157.

The entropy of a ray is, of course, also determined by its temperature. In fact, by combining equations [eqn:(138)] (138) and [eqn:(274)] (274) we readily obtain as an expression for the entropy radiation $𝖫$ of a monochromatic plane polarized ray of the specific intensity of radiation $𝖪$ and the frequency $\nu$, $𝖫=\frac{k{\nu }^2}{c^2}\{(1+\frac{c^2𝖪}{h{\nu }^3})\log (1+\frac{c^2𝖪}{h{\nu }^3})-\frac{c^2𝖪}{h{\nu }^3}\log \frac{c^2𝖪}{h{\nu }^3}\}\mathrm{\backslash Label}[eqn](278)\text{upshape (278)}$ which is a more definite statement of equation [eqn:(134)] (134) for Wien's displacement law.

Moreover it follows from [eqn:(135)] (135), by taking account of [eqn:(273)] (273), that the space density of the entropy $𝗌$ of uniform monochromatic unpolarized radiation as a function of the space density of energy $𝗎$ is $\Squeeze[0.95]{$\displaystyle \mathsf{s} = \frac{8\pi k\nu^{2}}{c^{3}} \biggl{ \biggl(1 + \frac{c^{3}\mathsf{u}}{8\pi h\nu^{3}}\biggr) \log\biggl(1 + \frac{c^{3}\mathsf{u}}{8\pi h\nu^{3}}\biggr) - \frac{c^{3}\mathsf{u}}{8\pi h\nu^{3}} \log\frac{c^{3}\mathsf{u}}{8\pi h\nu^{3}}\biggr}.$\}\mathrm{\backslash Label}[eqn](279)\text{upshape (279)}$ This is a more definite statement of equation [eqn:(119)] (119).