JOURNAL OF CHEMICAL EDUCATION
To the Editor: The following statement is a suggested modification of the usual presentation accorded Avogadro's law: "Equal volumes of all perfect gases for which the ratio P I T is the same will contain the same number of molecules." This has the value of being a broader generalization. The usual statement, "Equal volumes of perfect gases under the same conditions of temperature and pressure contain the same number of molecules," may be regarded as a special case of the statement proposed above. The argument favoring the broader statement can be stated as follows: Let us take V cc. of two perfect gases (A and B) a t a pressure P and absolute temperature T and suppose X is the number of molecules in each case. Now let us consider that the volume of gas A is increased to V' by increasing the absolute temperature to T' (the pressure being the same). That of gas B is also increased to V' by decreasing the pressure to P' (the temperature remaining the same). Since the mass in either of the cases remains constant, the number of molecules, i. e., X, must remain the same. Hence we have equal volumes of two different gases a t different temperatures and pressures (one a t T' and P, the other a t T and P') still having the same number of molecules.
To the Editor: I do not thiik that Luder's criticism' of I. Prigogine's new book2 "Thermodynamics of Irreversible Processes" represents the opinion of most physical chemists. It is not very often that a leading authority in a branch of science takes time off from his research to write an elementary text, hut this Prigogine has done and to my mind with great success. The topic is presented in an elegant manner, as simply as is possible without enfeebling the subject matter. This implies a degree of difficulty, and it is unlikely that the book can be read profitably by anyone without a sound knowledge of the principles of thermodynamics and some acquaintance L ~ E RW. , F., J. Cmmd. EDUC.,32, M)O (1955). PRIGOGINE, I., "Introduetian to Thermodynamics of Irreversible Processes," Charles C Thomas, Springfield, 1955. 1 2
with the laws of diffusion, conduction of heat, etc., in their mathematical form. Nevertheless, the book should enjoy wide usage by students attempting to learn the methods of irreversible thermodynamics since other works available are either too advanced3 or less general.' In his review Luder has raised some questions on (1) the nature of spontaneous processes and (2) the logical foundations of the thermodynamics of irreversible processes to which I would like to make the following replies: First, though the words "irreversible" and "spontaneous" have differentmeanings and connote two different aspects of a process, they are invariably associated with one another when applied with their usual thermodynamic definitions. To be sure, a spontaneous process can often he made (almost) reversible, but only by precisely balancing the thermodynamic forces of the system and thereby eliminating its spontaneity. All real processes are, by definition, spontaneous and to some degree irreversible. Indeed the equivalence of spontaneity and irreversibility is the essential content of the second law of thermodynamics. Second, Luder has evidently neglected the significance of the subscript i in Prigogine's equations when he states that, "He makes the postulate that the entropy change due to changes inside the system can never be negative in either part." What Prigogine actually states is that d,S 2 0 in both parts of the system, where d,S represents an entropy change which is produced entirely by processes which take place w i t h i the system considered. In other words, it is entropy change remaining after the entropy of heat transfer with the surroundings dQ/T has been suhtracted out. (The entropy of mass transfer must also be suhtracted for an open system.) The second law of thermodynamics states that duS 0 for an entire isolated system during an irreversible process. The fundamental postulate of irreversible thermodynamics states that this is also true for each part of the system. This postulate is not only appealing on the basis of statistical mechanics but has been justified by many successful applications to irreversible processes. The device of breaking up entropy changes into two parts is a feature of many of the continental schools of thermodynamics. Students of thermodynamics in Belgium, Denmark, Holland, and England are introduced to this method very soon after the statement of the second law. It is, of course, only a formal scheme, hut it is a useful one since it focuses the attention very directly on the irreversible phenomena which are responsible for the increase of entropy. JOHN A. SCHELLMAN
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UNIVERSITY OF MINNESOTA MINNEAPOLIS. MINNESOTA
a Ibid.,"Etude Thermodynamique des Phenomines Irreversible~,"Desver, Libge, 1947. ' DEGROOT,S. R., "Thermodyns.mics of Irreversible Processes," Interscience Publishers, Ino., New York, 1951. of the Steady s D ~ K. ~G., ~"The~ Thermodynamics ~ ~ , State," Methuen, London, 1951.
