91.

We have so far applied Wien's displacement law only to the case of black radiation; it has, however, a much more general importance. For equation [eqn:(95)] (95), as has already been stated, gives, for any original spectral distribution of the energy radiation contained in the evacuated cavity and radiated uniformly in all directions, the change of this energy distribution accompanying a reversible adiabatic change of the total volume.

Every state of radiation brought about by such a process is perfectly stationary and can continue infinitely long, subject, however, to the condition that no trace of an emitting or absorbing substance exists in the radiation space. For otherwise, according to [sect:51.] Sec. 51, the distribution of energy would, in the course of time, change through the releasing action of the substance irreversibly, i.e., with an increase of the total entropy, into the stable distribution corresponding to black radiation.

The difference of this general case from the special one dealt with in the preceding chapter is that we can no longer, as in the case of black radiation, speak of a definite temperature of the radiation. Nevertheless, since the second principle of thermodynamics is supposed to hold quite generally, the radiation, like every physical system which is in a definite state, has a definite entropy, $S=Vs$. This entropy consists of the entropies of the monochromatic radiations, and, since the separate kinds of rays are independent of one another, may be obtained by addition. Hence $s={\int }_0^{\infty }𝗌d\nu ,S=V{\int }_0^{\infty }𝗌d\nu ,\mathrm{\backslash Label}[eqn](113)\text{upshape (113)}$ where $𝗌d\nu$ denotes the entropy of the radiation of frequencies between $\nu$ and $\nu +d\nu$ contained in unit volume. $𝗌$ is a definite function of the two independent variables $\nu$ and $𝗎$ and in the following will always be treated as such.