Page:Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt.pdf/4

 and gas molecules will return its average energy to $$\bar{E}$$ by absorbing or releasing energy. Hence, in this situation, dynamic equilibrium can only exist when every resonator has an average energy $$\bar{E}$$.

We apply a similar consideration now to the interaction between the resonators and the ambient radiation within the cavity. For this case, Planck has derived the necessary condition for dynamic equilibrium ; treating the radiation as a completely random process.

He found:



\bar{E}_{\nu} = \frac{L^{3}}{8 \pi \nu^{2}} \rho_{\nu}. $$

Here, $$\bar{E}_{\nu}$$ is the average energy of a resonator of eigenfrequency &nu; (per oscillatory component), L is the speed of light, &nu; is the frequency, and &rho;&nu;d&nu; is the energy density of the cavity radiation of frequency between &nu; and &nu; + d&nu;.