THE PHYSICAL SIGNIFICANCE OF ENTROPY
AND OF THE SECOND LAW

[There is no difference between change of Entropy and Second Law, when each is fully defined.]

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INTRODUCTION

PURPOSE, ACKNOWLEDGMENTS, THE TWO METHODS OF APPROACH
AND OUTLINE OF TREATMENT

THIS article is intended for those students of engineering who already have some elementary knowledge of thermodynamics. It is intended to clear up a difficulty that has beset every earnest beginner of this subject. The difficulty is not one of application to engineering problems, although here too there have been widespread misconceptions,[1] for the expressions developed by CLAUSIUS are simple, have long been known and much used by engineers and physicists. The difficulty is rather as to the ultimate physical meaning of entropy. This term has long been known as a sort of property of the state of the body, has long been surmised to be of essentially a statistical nature, but with it all there was a sense that it was a sort of mathematical fiction, that it was somehow unreal and elusive, so it is no wonder that in certain engineering quarters it was dubbed the "ghostly quantity."

Now this instinct of the true engineer to understand things down to the bottom is worthy of all encouragement and respect. For this reason and because the matter is of prime importance to the technical world, the final meaning of entropy (i.e., of the Second Law) must be clarified and realized. Indeed, we may well go beyond this somewhat narrow view and say that this is well worth doing because change of entropy constitutes the driving motive in all natural events; it has therefore a reach and a universality which even transcends that of the First Law, or Principle of the Conservation of Energy.

In striving to present the physical meaning of entropy and of the Second Law, the writer cannot lay claim to any originality; he has simply tried here to put in logical order the somewhat scattered propositions of the leading investigators of this subject and in such a way that the difficulties of apprehension might be minimized; in other words, to present the solutions of his own difficulties, in the hope that the solutions may be helpful to other students of engineering and thermodynamics. In overcoming these difficulties, the writer owes everything to the books and papers by PLANCK and BOLTZMANN, pre-eminently to PLANCK, who has so clearly and appreciatively interpreted the life work of BOLTZMANN.[2] The writer furthermore wishes to say that he has not hesitated here to quote verbatim from both these investigators and not always so that their own statements can be distinguished from his own. If any part of this presentation is particularly clear and exact the reader will be safe in crediting it to one or the other of these two investigators and expositors, although it would not be right to consider them responsible for everything contained in this little book.

In considering the proper approach to the matter in hand we must remember that[3] "in physical science there are two more or less distinct modes of attack, namely, (a) a mode of attack in which the effort is made to develop conceptions of the physical processes of nature, and (b) a mode of attack in which the attempt is made to correlate phenomena on the basis of sensible things, things that can be seen and measured. In the theory of heat the first mode is represented by the application of the atomic theory to the study of heat phenomena, and the second mode is represented by what is called thermodynamics." In solving the special problem before us, as to the physical meaning of entropy and of the Second Law, our main dependence must be on the first mode of attack.

The second mode will furnish checks and confirmations of the results developed by the first, or we may say that the combination of the two modes will give the well-established characteristic equations and relations of bodies and their physical elements.

The whole discussion will now be taken up in a non-mathematical way, without the full proof required by a complete presentation, and about in this order:

(a) The definitions, general preliminaries and current statements of the matters considered.

(b) More or less precise statement of the primary relations and theorems.

(c) The physical interpretations.

(d) Summary of the connection between probability, irreversibility, entropy and the Second Law.

(e) Reach or scope of the Second Law.

On account of the difficulty which every student experience in realizing the physical nature of entropy we will in the main confine our attention here to gases and indeed to their simplest case, the monatomic gas, and will as usual assume that the dimensions of an atom or particle are very small in comparison with the average distance between two adjacent particles, that for the atoms approaching collision the distance within which they exert a significant influence on each other is very small as compared with the mean distance between adjacent atoms, and that between collisions the mean length of the particle's path is great in comparison with the average distance between the particles. Later on we will indicate in a very general and brief way how the entropy idea may be extended to other states of aggregation and to other than purely thermodynamic phenomena. Mostly, therefore, we will only consider states and processes in which heat phenomena and mechanical occurrences take place.