar Subscripts I component i m mixture o standard state reference state Now this may appear to be an arbitrary choice of paths; but it is not. It constitutes a unique com bination of reversible paths leading from (1) to (e), that allow heat and mass transfer to occur only when the system is at the potentials of its en vironment. These are paths that take the system isentropically and at constant molarity, (12), to the temperature of that environment; and then isothermally, (2+e), to the chemical potential of the environment. And it is rather easy to prove, again graphically, that no combination of reversi ble process paths connecting states (1) and (e), can produce more work. PROOF Curve (1ke) in Fig. 1 traces a reversible but arbitrary process path taking a system from state CHEMICAL ENGINEERING EDUCATION Copyright ChE Division, ASEE, 1983 (1) to state (e). The area under (1ke) is clearly greater than the area under the path (12e) com prising the path producing "maximumwork". Therefore Q (1ke) > Q(12e) (1) and because, W = QAUie (2) and AUie is the same for all paths; it follows that W(1ke) > W(12e) (3) which appears to contradict the answer to the above "maximumwork" question (??). But, consider path (1abe) consisting of isen tropic and isothermal processes, with the isotherm, ab, located so that the area under (1abe) equals that under (1ke), so that W(1ke) = W(1abe) (4) That any reversible progress can be replaced by combinations of isentropic and isothermal processes with equal heat and work effects is some times called Clausius' Theorem [1]. The work of process (1abe) exceeds that of process (12e) by Area (2abe2) so that Eq. (3) may be written as an equality: W(Ike) = W(12e) + Area (2abe2) But process (1abe) involves an isothermal expansion, (ab), that must absorb heat at a tem perature, Ta that is higher than the temperature of the environmental heat reservoir, Te. M. V. Sussman is professor of chemical engineering at Tufts Uni versity. His work in thermodynamics includes the books "Availability (Exergy) Analysis" (Mulliken House 1980) and "Elementary General Thermodynamics" (AddisonWesley 1972). He is the inventor of the "Maxwell Demon Bottle." Previous articles in Chemical Engineering Education are "Seeing Entropy: The Incompleat Thermodynamics of the Maxwell Demon Bottle" and "Thermodynamic Heresies." Where can this heat come from? If there are other sources of heat present, than our initial question is meaningless. The question has meaning only if heat interactions are restricted to the sys tem and its environment. Such heat interaction can occur reversibly only if a heat pump is used to move heat from Te to Ta. The minimum work input to this pump is that of a Carnot heat pump, and is exactly equal to: Area (2abe2). The net work output from arbitrary path (1ke) is there fore equal to that from path (12e). Q.E.D. Analogous considerations hold for open sys tems where mass as well as heat are exchangeable with the environment. For maximum work the FIGURE 1 mass exchange occurs only at the potential of the environment so that process path (12e) on a tj ni diagram (identical to Fig. 1, except with [i as ordinate and ni as abscissa) is analogous to the maximum work path on a TS diagram, and a sim ilar proof applies [2]. THE MAXIMUM WORK FUNCTION As a consequence of the Fig. 1 proof, and the constraint of heat transfer only at Te, Eq. (2) is transformed into an equation for maximum work W.e5 = WMAx = TeASi,AUie (5) where the double subscript should be read as "from state 1 to state e". THE AVAILABILITY FUNCTION Part of this work is expended against the at mosphere and is therefore not available. The net useful or available work is the difference between SUMMER 1983 FIGURE 2 the maximum work and the work expended in pushing back the surrounding environment WMA PeAVe = B (6) The symbol, B, is assigned to this quantity and it is called the "Availability Content", "Net Useful Work", or the nonflow "Availability" of the sys tem in given state (1). We may combine Eqs. (5) and (6) to obtain the classical definition [3] B = [AUi. TeASie + PeAVie] (7) B IS POSITIVE DEFINITE B may be represented as the area of a cycle on a PV plane (Fig. 2). In accord with Eqs. (5) and (6) the cycle moves along the WMAX path, isen tropically from 12 and isothermally from state (2) to the environmental equilibrium pressure Pe; (2>e). A constant pressure process (e>3), from Ve to V1, representing the atmospheric work loss, (P.AV1I), effectively completes the cycle. The area enclosed is the integral around the clockwise closed path 12e31. The direction of integration is always clockwise irrespective of the placement of state (1) with respect to state (e), so that the enclosed area is always greater than zero. When P, > Pe, the work output from 1>e exceeds the input from the environment, e>3. When P, < Pe, the work input in moving from 1e is exceeded by the work output gained from the atmosphere. Net output always exceeds input. This is also true when the temperature of the initial state (1') is below that of its environment. Fig. 2 shows integration cycles representing B for states (1) and (1') having temperatures and FIGURE 3 To examine the graphical character of (4, we rewrite Eq. (9) by expanding the AH and A(PV) terms ) = (AU,, TeASie + ViAPie + PeAVie) (10) Now using Eq. (7) and (10), we see that S= B VAPi = B V(P P) (11) Eq. (11) tells us that 4, unlike B, is greater than zero only when the ViAPie term is negative or is less than B; that is, for all values of P, > Pe and CHEMICAL ENGINEERING EDUCATION pressures above and below that of state (e). The cycles always move clockwise. Consequently B > 0 (8) STEADY FLOW AVAILABILITY; ANOTHER, MORE USEFUL FUNCTION In a steady flow system in which potential and kinetic energy effects are unimportant, the work that may be extracted via a shaft or cable when a stream entering the flow system exits in equilib rium with its environment is WSHAFT = (AH Q) For a reversible process from (1) to (e) WSHAFT (AHe TdS) 1 and this work is a maximum if, as before, heat transfer occurs only when the system has reached T,. Consequently WSH(MAX) (AHe TeASe) (9) Eq. (9) defines the steady flow availability function, [3] to which we assign the symbol, 4. for a limited range of values of P1 < Pe. Usually, if P, < Pe, 4 will be negative and work will have to be supplied to the system for it to flow into equilibrium with the environment. This point is illustrated in Fig. 3 by states (1) and (1') whose pressures are both below Pe. 4 of state (1) is nega tive because the area of V1 (Pe P1) exceeds that of B. ) of state (1'), however, is positive because area V,, (Pe P,) does not exceed B'. On the other hand, Eq. (11) shows that the relative magnitude of T, and Te does not affect the sign of 4. Eqs. (9) and (11) apply to chemical as well as physical steady flow process as is shown in the fol lowing section. CHEMICALLY REACTIVE SYSTEMS STEADY FLOW In a steady flow system in which chemical re action occurs, but where kinetic and potential energy effects and nonshaft work interchanges, other than volume change, are negligible, an ac counting of all the energy entering or leaving the system in a differentially small time interval yields the equation dQ dWSH = dU + d (PV) (12) which may be written as dWsH = dU + d(PV) TedS (13) if all heat is transferred reversibly at Te. But in a reactive or diffusive system at Te dU = TedS PdV + Yjidn, (14) so that Eq. (13) becomes dWsa = VdP + /xidni (15) In a reversible isothermal reaction process that is also isobaric at Pe, for example, an electrochem ical cell, the integral f VdP = 0 1(P) and therefore Eq. (15) becomes WSH(max) = 4f idni = AGie (16) 1 (P,T) 1(P,T) A ~6~ 18/,") ... consider the question, "What is the maximum work a system can perform in moving into equilibrium with the temperature and pressure of its environment?" If, however, P varies as the system moves reversi bly from 1le, as through a Van't Hoff equilibrium reactor (Fig. 4), then S idni = 0 across the equilibrium reactor and the reversible turbines connected to the reactor (because ni's are constant), so that Eq. (15) becomes  VdP = AGe = Ws(nmx) (17) 1(T) Consequently, from Eqs. (16), (17), and (13) WSH(max) = AHie TeASie 4) (18) The subscripts (P,T) and (T) on the integra tion signs in Eqs. (16), (17) and (18) indicate that the integrals are at constant pressure and temperature, and at constant temperature, respec tively. Eq. (18) and the discussion leading to it demonstrate that the steady flow availability has the same form in chemical reactive processes as in physical processes. The chemical potential terms are implicit and need not be appended to the equa tion. NONFLOW SYSTEM If a system can change its composition or mass and exchange expansion work with its environ ment, then the differential of its internal energy is dU = TdS PdV + Xqidni (19) If in addition all mass and heat transfer occur re versibility at the potentials of the environment, then Eq. (19) becomes dU = TedS PdV + /xid,e dn (20) which we rearrange and integrate to obtain an expression for maximum expansion work that has one more term than Eq. (5). e Wmax le f PdV = S TedS dU + Zx,,dni = TeASie AUi. + 1i,e Ani,.i SUMMER 1983 sFI crE 4 FIGURE 4 (21) The net useful work or nonflow availability is then found as in Eqs. (6) and (7) Chem. Eng. Edu. Vol. 17, No. 3, Sum. 14283 B PdV (PeAVIe) (22) 1 =[AUie + PeAVe TeASie /pseAn,lel] which is the defining equation for nonflow avail ability found in Gibbs and elsewhere [4]. Now imagine a system that moves from an initial state (1), through isentropic (1>2), and isothermal (2>3) processes, into temperature and pressure equilibrium with its environment and then displaces its contents, wholly or in part into that environment, if need be through a semi permeable membrane that allows transfer of the to the area (123a1). Consequently, the second bracket must equal zero, or AUse + PeAV3e TeAS3e = 2/Xt,eAni,ie Therefore (24) (25) Bie = (AU 3 + PeAV, TeAS, 3) where state (3) is isomolar with (1) but in equi librium with the environment. For reactive systems or materials that trans form chemically before passing into the environ mental state; for example ZaAi > bB, i j in equilibrium with an environment B = (AUi 3 + PeAVi 3 ToAS, 3) (26) (AU3e + PeAV3e TeASIe) j where "i" refers to reactants, and "j" to products. State (3) is the reaction equilibrium state and state (e) is the environmental state. For the rea sons given in Fig. 3 and 5, B remains positive definite. O REFERENCES 1. Zemansky, M., "Heat and Thermodynamics" fourth ed., p. 168 (McGrawHill, New York, 1957). 2. Sussman, M. V., Nature, 256, 5514, 195198 (1975). 3. Keenan, J. H., Thermodynamics, 1st MIT Press Ed: Cambridge, MA, 1970. Originally published by Wiley, New York, 1941. 4. Gibbs, J. W., The Collected Works, Volumes I, II, New York: Longsmans, Green and Co., (1931). FIGURE 5 contents at its environmental potential or partial pressure. The process would appear as process 123e in Fig. 5. The work of this process is the maximum work as given in Eq. (21), and is rep resented by the sum of area (123a1) and area Pe (Ve V,). The net work of the process, or the nonflow availability, is according to Eq. (22), the maximum work minus Pe (Ve Vi), or simply the area (123a1), that is always positive definite. It is interesting to note that Eq. (22) may also be written as B = (AUeo + PAVi 3 TeASi ) (23) (AUse + PeAVse TeASoe YPi,eAni(,e)) The first bracket in Eq. (23) is exactly equal LETTER TO THE EDITOR Continued from page 103. systems . .". Then some conclusions are derived about one's freedom to select reference states for internal energy, enthalpy, and entropy in terms of chemical com pounds or chemical elements, with or without the possi bility of chemical reaction. However, identical conclusions are easily derived from corresponding statements applic able to a simple closed system. Further the open system equations can only be obtained by derivation from the closed system relations. Thus the derivation of reference state constraints from the open system equations is not so much a proof as it is a partial check on the deriva tion(s) which led to the open system equations. To illustrate the closed system approach, consider the familiar first law statement: E2 El = Q W CHEMICAL ENGINEERING EDUCATION As Kestin points out [1]: ". .The concept of energy is connected with two different states of a single closed system and a numerical value can only be ascribed to the difference E2 El be tween the energies in the two states, because only this difference, or its negative, can be measured by means of an adiabetic, irreversible process . ." Thus for any closed system, we may arbitrarily choose to assign an absolute numerical value to any one state of the system. Most often this is a numerical value of zero at a socalled reference state. Because of the requirement to satisfy equation #1, we have no more freedom of choice and corresponding absolute energy values are determined for all other possible states of our single closed system. The conclusions about reference state selection reached in the article follow in a direct way from equation #1 and the corresponding second law statement. As one example, let us define a reference state for a single closed system to consist of a collection of subsystems, each of which contains one pure element in some arbitrary state. If we assign a numerical value of zero to the energy of each subsystem, we have set the value of reference state energy equal to zero for the entire closed system. Clearly this choice of reference state is alawys available, regardless of what particular chemical compounds might be present, and further there is no constraint on what specific refer ence states we select for the individual pure elements. So this method of assigning absolute energy values is always acceptable in principle, whether or not chemical reactions are possible in a particular closed system. Similar results can be obtained in the case of entropy. Not only is the closed system approach a simpler way to obtain information about acceptable reference states, but it also avoids possible misleading interpretations of total energy or entropy values. As Kestin points out [2]: ". .no physical meaning can be attached to the difference between the energies of two different systems, even if the two systems merely represent different masses of the same homogeneous system . ." In the CEE article, Profesor Fredrickson uses the notions of total internal energy and total entropy in de riving reference state constraints. Then the results are applied to interpretation of a problem from the classic text by Modell and Reid [3]. The problem involves computation of heat transfer to the helium in a tank which will main tain total internal energy at a constant value despite the flow of gas from the tank. The comment is made that ". we cannot know how to adjust the heat transfer rate to the gas so that its absolute total internal energy remains constant as its mass changes . .". The implication of this and other remarks in the article is that there does exist a unique absolute energy value for any particular collection of matter, even though we cannot in principle determine what it is. But as discussed above, there is no one unique absolute internal energy for a particular system. We can assign absolute energy values, but the only unique values are for changes of state of a simple closed system. If we allow changes of system mass to occur, as in an open system, there is no physical meaning even to the numerical value of changes in the system (total) internal energy. By our freedom to select reference states, we can force an open system energy change to have whatever numerical value we may desire. Even the notion of holding the energy of an open system constant has no physical mean ing. The lack of direct physical meaning for total internal energy does not invalidate the open system equation which contains such a term. Rather in that equation, the input, accumulation, and output terms in combination have the effect of making the open system balance equivalent to a closed system balance in disguise. The open system equa tion is valid, but the total energy term by itself has no physical meaning. Finally, it can be noted that not all "state functions" are created equal. We commonly refer for example to internal energy, specific volume, and Gibbs free energy as state functions. But these are really not the same. The volume term, in common with pressure and temperature, is accepted as an inherently absolute quantity, except for choice of units. There is no issue of a reference state. In ternal energy, however, can take on any desired numerical value at any one state. It is only changes of internal energy that must always be the same. Another such function is enthalpy. Clearly the product of two absolute quantities, PV is also an absolute quantity, and so the linear sum of internal energy and PV which we call enthalpy preserves the property that changes of enthalpy depend only on state changes and not upon choices) of reference statess. Still a third kind of "state function" is exemplified by Gibbs free energy, defined as: G = U + PV TS (2) An arbitrary set of absolute values for G is deter mined by the selection of reference states for internal energy and entropy. But these absolute values do not be have in the same manner with respect to changes of state as do internal energy or entropy values. Comparing two different states, we have: G2 G1 U2 U1 + P2 V2 P1 V1  T2 S2 + T1 S1 (3) Clearly it is only in the case that T2 = T1 that we can be assured that changes in G depend only on changes in state. In any other case, it is generally possible to affect the numerical value of the change in G by an arbitrary se lection of the reference states) for entropy. Since we are always free to make such selectionss, and since no legiti mate thermodynamic conclusion can be thereby affected, we conclude that Gibbs free energy is a third kind of state function. If the system is isothermal, free energy changes are unique. If the system is not isothermal, there is no physical meaning to the numerical value of free energy changes. This lack of meaning is a fact whether the system is open or closed. W. H. Abraham Iowa State University 1. J. Kestin, "A Course in Thermodynamics," p. 157 (Waltham, Massachusetts: Blaisdell Publishing Company, 1966). 2. Ibid pp. 158159. 3. M. Modell and R. C. Reid, "Thermodynamics and its Applications," p. 141 (Englewood Cliffs, N.J.: Prentice Hall, Inc., 1974). SUMMER 1983 jPl classroom PUTTING PROBLEM SOLVING TO USE IN THE CLASSROOM RICHARD D. NOBLE University of Colorado Boulder, CO 80309 PROBLEM SOLVING HAS become an area of in tense interest and study [110]. Textbooks have been written on the subject and separate courses are being offered. While it would be impractical for all engineering educators to attempt separate offerings in problem solving, the concepts and ap plication of problem solving can be utilized in ex isting courses. This can be done without any loss of material coverage. The objective of this paper is to indicate spe cific areas in a course being taught where the problem solving approach can be utilized and why this approach can be useful. BACKGROUND There are a large variety of problem solving strategies but most contain the elements initially described by Polya [11] and expanded by Woods [1]: 1) Define the problem, 2) explore possible solution procedures, 3) develop a solution plan, 4) carry out the plan, and 5) check your results. This is often not a straight linear process since the problem solver may have to loop backwards at any stage of solution process to redefine the Richard D. Noble received his B.E. degree in 1968 and M.E. degree in 1969 from Stevens Institute of Technology. In 1976, he received his PhD degree from the University of California, Davis. His current research interests include facilitated transport in liquid membranes, transient heat transfer, and problem solving skills. O Copyright ChE Division, ASEE, 1983 problem or develop new solution strategies if the initial attempts fail. The degree of difficulty in solving problems can be related to the level of difficulty outlined in Bloom's taxonomy of knowledge [12] (see Table 1). As problems re quire higher levels of thinking, students ex perience increased difficulty since they have had little or no practice in problems at higher think ing levels. Most problems at the end of a chapter in an engineering textbook require application. Problems requiring analysis and synthesis are rarely encountered by students. Once encountered, students have no structured process for solving these problems. Even problems requiring applica tion of material presented can be difficult. Students expect exactly the right amount of in formation given to solve the problem and a de finitive statement of what the problem requires for a solution. Even at this point, if students cannot plod straight through to the solution, they sometimes become confused and cannot develop a solution. Overcoming anxiety and frustration then also becomes an important component of problem solving [13, 14]. This paper will present a series of different approaches which can be used with a class to de velop their problem solving skills. These tech niques require some time and effort to imple ment. LEVEL OF PROBLEMS ASSIGNED Refering to Bloom's taxonomy (Table 1), most problems at the end of a textbook chapter or on an examination require application. Typically, the exact amount of information required to solve the problem is given and the student applies knowledge learned in the chapter to the problem. Higher levels of thinking such as analysis and synthesis, are normally not encountered. There fore, students get no practice in applying newly learned knowledge as part of a more complicated or vague problem. To overcome this limitation, a mixture of CHEMICAL ENGINEERING EDUCATION problems requiring application, analysis, and synthesis will reinforce a student's learning and use of this knowledge in expanded situations. This will require some additional work on the part of the instructor since development of analysis and synthesis problems would be required. TYPE OF EXAM QUESTIONS The type of question given a student on an examination can certainly put to use the problem solving skills of the students. Using problems which just require comprehension or application do very little to test the student's problem solving TABLE 1 Bloom's Taxonomy of Knowledge KnowledgeRecall memorized information. Course What is Fourier's law of heat conduction? Laboratory Measure velocity of fluid in a pipe at five points along the crosssection. ComprehensionSolve recognizable problem. Course If the temperature gra dient through a place wall is tripled, what is the resulting change in the heat flux ? Laboratory Compare the measured ve locity distribution with laminar flow theory. ApplicationUse memorized knowledge to solve un familiar problem. Course What is the steadystate heat flux through a com posite wall, given k's and boundary temperatures. Laboratory Determine the relevant data needed to test the laminar flow theory in pipes. AnalysisBring together remote relationships to solve problem. Course Laboratory A fire breaks out in a room adjacent to a fuel tank. How long before the fuel explodes ? Determine why the experi ment for flow through a pipe does not agree with laminar flow theory. SynthesisCreate alternative solutions to an openended problem and select best one. Course Laboratory Design a heat exchanger. Design an experiment to Specify type and con measure the velocity dis struction details. tribution in pipes. To overcome this limitation, a mixture of problems requiring application, analysis, and synthesis will reinforce a student's learning and use of this knowledge in expanded situations. skills as well as knowledge. Adding a problem which requires analysis provides the framework for students to make better use of their problem solving skills since the degree of difficulty in creases. This is not to say that solving problems requiring comprehension or application do not make use of problem solving skills but adding more difficult problems can increase a student's problem solving skills. If we test students on prob lems requiring analysis or synthesis, it is im portant that we have provided some prior practice in solving problems at these thinking levels. EXAMPLE PROBLEMS IN CLASS The use of example problems can serve as a tool for developing problem solving skills as well as knowledge. All aspects of a problem solving strategy can be utilized in an example problem. Once the problem statement is read from the text or handout, I ask the class to determine the given facts, what we are asked to find, and draw a diagram. Once this is completed, I ask the students to provide the solution steps. If a step is incorrect, we will still follow it until the class realizes that something is wrong. This shows students that it is OK to make a mistake, a common emotional block to creativity. By testing each solution procedure, we can determine errors in reasoning and also show alternate solutions. We check our results at each step in the process to determine the reason ableness of our answer. Different heuristic tech niques can be utilized with different example problems to aid in the solution process [15] (see Table 2 for examples). Students can be asked to provide heuristics. Another approach is to try at least one new heuristic each week in class. Once the solution is obtained, the answer is checked to insure reasonableness and accuracy. If difficulty arises at any step in the process, this is the time to let the students loop back through the process or use heuristics to become "unstuck." Once the solution is complete, I ask the students questions which relate to the problem to increase their understanding. Which variable can we control? What happens to the solution if various variables are changed? It may be necessary to guide the SUMMER 1983 students in this process. As their skills develop, the guidance can be reduced. TIME FACTOR IN EXAMINATIONS One key aspect of problem solving is the realization that people usually do not progress directly through a solution process to the answer. There can be false starts, redefining the problem, alternate solution paths, and finally, checking the answer. The point of this is that people need sufficient time to allow the problem solving pro cess to be fully utilized. By assigning difficult problems and allowing a relatively short period of time for the student to respond, the student can be placed in a high anxiety situation where his performance will be low. One method to deal with this problem is to allow two hours for a one hour examination. If a student makes a mistake, this allows sufficient time to recover and proceed through to a proper solution. My experience has TABLE 2 Some Heuristics or Guides 1. Solve a simpler problem. Many times a student can be come immersed in a complicated problem and become "stuck." Simplifying the problem to a stage where the student recognizes the solution approach can aid in developing the actual solution procedure. 2. Overcome excess anxiety. When a student becomes "stuck," they can develop a large amount of anxiety which prevents effectively developing a solution. Awareness is the first step to combating this. 3. Communicate your difficulty to another person. It is sometimes very beneficial to try to explain your situ ation to another person who is familiar with the subject. Describe what you have done and what you are trying to do. Often this will help to point out ad ditional information or errors in reasoning. 4. Brainstorming. When "stuck" on a problem, generate a list of words or phrases which immediately come to mind. Write everything down and defer judgment until you have exhausted the flow of information. Once this is completed, analyze the list and use judgement to de termine any new relevant information. 5. Personal analogy. Pretend that you have entered the system under study. Try to imagine what you see, feel, etc. This helps to "visualize" the situation. 6. Look at extreme cases. Ask yourself a lot of "what if" questions to get a "feel" for how you think the system will respond. Have will to doubt. Focuses attention on different aspects of problem. 7. Incubation. Sometimes it is helpful to stop actively working on the problem when "stuck." Let the problem "incubate" for awhile. Some insight may "pop up" into your conscious domain or, upon your return to the problem you can see errors in reasoning or other ob stacles to the solution that were not previously ob vious. been that students will respond very well to taking evening exams with the extra time allotted. Engineering problems, especially in junior and senior level courses, require more than a few minutes to complete a good solution procedure. Allowing the extra time allows the instructor to assign problems requiring analysis instead of just application. GRADING The method that you use to grade exams and homework problems can influence a student's problem solving behavior. If the major credit is given for a right answer, a student will become mainly concerned with the answer and not the solution process. If a student stops getting credit as soon as he or she makes a mistake, they can develop a great deal of frustration and anxiety. Fear of making a mistake is an emotional block to creativity. They lose perspective on the problem solution and deal mainly with frustration. If the student receives the major portion of credit for a proper solution, the student will work at de veloping a correct solution without a high degree of anxiety over making a mistake. HELP OUTSIDE THE CLASSROOM If a student comes into your office for as sistance, it is very easy to simply show them how to do the problem and have them leave. A more effective technique would be to help them work through the method of solution. Whimbey and Lockhead's problemsolving pairs is one example [4]. By guiding the student but not giving them the answer, you help them not only to solve the problem but to develop problem solving skills along the way. Wankat [16] and Miller [17] de scribe some useful approaches in talking with students that could prove helpful in these situ ations. BEHAVIORAL OBJECTIVES The use of instructional objectives in a class can be a major asset to problem solving. Out lining the major concepts and explaining what is required for a particular topic gives the student a framework for developing a solution strategy. In structional objectives can also include such items as ability to check reasonableness of an answer or the ability to develop an alternative solution procedure. Mager's book [18] is an excellent source to learn about using instructional objectives. CHEMICAL ENGINEERING EDUCATION There are also additional references concerned specifically with instructional objectives for engi neering classes [19, 20]. CONCLUSION The use of problem solving skills in various class situations has been discussed. It has been shown that the thinking level of assigned problems, type of examination questions, example problems in class, time factor in examinations, grading, help outside the classroom and be havioral objectives are all areas where problem solving skills of students can be incorporated. This allows the class experience to be one where both an increase in knowledge and problem solving skills can be attained. FO REFERENCES 1. McMaster University Problem Solving Group, "De velopment Stype in Solving Problems," Engineering Education, Vol. 69, No. 7, April, 1979. 2. Greenfield, L. B., "Student Problem Solving," Engi neering Education, Vol. 69, No. 7, April, 1979. 3. Rubinstein, M., "Patterns of Problem Solving," PrenticeHall, Inc., 1975. 4. Whimbey, A. and J. Lockhead, "Problem Solving and Comprehension: A Short Course in Analytical Reasoning," Franklin Institute Press, 1980. 5. Adams, J. L., "Conceptual Blockbusting," W. W. Norton and Co., Second Edition, 1979. 6. McMaster Problem Solving Group, "What is Problem Solving," Chemical Engineering Education, Summer 1979, pp. 132137. 7. Woods, D., "On Teaching Problem Solving, Part I: What is Being Done?" Chemical Engineering Edu cation, Spring, 1977, pp. 8694. 8. Woods, D., "On Teaching Problem Solving, Part II: The Challenges," Chemical Engineering Education, Summer 1977, pp. 140144. 9. Noble, R. D., "Mathematical Models in the Context of Problem Solving," Mathematical Modeling, Vol. 3, 1982, pp. 215219. 10. "Problem Solving," AIChE Symposium Series, Edited by D. R. Woods, J. T. Sears, and R. D. Noble, 1983. 11. Polya, G. "How to Solve it," Second Edition, Double day Anchor, 1957. 12. Bloom, B. S. and L. G. Broder, "ProblemSolving Pro cesses of College Students," Supplementary Edu cational Monographs, No. 73, Univ. of Chicago Press, 1950. 13. Richardson, S. A., R. D. Noble, and M. Hawkins, "The Use of Relaxation in Overcoming Anxiety in Problem Solving," Engineering Education, Nov. 1980. 14. Richardson, S. A., and R. D. Noble, "Anxiety: Another Aspect of Problem Solving," AIChE Symposium Series on Problem Solving, 1983. 15. Schoenfeld, A., "Explicit Heuristic Training as a Variable in Problem Solving Performance," J. for Research in Mathematical Education, May 1979. 16. Wankat, P. C., "The Professor as Counselor," Engi neering Education, November 1980, pp. 153158. 17. Miller, P., "Nonverbal Communication: How to Say What you Mean and Know What They're Saying," Engineering Education, November 1980, pp. 159161. 18. Maker, R. F., "Preparing Instructional Objectives," Fearson, 1962. 19. Leuba, R., "Instructional ObjectivesA Guide to Ef fective Teaching," American Society for Engineering Education publication, 1980. 20. Stice, J., "A First Step Toward Improved Teaching," Engineering Education, Vol. 66, No. 5, Feb. 1976, pp. 15. O book reviews FUNDAMENTALS OF MULTICOMPONENT DISTILLATION By Charles D. Holland McGrawHill Book Company, NY 626 pgs, $39.95 Reviewed by William L. Bolles Monsanto Company, St. Louis, MO This book may be regarded as the "Bible" on calculating the detailed mass and energy balances on a platetoplate basis for distillation columns processing multicomponent systems. It may also be regarded as the prime textbook for those writ ing computer programs for the same. The book is intended to completely replace the 1963 volume by the same author, entitled "Multi component Distillation". The principal problem attacked is achieving the complete component mass and energy balances for the "complex distillation column": i.e., one with multiple stages, multiple feeds, multiple side draws, either liquid or vapor, and multiple stage heat exchangers. Also, it is assumed that any multicomponent nonideal phase equilibria and enthalpy models may apply. The approach is rigorous insofar as the Frst Law of Thermo dynamics is concerned. The author develops his subject in a very orderly manner, including the following major topics: introduction to the fundamentals, develop ment of computational convergence methods, ap plication of convergence methods to complex col umns, systems of columns, the NewtonRaphson method application, azeotropic and extractive dis tillation, systems of columns with energy exchange between streams, distillation accompanied by chemical reaction, optimum design and operation, SUMMER 1983 the problem of minimum reflux, and thermody namic relationships for multicomponent mixtures. There are also chapters on the fluid mechanics and mass transfer efficiency relationships of com mercial equipment, including the design of sieve and valve trays. The approach used throughout the book is to begin with established theoretical realtionships such as the First Law, and then proceed with complete mathematical derivations of all the equa tions required in practice. There are numerous numerical examples, as well as many problems for classroom and home work assignments. There is also available, from the publisher, a "Solutions Book" to the problems, free to educators. El NONLINEAR ANALYSIS IN CHEMICAL ENGINEERING By Bruce A. Finlayson McGrawHill Chemical Engineering Series 366 pages Reviewed by A. G. Dixon Worcester Polytechnic Institute This graduatelevel text, which provides an introduction to modern methods of obtaining solu tions to nonlinear ordinary and partial differential equations, is a welcome addition to the ranks of chemical engineering mathematics books. The author's aim is to teach students how to apply such techniques as perturbation, orthogonal collocation, finite difference and finite element methods to typical chemical engineering problems. He demon strates these using case studies drawn largely from his own experiences in chemical reaction engineering, heat transfer and polymer flow in vestigations. In a brief introduction (Chapter 1) the author illustrates the types of equations considered in this book: initialvalue and boundaryvalue ODEs, parabolic PDEs and elliptic PDEs. Hyperbolic PDEs are, unfortunately, not covered. In Chapter 2 a short discussion of the solution of nonlinear algebraic equations is given, to pro vide background for the methods which follow in later chapters. Only the successive substitution and NewtonRaphson methods are presented, and some convergence proofs are given. No worked examples are provided. Chapter 3 presents standard methods for initialvalue ODEs with special attention being paid to concepts of stepsize control, stability and stiffness. Computer subroutine packages are ex amined and a comparison of methods is made. This chapter is a reasonable review for those familiar with the material, but will make rather dry reading for beginners. The presentation is similar to that in mathematics texts, and no chem ical engineering examples are worked out to il lustrate the methods. The main value of the book lies in the final three chapters, which together make up twothirds of the whole. Chapter 4 deals with boundaryvalue problems, while Chapter 5 and 6 treat parabolic and elliptic PDEs respectively. Each chapter fol lows the same pattern: the various methods are introduced through such examples as diffusion and reaction in a catalyst particle and packed bed re actor analysis, some case studies are described, and a comparison of methods is made based on operation counts and convergence rates. At times the discussion of errors and computation times seems rather lengthy for a text directed to engi neering students. Particular attention is paid to the method of orthogonal collocation for spatial approximation in Chapters 4 and 5, especially when combined with a finite element approach. In Chapter 6 the Galerkin finite element method is thoroughly de scribed, different types of element being illustrated and compared. At the end of most chapters the author pro vides study questions, homework problems, a short bibliography and some references. The study ques tions give the reader a convenient "check list" of the more important points in the development, while the homework problems serve to extend the formal material. Many of the problems ask for derivations of results used earlier, while other ex tend the case studies, often requiring the use of FORTRAN computer programs provided in an appendix. Some of these programs are general matrix inversion subroutines, while others solve specific problems. The layout of the book makes it pleasant to read; the text is interspersed with tables and diagrams to illustrate the results, and the print does not tax the eyes. There seem to be fewer typo graphical errors than one might expect in such a mathematical work. Professor Finlayson's style is clear and direct, making the book suitable even for beginning graduate students. CHEMICAL ENGINEERING EDUCATION In summary, the book will make a good text for a graduatelevel chemical engineering mathe matics course oriented towards numerical meth ods. The instructor will find it necessary to amplify some parts of the book, and will generally wish to use a broader range of examples and homework problems than it provides. O AVAILABILITY (EXERGY) ANALYSIS By M. V. Sussman Mulliken House, Lexington, MA 02173 Reviewed by J. D. Seader University of Utah This is a 100page selfinstruction manual, which is divided into four parts. In Part I, the concept of availability, also referred to as exergy, is defined, explained, and related to enthalpy and entropy. Applications are given for a number of simple physical processes. In Part II, changes in availability for chemicalreaction processes are analyzed, with the results presented in graphical form. Secondlaw efficiencies based on availability, are defined in Part III. Available energy costing (thermoeconomics) is considered in Part IV. An appendix tabulates standard chemical availabil ities referred to 25C, latm and a set of final ref erence products for 137 different compounds. Pro fessor Sussman advises the reader to read the manual in a sequential manner. However, keyword or short summaries placed in the margins permit the reader to readily skip material that is already familiar. In order to follow the presentation of material in the manual, the reader should have at least a fundamental understanding of the first and second laws of thermodynamics and be able to compute changes in enthalpy and entropy for pure com pounds and ideal mixtures. Such background is gen erally the subject of an undergraduate course in engineering thermodynamics. In addition, some elementary knowledge of solution thermodynamics would be helpful. A pretest, included before Part I, permits the reader to determine if he (she) is properly prepared to proceed. At the end of each of the four parts, exit tests, with detailed solutions, are provided to help determine if the reader has mastered the material. In Part I, the following points are developed in a lucid, interesting, and sometimes historical fashion: 1. Both quantity and quality of energy should be con sidered. 2. The quality of energy refers to the fraction of that energy that can be extracted as useful work. 3. The first law makes no distinction based on the quality of energy. 4. Maximum work extraction occurs in an ideal (reversible) process. 5. The availability, which is a state property closely related to the Gibbs free energy, is a quantitative measure of the quality of energy and depends on the choice of the environmental reference (dead) state. 6. The change in availability is independent of the process path and the choice of dead state. Throughout Part I, the chemicals considered are mainly water, air, nitrogen, and oxygen; that is, chemicals that are found in the environment. For these, examples are given of calculations of both availability and change in availability. When other chemicals are involved, only the change in availability is considered. Part I is concluded by 12 excellent examples of the calculation of availability or the change in availability for process involving no chemical reaction. Of particular importance are some additional concepts that are presented in: 1) Example (c)iii, which illustrates the effect on availability of bringing the material of a given composition to a different deadstate composition; 2) Example (k), which defines the work equiv alent of heat; and 3) Example (1), which notes that shaft work and electrical energy are exactly equivalent to availability. It is unfortunate that these very important concepts are buried in ex amples and are not discussed thoroughly in the main text. In Part II, chemical reactions are considered, and it now becomes necessary to carefully eluci date the composition of the environmental refer ence (dead) state. This has been the subject of much discussion and controversy among research ers, with no general agreement. As an example, Gaggioli and Petit [Chem Tech 7, 496506 (1977)] use the following dead state: T = 25C, P = latm Gas: Constituent N2 02 H20 A Mole Fraction 0.7567 0.2035 0.0303 0.0091 0.0003 0.0001 1.0000 Liquid: Pure H20 Solids: CaCO., CaSO, 2H20, NaCI, etc. Sussman uses a different dead state; namely, SUMMER 1983 the standard products of combustion, e.g., H2O (1) CO2 (g), SO2(g), etc., in their pure state at 25C and 1 atm. Thus, he does not deal with a single dead state, but with a collection of dead states. These two approaches can lead to different values for the standard availability of a pure chemical in a particular state of aggregation at 25C and 1 atm as shown in the following table: Standard Availability, Btu/lb mole Chemical Species H2(g) H,0 (g) H,0 (1) Co0(g) CH, (g) SO, (g) Gaggioli & Petit Sussman 101,190 3,700 0 8,650 357,130 122,670 102,100 3,700 0 0 352,100 0 The differences are considerable for CO. (g) and particularly SO,(g). If only the change in availability is of importance, then the dead state basis cancels out and is not a factor. If the actual availability is of importance, then the choice of dead state is very important. Gaggioli and Petit assume that the ultimate dead state of the sulfur atom is as CaSO4.2HO(,) and not as pure SO,(g). Also, they assume that CO2 (g) ultimately becomes CO2 (g) at a mole fraction of 0.0003 and not pure CO2 (g), which serves as Sussman's basis. To ob tain Sussman's values for standard availability, one need only compute, from free energies of formation, the negative of the standard change in free energy for combustion of the particular com pound. Calculated values for 137 different com pounds appear in the Appendix. The major portion of Part II is devoted to a series of three excellent detailed examples involv ing chemical reaction, the last of which deals with a complete methane reforming process. Availabil ity diagrams are used to conveniently illustrate availability flows, and particularly availability losses, in each process example. It is made clear that while energy is conserved, availability is not. The exit test involves further calculations on the methane reforming process and directs the reader to assess the points of greatest availability loss and to find ways of reducing availability losses. Just prior to the exit test, Sussman lists some reasons why availability losses occur. Part III is a short chapter, which begins by defining an overall secondlaw efficiency for a process as the ratio of availability outputs to availability inputs. By means of examples, this efficiency is contrasted to that given by the first 140 law. Sussman shows clearly that this definition of secondlaw efficiency can give negative results when the chosen reference state does not cor respond to that of the lowest free energy. An alternative definition extractivee secondlaw ef ficiency) is also presented, but it is not general either because it only applies when streams enter ing a process do not mix with other streams. The exit test questions are relatively short exercises. An introduction to thermoeconomics is pre sented in the final chapter, Part IV. The problem is how to determine a cost for a stream of energy. Based on availability considerations, a joule of electricity should be worth more than a joule of highpressure steam, which should be worth more than a joule of lowpressure steam. Methods for assigning costs are developed by applying various costing rules to a process that cogenerates these three energy streams. The simplest rule presented assumes that all three energy streams have the same cost per unit of availability. The resulting costs per kwh of energy content are $0.0211, $0.0080, and $0.0053 for electricity, 250 psia steam, and 50 psia steam, respectively. Other cited costing rules involve such matters as whether the energy streams are for internal or external use and if they must compete with the open market. The exit test at the end of Part IV involves the application of one of these alternative costing rules to the same cogeneration process. Although written by a chemical engineer, the chemical engineering literature on secondlaw analysis is essentially ignored in the manual. In particular, the paper by Denbigh [Chem. Eng. Sci., 6, 19 (1956)], in which he derives the availability function and availability loss by combining the first and second laws, is not mentioned. Denbigh's derivation is much more general than the deriva tion of Equation (8) in the manual. Separation processes, such as distillation, which are very important industrially and gen erally inefficient from a secondlaw analysis, are almost totally ignored. Nevertheless, the beginner, who knows little or nothing about secondlaw analysis will find his time well spent by studying the concise text and the many execellent, detailed examples and exit tests. He can then strengthen his understanding, learn of other viewpoints, and see other applications by reading the previously mentioned papers by Denbigh and by Gaggioli and Petit, in addition to de Nevers [Chem. 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