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Physical significance of entropy or of the second law

Chapter 17: SECTION C NEGATIVE CHANGE OF ENTROPY; SOME OF ITS PHYSICAL FEATURES OR NECESSARY ACCOMPANIMENTS
By Joseph Frederic Klein
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About This Book

The author explains the Boltzmann–Planck interpretation that entropy equals the logarithm of a state's probability, identified with the number of its complexions, and thus measures the permutability or disorder of microscopic motions. He contrasts microscopic and macroscopic descriptions, introduces the hypothesis of elementary chaos, and shows how the calculus of probability applies to aggregates of microstates with many degrees of freedom. The discussion distinguishes settled and unsettled stages, formulates reversibility and irreversibility (including the H-theorem), and treats entropy as the universal criterion and quantitative measure of irreversibility, using these ideas to clarify thermodynamic statements and practical difficulties.

SECTION C

NEGATIVE CHANGE OF ENTROPY; SOME OF ITS PHYSICAL FEATURES OR NECESSARY ACCOMPANIMENTS

A negative transformation in any part of a system is the diminution of entropy which it experiences, and this we know means a diminution in the number of complexions of the part considered. But there are some features of such negative transformations which, while they do not in themselves constitute any additional principle, deserve special mention.

Before we make such mention, however, we will anticipate a little, and state the Second Law in forms which will make said features obvious:

In an irreversible cycle the sum of the changes of entropies experienced by all the bodies concerned is greater than zero. When the cycle is reversible in all of its parts, then said sum of entropy changes is equal to zero.

A corollary from this theorem is that, in a cycle,

All the negative transformations present all the positive transformations that occur.

When there is simply process without the cyclic feature, then the sum of the entropies of all the bodies participating in any one occurrence is, at the end of the change of condition that at the beginning.

From this we see that a negative change of entropy always keeps company with an equal or greater positive change of entropy.

Again, for sake of simplicity, use a gas as an illustration; then we may say: (1) Every possible negative transformation in a gas is always accompanied by a net positive transformation in the other and necessary external agencies. (2) All possible negative transformations in a gas are reversible ones. We here use the word possible because there is an impossible class of negative transformations, namely, those which, so far as order and directness are concerned, are the very opposites of the so-called spontaneous changes of state.

It will suffice here to enumerate these opposites: Without external help (a) to pass heat from a cold to a hot body, (b) to decrease the volume of a gas, (c) to convert the heat of friction directly back into the work which called it forth, (d) to separate the gaseous constituents of a mixture.

By way of contrast we may add, that the so-called spontaneous (irreversible) processes were all positive transformations which took place without any change whatever in surrounding bodies.