THERMODYNAMICS for CHEMICAL ENGINEERS* E. W. COMINGS University of Illinois, Urbana, Illinois
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HE subject of thermodynamics for chemical engineers has been treated in such a variety of ways in diierent schools that its meaning is vague. This vagueness is enhanced by the lack of an adequate text. With this in mind, it was felt that a definite outline of such a course with references to serve in the absence of a text would be of interest. Before arranging such an outline i t is well to consider how a chemical engineer will apply thermodynamics. The limitations of a simple heat balance as taught in stoichiometry bring out the need of a more basic concept for handling problems of greater complexity. Thus, in setting up such a balance around a limekiln, i t is possible to account for all the heat entering in the charge, fuel, and air as leaving in the solid products, in the flue gases, or as losses through the walls of the kiln when proper values are used for heats of combustion and decomposition of the fuel and limestone, respectively. If a similar balance is run around a system comprising a compressor, heat exchanger, and reaction chamber, it is a t once evident that other forms of energy in addition to heat must be considered. The balance which is universally applicable is an energy balance and, of course, depends on thefirst law of thermodymmics. With this fundamental balance in mind i t is a logical step to Bernoulli's mechanical energy balance as a basis for fluid flow. Thefirst law allows a clear understanding of such simple processes as expansion through a valve, expansion into an evacuated or partially evacnated cylinder, the evaporation of a liquid and its removal from a batch system as distinguished from evaporation in a steady flow system, as well as others which will be mentioned later.
The second law is of utility to the chemical engineer because of the varied conclusions which can be built up from it as a basis. The determination of the physical properties of pure compounds or mixtures from a limited amount of experimental data is a good illustration. Entropy and free energy have served to predict chemical equilibria where direct measurement would have been diicnlt if not impossible. The Clapeyron equation follows directly from the concepts of the second law. Its use in predicting vapor pressures is well known. A chemical engineer should be to some extent familiar with these applications. It is not our purpose to name all the applications of thermodynamics. The above are samples. The subject is a fundamental one and therefore definitely belongs in academic training. To provide a course in these fundamentals with a clear understanding of their application is the rble of chemical engineering thermodynamics. A course in the subject might well handle the following general subjects. (1) A background is provided by discussing fundamental concepts such as temperature ( 4 ) , pressure, specific volume, work (7), heat, energy, heat capacity, state, system, change of state, process, reversible and irreversible changes ( 4 ) , cyclical changes and batch and steady flow processes. (2) ThefLrst law is explained for a batch process by visualizing changes in state as taking place in a cylinder (10)fitted with a frictionless piston and entirely non-conducting of heat or conducting as desired. Such simple illustrations provide a picture in the student's mind and simplify the presentation over that given in some texts (8). With the gas already in the cylinder these processes may be analyzed, isothermal, constant pressure, adiabatic, constant volume, poly* Presented before the Fourth Annnd Meeting of the Illin&Indiana Section of the Society for the Promotion of Engineering tropic, and (by the substitution of a diaphragm for the Education, Tern Haute, Indiana. May 7. 1938. piston) free expansion. These can be illustrated using
a perfect gas in the cylmder, but the more general nature of the results should be pointed out. The distinction between a steady flow process and a batch process must be made clear with a discussion of the general energy balance for both types (7,12). The definition of enthalpy is introduced; i t is pointed out that the changes in this property ( l i e changes in the internal energy and other thermodynamic properties to be introduced later) depend only on the initial and final state and that only in special processes can these changes in enthalpy be interpreted as a quantity of heat. Numerous problems are required to jix these concepts thoroughly in the student's mind. A good example is supplied by the following problem (10) which requires a choice of the proper system and a f d understanding of internal energy and work in the thermodynamic sense. Problem: A totally evacuated steel shell, having a of 30 cu. ft. is to be filled with hydrogen from a gasometer in which the hydrogen is at 2 atms. abs. and 60°F. The flaw takes place through a relatively small valve, and the volume of the gasometer, therefore, decreases slowly during the flow, the pressure in the gasometer remaining constant at 2 atmospheres absolute. The gasometer, shell, and connections may be considered non-conductive to heat. W h e n the pressure in the sheu reaches 2 atmospheres absolute, what is the temperature of the hydrogen in the shell, and by how much has the volume of the gasometer decreased?
(3) The second law gives the student a better understanding of the relation between work and heat and defines the impossibility of changing a quantity of heat completely into work without compensating changes in the surroundings, despite the equivalence of the two forms of energy as stated by the first law. Entropy then provides a quantitative statement of this principle and furnishes another useful property for analyzing processes. Graphical methods aid in visualization and a treatment of enthalpy-entropy (Mollier (6)), temperature-entropy, pressure-volume (4, 7), and temperature-internal energy (11) charts is recommended. If numerous problems are used, the student should now have a fairly clear idea of the basic concepts of thermodynamics and will raise the question as to what is the use of all this theory. Several applications in addition to those which have already been evident are appropriate a t this time. (4) Thermodynamics provides a means of correlating numerous physical properties which will be useful to the chemical engineer and in this application can greatly reduce experimental work. Some knowledge of partial differentiation will be required here, and a review of two mathematical theorems (13) will give an adequate foundation (7). Since 9-w-t data are the least difficult to collect, such other properties as enthalpy, entropy, heat capacity, energy, and so forth, should be derived from them, supplemented by heat-
capacity data a t atmospheric pressure. By defining F and A (8) (Gibbs (3) S- and +) the Maxwell Relations (7) easily follow, and these are useful in transforming partial differential coefficients involving entropy to equivalent coefficients involving only p, v, and t. A convenient and accurate procedure for deriving these related properties is by the method of residuals (1) and graphical calculations. (5) The possibility of chemical engineers using extensively any accurate algebraic equation of state except in the cases of a few common gases seems somewhat remote. This is due to the complex nature of the equations required to fit the p-v-t data even over limited ranges. However, the approximate graphical correlations based on reduced temperature, pressure, and volume (5, 2) are capable of extensive use. These correlations when combined with the above thermodynilmic principles lead to convenient general relations between the uro~erties. (6) l-he examination of a system to determine whether a spontaneous change is possible (3) and the Use of thermodynamic properties in predicting equilibrium relations are an important application with which chemical engineers should be familiar. The relation between free energy and the equilibrium constant is essential. The free energy can best be introduced by defining it as a new property which depends only on the state of the system. The possibility of an increase in entropy is then shown to be the criterion of the possibility of a spontaneous change taking place in an isolated system. For a system which is not isolated but subject only to a constant pressure and temperature the possibility of a decrease in free energy becomes the corresponding criterion (9). The activity coefficient and fugacity in their relation to free energy and the equilibrium constant should be studied. It is realized that an adequate treatment of the material outlined will probably require more than one semester. If only one semester is available, it is felt that greater benefit will be derived from a thorough treatment of the fundamentals as outlined in (I), (2), and (3) above and presented with the object of providing a good basic understanding of the thermodynamic principles involved than would result from slighting these principles in favor of the applications given in (4), (5), and (6). Briefly, then, the utility of thermodynamics to the chemical engineer is illustrated by its applications to fluid flow; general processes involving both physical and chemical changes of state; the measurement, calculation, and correlation of physical properties; and the calculation of both physical and chemical equilibria. A general outline for presenting the fundamentals of the subject together with their applications is given. &
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BIBLIOGRAPHY
(1) DEMING, W. E.
AND
L. E. SAUPE,Phys. R m , 37, 638
(1931). (2) E D ~ S T EW. R , C.. Ind. Eng. Chem., 30, 352 (1938).
(3) DONNAN, F. G. AND A. HAAS, editors, "A commentary on the scientific writings of J. Willard Gibbs. Volume I, Thermodynamics," Yale University Press, New Haven. Conn., 1936, pp. 55. 87.
(4) Gom. J. A,, "Notes on thermodynamics," 2nd ed.. Jahn S. Swift Co., Urbana, Ill., 1937. (5) HOUGEN,0. A. AND K. M. WATSON,"Industrial chemical calculations." John Wiey & Sons. Inc., New York City, 1016
(6) KEENAN, J. H. AND F. G. KEYES,"Thermodynamic properties of steam," John Wiley & Sons, Inc., New York City, 1016
(7) KIEaER, P. J. AND M. C. STUART, "Principles of engineering thermodynamics," Jahn Wiley & Sons, Inc., New York City. 1930. (8) LEWIS. G. N. AND M. RANDALL, "Thermodynamics." McGraw-Hill Book Co.. Inc., New York City, 1923.
(9) MACDOUGALL, F. H.. "Thermodynamics and chemistry," 2nd ed.. John Wiley & Sons, Inc., New York City, 1926, p. 106. (10) "Massachusetts Institute of Technology notes on thermadynamics." (11) PERRY. J. H. AND W. S. CALCOTT.editors, ''Chemical engineers' handbook," 1st ed., McGraw-Hill Book Co., Inc., New York City, 1934, p. 611. (12) WALKER,W. H., W. K. LEWIS,W. H. MCADAMS, AND E. R. GILLILAND,"Principles of chemical engineering." 3rd Book Co., Inc., New York City,
eci3-McGraw-Hill 'Y..
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(13) Woons. F. S., "Advanced calculus," Ginn and Co., Boston, Mass.. 1926, pp. 81. 9 3 4 .
