derived by PLANCK (p. 63 of Vorl. ü. Theor. Physik), from probability considerations, for the state of thermal equilibrium. Here
is the universal constant (see [p. 66]) and the other terms have the same meaning as before.
Isentropic Change
The last reversible process, to be here physically interpreted, is isentropic change from the initial state of thermal equilibrium to its final state. Evidently only the physical elements underlying the bracketed term in Eq. (31) need to be considered.
As we are considering isentropic change (
), it does not make any difference whether on the one hand we think of this isentropic change as accompanied by an increase in temperature and decrease in volume, or on the other hand think of said change as taking place with decrease of temperature and increase of volume. Suppose we assume the latter kind of change. Then from what has preceded we know that increase of volume by itself would increase the number of complexions of the final state, also, from what has gone before, we know that the drop in temperature by itself will lead to decrease in the number of complexions in the final state. These two influences acting simultaneously therefore tend to neutralize each other and if they exist in the proper ratio, derivable from the bracketed quantity in Eq. (31), they will completely balance each other and produce no change whatever in the number of complexions while passing from the initial to the final state of equilibrium, i.e., will produce no change whatever in the entropy of the gas under consideration. In isentropic change Nature has no preference for its various states.
The temperature-entropy diagram considers mainly thermal changes, and as we have considered the influence of both of its co-ordinates in the number of complexions, we can ascertain by proper combination, for any reversible change of state, the corresponding character of the change in the number of complexions. It is evident, too, that in the diagram any reversible change of state is equivalent, so far as the change of entropy in the one body is concerned, to an isentropic change combined with an isothermal change, the latter only affecting the result, so far as change in number of complexions is concerned.