JOURNAL OF CHEMICAL EDUCATION
GRADUATE THERMODYNAMICS IN CHEMICAL ENGINEERING1 ROBERT YORK, JR. Carnegie Institule of Technology, Pittsburgh, Pennsylvania T m s PAPER gives the objectives and a description of the subject matter of courses on Thermodynamics for graduate students in chemical engineering. In June, 1941, a similar paper (40)was presented at the Ann Arbor meeting, but this was directed at the undergraduate level: In contrast to the underlying theme of the 1941 paper, it has not been found necessary to devote as much attention t o pedagogy. The problem of creating interest by showing application is no longer pressing, since most students beginning their graduate study have had some undergraduate thermodynamics in physical chemistry and in either mechanical or chemical engineering department. Our experience has shown that it is desirable t o give a basic course for entering candidates for the master's degree who have not had the equivalent of our undergraduate course; otherwise, a third to a half of the semester will be spent on the First and Second Laws. Consequently, our graduate courses of instruction in chemical engineering thermodvnamics are divided into this basic course and a -
1 Presented before The Chemical Engineering Division, A. S. E. E. Meeting, Minneapolis, June 18, 1947. 2 Present addre?: 1700 So. Second Street, St. Lorlis 4, Missouri.
regular application course for master's candidates and .then a second-level course for doctor's candidates. Each of these is described at length below. BASIC MASTER'S COURSE
The objective of this basic course is to develop a thorough understanding of the First and Second Laws with practical problems, but definitely not including topics of the application course. The subject matter for this one-semester (16 weeks) basic course is much the same as outlined in the author's 1941paper (do), although a fern topics have been deleted because of the time available. The topics are similar to those given in Weber's "Thermodynamics for Chemical Engineers" (36)and include: fundamental concepts; First Lam applied to closed and open systems; heat capacity; heat of reaction; perfect gases; gas compressors operating on perfect gases; Second Law including simple entropy calculations; free energy and availability, power cycles; steam engines and turbines: refrigeration; and generalized P-V-T relations. The method of teaching is also similar t o that employed in the undergraduate course, except that the class, beranse of smaller size, is somewhat more infor-
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mal, with the result that many discussions take place. The problems on each topic listed above are more complex than those in the undergraduate course and include, for example, filling and discharging a steam accumulator and evacuating a tank with a vacuum pump, in contrast to correspondingly simple problems on the same subject in the undergraduate course. MASTER'S APPLICATION COURSE
The objective of our regular master's course is to study and to develop an understanding of those topics in thermodynamics which will be useful and applicable to master's candidates who will enter the chemical and petroleum industries. Such applications as power cycles, steam engines, and turbines, refrigeration, and gas compressors have already been mentioned in connection with the basic course and the undergraduate course (40). It is now desirable to take up methods for evaluating and estimating properties of compounds used in industrial processes; to show, a t least in part, how these properties may be used for calculations in such unit operations as distillation, gas absorption, and solvent extraction; and to solve problemswhich cannot otherwise be solved. The subject matter included in this application course is somew& as follows: Fugaeity, Activzty, and Isothermal Work of Separation. This includes a discussion of the terms used and problems on the following: computing fugacity for a gas from its P-V-T relations and from generalized correlations; selection of standard states and calculation of activity; isothermal work of separation, especially for systems with two volatile components by different methods (which are to be checked later for consistency by the Duhem equation). Effect of Pressure, Volume, and Temperature on Thermodynamic Properties. This includes the de~ivation and discussion of equations for the effect of pressure (or volume) and temperature on such properties as internal energy, enthalpy, entropy, free energy, and heat capacity. It includes a discussion of equations of state and evaluation of properties for the two distinct cases: (a) when V and T arg the independent variables; and (b) when P and T are the independent variables. Emphasis through probkms is placed on the fact that case (a) gives equations (agreeing with the kinetic theory of gases) of the van der Waals, straight-lineisometric, Keyes, or Beattie-Bridgeman type, from which internal energy and entropy changes at constant temperature may be readily evaluated; and that case (6) gives equations of the volume-residual form, virial form, or the Goodenough, Callendar, or Linde type equations for steam, from which enthalpy and entropy changes at constant temperature may be evaluated. Such equations are apphed to evaluate properties of steam, refrigerants, and hydrocarbons, including a discussion of minimum data needed, method of handling data by algebraic and graphic methods, and checking the data for consistency from such other measurements,
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for example, as Joule-Thomson coefficientsand enthalpies of vaporization. Generalized Correlations of Properties. This consists of the derivation of equations from P-V-T relations for properties on a reduced basis, that is, in terms of ratios to P, V, or T a t the critical state. I t consists of correlations obtainable from straight-line isometrics and the compressibility factor chart. It also consists of generalized correlations for P-V-T, fugacity, and isothermal variations in enthalpy and entropy. These correlations are applied to estimate and to compare results in isothermal enthalpy changes obtained by several methods for a gas such asmethane, propane, or butane. Compression of Nonideal Gases. After a brief review of factors affecting volumetric and compression efficiencies, the method of calculating isentropic changes in enthalpy is discussed and illustrated by problems. This is then applied to estimating the capacity and power requirements of compressor cylinders handling nonideal gases (SO). Standard Free Energy, Equilibrium and Constant Changes with Temperature. This includes a study of the relation of standard free energy and equilibrium constant; the use of the fugacity rule for estimating equilibrium conversion of chemical reactions at moderate pressures. Changes of free energy and of enthalpy with temperature are applied to adiabatic reactors, especially for sulfur dioxide oxidation, ammonia synthesis, and endothermic dehydrogenation reactions. The problem of estimating the feasibility of readions according to standard free energy values at different temperatures is also included. Partial Molal Quantities. This consists of the derivation and discussion of equations relating to partial molal quantities and the evaluation of partial mol'al quantities by algebraic and graphic methods. The following types of problems are solved: partial molal volumes from P-V-T values of gas mixtures and corresponding thermodynamic properties obtainable from such volumes and their derivatives; partial molal enthalpy changes involving physical and chemical reactions such as the dehumidification of air by sulfuric acid and the absorption of sulfur trioxide by strong sulfuric acid; isothermal change in enthalpy for hydrocarbon gas mixtures through partial molal quantities (30) and a comparison of results obtained from gener&inid borre~atiois. Vapor-Liquid Equilibria. This study consists of the derivation of the Duhem eouatiou and the solution of a problem on partial molal free energy relations to check partial pressures in binary systems for consistency (usually the ammonia-water system). I t consists of the application of the van Laar, Margules, and Scatchard-Hamer equations (8) for estimating actiyity coefficients and subsequently vapor-liquid equilibria a t one temperature to practical systems in distillation. It also consists of a study of the variation of activity coefficient with temperature as related to relative partial molal enthalpy. It concludes with an estimation of vapor-liquid equilibria for binary systems under con-
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stant total pressure (limited to pressure where gas laws may be applied to vapors). Enthalpy-Concentratzon Diagram. This includes the construction of a portion of a diagram and the checking of this for thermodynamic consistency. Usually the diagram is applied to caustic evaporation, absorption refrigeration, and fractionation near the critical state or involving large heats of solution in other courses, because of a time limit. Comprehensive Problems involving several topics given in these two master's courses are solved for such industrial processes as ammonia oxidation to nitric acid and the hydration of ethylene to ethanol. It seems appropriate to mention that as far as texts are concerned, both Weber (36) and Dodge (10) are used. Material is worked in together for reading assignments of new topics which is ultimately followed by sets of problems. Frequent reference is made to articles in the literature, particularly on properties. About five one-hour quizzes and a three-hour final examination, usually open-book, are given through the semester. SECOND-LEVEL COURSE
The request for advanced courses in our chemical engineering department came from the graduate students. h h e s e students pointed out that advanced courses above the master's level had to be chosen from outside departments, particularly chemistry, physics, and mathematics. The viewpoint of these outside departments leans toward that of pure science and, while the courses are broadening, the reaction of the students is not altogether as favorable as to their departmrntal courses. The rather provoking question must then be asked: What constitutes a graduate course a t the second level in chemical engineering thermodynamics? After considerable discussion we decided that such a course may include some of the ssme material presented in other conrses from several different but precise points of view; that it may well be mathematical and philosophical in nature; that it should emphasize scientific logic; that it should extend previous fields of study further; and that it should contain new fields, partitularly in those subjects which have applications in the process industries and which cannot otherwise be dealt with satisfactorily. A tmo-semester course was offered for the academic year 1946-47, informal in nature like an advanced seminar. Textbooks were used for reference or for a single topic, since no book thus far published contains what we had in mind for our outline. To prevent the course from becoming a literature survey and to emphasize applications, problems were assigned after a discussion of each major topic. The subject matter is as follows: First and Second Laws. This is a discussion of Chapter I of Guggenheim (1Y) (which is a brief study of the two laws and the development of equations leading to Gibbs' chemical potential), and a parallel discussion of
JOURNAL OF CHEMICAL EDUCATION
the logic behind the two laws and the approach by Weber (56), Dodge (lo), Keenan (go), Kiefer and Stuart (22), MacDougall ( B ) , and Planck (27). I t is also a discussion of the several chemical potentials and their relations; of physical and chemical equilibria; and of the open system according to Gillespie and Coe (15). The mathematical background includes properties of homogeneous functions, Euler's theorem, and relations to extensive and intensive properties. This study differs considerably from that of the earlier courses in that the method of Gibbs, ~vhichis unsurpassed in elegance of treatment, is follo~vedboth in this and in succeeding parts. Themnodynamic Relations of General Valzdzty. This is a detailed study of Chapter I1 of Guggenheim (17). which includes partial molal quantities and their properties as homogeneous mathematical functions, as TI-ellas the effect of P, V, T , and composition on properties. Systems of One Component. This is a discnssion of Chapter I11 of Guggenheim (I?), including gas thermometry, properties of a single perfect gas, heat capacities of two nhases in eouilibrium. and tem~eratnrecoefficients of heats of evaporation and of fusion. Gaseous Miitures. This is a study of Chapter IV of Guggenbeim (17), including Dalton's law of partial pressures and membrane equilibrium, law of mase action (in terms of chemical potentials), and temperature coefficients of equilibrium constants, fugacities, and activities of gases. (This. comprises about 75 pages of Guggenheirn and is sufficientfor our purpose of review and of studying the methods of Gibbs. I t is easier to follow than the original writings of Gibbs or the commentaries contributed by different authorities.) Chemical Equilibria by Gibbs' Method and Equation of State. This is a detailed study of a series of articlesby the late Professor L. J. Gillespie (14) and by Professor J. A. Beattie (3, 4, 5) on propert,ies of gases and gas mixtures as applied to chemical equilibrium of gases under pressure, particularly ammonia synthesis. This includes Beattie's use of an equation of state to evaluate properties and chemical potentials in mixtures, of which the use is elegant in the mathematical treatment of the extention of Gibbs' method to actual gases. I t includes Beattie's development of egnations for the two cases: ( a ) where pressure, temperature, and number of moles are independent variables, and (b) where volume, temperature, and number of moles are independent variables. It also includes a rational treatment of properties of gas mixtures as the total pressure approaches zero or as the volume approaches infinity. A problem was assigned on the pressure correction for t,he methanol equilibrium, comparing the use of Beattie'smethodwith that of the simpler fugacity rule. The class vas astounded a t the difference in results, in fact so much so that considerable time was spent in studying calculated and measured volumes of mixtures. Vapor-Liquid Equilibria of Nonideal Systems. As a background for the behavior of binary solutions, the first sixty pages of Hildebrand's "Solubility" (18) were studied and discussed. With this as a background, the
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paper of Carlson and Colburn (8) was studied in detail. est to chemical engineers entering the petroleum indusProblems were assigned on the calculation of vapor- try is the set of hydrocarbon properties compiled under liquid equilibria for such nonideal binary systems as American Petroleum Institute Project Number 44. An propanol-water and isobutanol-water. explanation of the methods used is given by Roxsini, Next, papers of Scatchard (31, 32, 33, 34) were dis- Piteer, and others ($9). Similar properties of inorganic cussed briefly to show the basis for using volume frac- compounds have been compiled by Kelley (21) and are tion in solution calculations and also to give a picture being revised as better data are obtained. I t is interof the complexities of the liquid phases. esting to note that this study of quantum-statistical Actual experimental data were tested for a ternary methods not only gives a technique for calculating system according to the Gibbs-Duhem equation. thermodynamic functions but it also furnishes a backConsiderable time was spent on partial differentiation ground for recent developments in reaction kinetics aa as related to physical significance, application of homo- proposed by Glasstone, Laidler, and Eyring (16). I t geneous functions, and the transformation of mole should not be surprising to find more satisfactory exnumbers to moli fractions. (Mathematics texts (12, planations of kinetics mechanisms based on this back24, 55), MacDougall (23), and Epstein (11) were help- ground. ful in this phase of the subject.) Equations involving There will no doubt be improvements in these courses different partial derivatives were 'developed to show as different modifications are tried out and as more data three different and independent ways of checking on properties become available. By this arrangement measured values. The system tested was acetone- the master's candidates have not, in our opinion, been acetic acid-water (41) and the results were found to be sold short; that is to say, they have been given what reasonably consistent. It may be noted that this pro- thermodynamics they will need in most industries and cedure for checking values is different from fitting about as much as they can absorb in the time available. empirical equations to activity coefficient-composition On,the other hand, doctor's candidates can elect still curves. another year of thermodynamics in the chemical en& For practical applications of these equilibria to azeo- neering department in preparation either for teaching tropic andextractive distillation, the papers of Colburn or for entering advanced technical work in industry. and Schoenborn (9) and of Benedict, Rubin, and others (6, 7) vere studied. As a matter of fact, this is a de- LITERATURE CITED sirable background for an advanced course in aseo(1) ANDERSON, J. W., G. H. BEYER,AND K. M. WATSON,Nat. tropic and extractive distillation. Pet. News (July 5, 1944). Properties by Third Law a d Quantum-Statistical. G,, Chm, Rev., 2,, 59 (1940). (2) Methods. Advanced courses in mathematics, physics, (3) BEATPIE,J. A,, AND S. IKERARA, P m . Am. Acad. Arts and and statistical mechanics are highly desirable for a Sci., 64, 127 (1930). (4) BEAITIE,J. A,, Phys. Rev., 36, 132 (1930). thorough understanding of the computations of thermo(5) B E A ~ EJ., A., i W 31, 680 (1928); 3 4 691 (1928); 321 dynamic properties by quantum-statistical methods, 699 (1928). Nevertheless, certain equations being accepted as tor(6) BENEDICT, M., AND L. C. RURIN,T T ~ S Am. . Inst. Chem. rect, it is possible to ascertain the methods by which Engrs., 41, 353 (1945). (7) BENEDICT, M., C. A. JOHNSON, E. SOLOMON, IND L. C. many properties of solids and ideal gases are computed RUBIN,ibid., 41, 371 (1945). today. As a beginning, Chapter XVIII of MacDougall H. C., AND A. P. COLBURN, Id..Eng. C h m . , 34, (8) CARLSON, (23) is studied, while the mathematical equations are 581 (1942). checked and discussed in class. Parallel reading in (9) C O L B ~ A. N ,P., AND E. M. SCHOENBORN, Tmn~.Am. Inst. Richtmyer and Kennard (28) has proved satisfactory Chem. Engrs., 41,421 (1945). since LZacDougall's treatment is necessarily brief. (10) DODGE,B. F., "Chemical ~ngineering~hermodynamics," McGraw-Hill Book Company, New York, 1944. These assignments include subject matter on the Third (11) EPSTEIN, P. S., "Textbook of Thermodynamics," John Law, Einstein and Debye's heat capacity equations for Wiley and Sons, Inc., New York, 1937. solids and the thermodynamic properties derived there- (12) FRANKLIN, P., "Methods of Advanced Calculus," McGrawHill Book Co., New York, 1944. from; radiation, quantum statistics, partition functions, (13) GIA~QUE, W. F., J. Am. C h m . Sac., various Papers from thermodynamic functions of differentmolecules. 1928 to date. pa*icuof Wenner ("1 is Next, Chapter (14) GILLESPIE, L.J., Phys. Rev., 34,352 (1929); 34,1605 (1929). Iarly the numerical examples, to unders:and,how the (15) GILLESPIE, L. J., AND J. R. COE,J. c h m . ~ h y s . I, , 102 different functions are computed from vlbratlonal fre(1933). S., J. K. LAIDLER,AND H. EYRING,"The pencies and quantum weights. Finally Chapter VIII (16) GLASSTONE, Theory of Rate Processes," McGraw-Hill Book Co., New of Wenner on the estimation of properties from strucYork, 1941. tnre is taken up and the results are compared with those ( ~ Gn ~ E_ A,, t # ~ o d e r ~n ~ h ~ ~by the~ obtained by methods proposed by Andersen, Beyer, and Methods of Willard Gibhs," Methuen and Company, Watson (1). London, 1933. J. H., "Solubility of on-~lectrolytks," (2), pitaer (25, $6), ( 1 8 ) HILDEBRAND, **icles by ~i~~~~~ (13), Reinhold Publishing Company, New York, 1936. Kassel W, Wilson (38) and others describe methods (lg) L. S., Chm. Rev., 277 (1936). for calculating properties of organic corqpounds (20) KEENAN, J. H., "Thermodynamics,"John Wiley and So&, these quantum-statistical methods. Of particular InterInc., New York, 1941. J,
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(21) KELLEY,K. K., U. S. Burem of Mines, Bulletins 371, 383, 384, 393, 394,406, 407,434 (1934-1940). (22) KIEFER,P. J., AND M. C. STUA~T, "Principles of Engineering
Thermodynamics," John Wiley and Sons, Inc., New York, 1930. 123) MACDOUGALL. F. H.. "Thermodvnamics and Chemistrv." -, John ~ i l e y ' m dSons, Ino., ~ e York, w 1939. OSGOOD, W. F., "Advanced Calculus," The Maomillan Co., New York, 1925. PITZER,K. S., Chem. Rev., 27,39 (1940); J . C h m . Phys., 8, 711 (1940).
PITZBR,K. S., Ind. Eng. Chem., 36,829 (1944). PLAN=, M., "Treatise on Thermodynamics," translated by A. Om, Longmans, Green and Company, 1921. RICRPMYER, F. K., AND E. H. KENNARD, "Introduction to Modern Physics," MoGraw-Hill Book Company, Ine., New York, 1942. ROSSINI,F. D., K. S. PITZER,ET AL.,J . Resemeh, Nal. Bur. qf Stds., various papers from 1945 to date. SAGE,B. H., W. N. I~ACEY, ETAL.,Ind. Eng. Chem., various papers from vol. 26 (1934) to date.
D , Chem. Reu., 8, 321 (1931); Tram. Fwadoy (31) S C A T C ~ RG., Soc., 33,160 (1937). (32) S C A T C ~ RG., D , AND W. J. HAMER,J . Am. C h a . Soc., 57, 1805 (1935). (33) SCATCHARD, G., AND C. L. RAYMOND, {bid., 62,1278 (1938). 134). SCATCHARD. G.. S. E. WOOD.AND J. M. MOCHEL.ibid.., 62., 712 (1940). ' (35) SOKOLNIKOFF, I. S., AND E. S., "Higher Mathematics for
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Engineers and Physicists," McGraw-Hill Book Company, New York, 1941. WEBER,H. C., "Thermodynamics for Chemical Engineers," John Wiley and Sons, Inc., New York, 1939. WENNER, R. R., "Thermochemical Calculations," McGraw HillBook Company, New York, 1941. WIL~ON, E. B., C h a . Rev., 27,17 (1940). YORK,R., I d . Eng. Chem., 34,535 (1942). YORK,R., J. CHEM.EDUC.,19, 376 (1942). YORK,R., AND R. C. HOLJIES,I d . Eng. Chen., 34, 345 (1942).
