96.

By means of equations [eqn:(118)] (118) and [eqn:(119)] (119) it is possible to give to the laws of reversible adiabatic compression a form in which their meaning is more clearly seen and which is the generalization of the laws stated in [sect:87.] Sec. 87 for black radiation and a supplement to them. It is, namely, possible to derive [eqn:(105)] (105) again from [eqn:(118)] (118) and [eqn:(99b)] (99b). Hence the laws deduced in [sect:87.] Sec. 87 for the change of frequency and temperature of the monochromatic radiation energy remain valid for a radiation of an originally quite arbitrary distribution of energy. The only difference as compared with the black radiation consists in the fact that now every frequency has its own distinct temperature.

Moreover it follows from [eqn:(119)] (119) and [eqn:(99b)] (99b) that $\frac{{𝗌}^{\prime }}{{\nu }^{\prime 2}}=\frac{𝗌}{{\nu }^2}.\mathrm{\backslash Label}[eqn](125)\text{upshape (125)}$

Now $𝗌d\nu V=𝖲d\nu$ denotes the radiation entropy between the frequencies $\nu$ and $\nu +d\nu$ contained in the volume $V$. Hence on account of [eqn:(125)] (125), [eqn:(99a)] (99a), and [eqn:(99c)] (99c) ${𝖲}^{\prime }d{\nu }^{\prime }=𝖲d\nu ,\mathrm{\backslash Label}[eqn](126)\text{upshape (126)}$ i.e., the radiation entropy of an infinitely small spectral interval remains constant. This is another statement of the fact that the total entropy of radiation, taken as the sum of the entropies of all monochromatic radiations contained therein, remains constant.