# Equidistribution 1

Equidistribution in our wave model of blackbody radiation means that the internal energy of different frequencies is the same, that is, all frequencies have the same temperature. More specifically, the internal energy $IE_\nu$ of the wave component of frequency $\nu$ with amplitude $U_\nu$ is measured by (with subindices indicating differentiation with respect to time $t$ and space $x$ and integration in space and time over a period)

• $IE_\nu = \frac{1}{2}\int (U_{\nu ,t}^2+U_{\nu ,x}^2)dxdt$.

Equidistribution means that $IE_\nu$ is the same for all frequencies and then defines a common temperature $T =IE_\nu$.

In the piano model equidistribution corresponds to pressing all the keys with the same force to give all strings of the piano the same string energy.

Planck’s Law $E(\nu ,T) =\gamma T\nu^2$  assumes equidistribution with all frequencies having the same internal energy measured by temperature $T$.

With equidistribution as a characteristic of blackbody radiation the radiation intensity spectrum shows the characteristic quadratic increase with frequency.

Without equidistribution the spectrum can show different dependence on frequency.