Temperature scaling of thermal photon number and energy densities (source code)

= Temperature scaling of thermal photon number and energy densities

Changing variables to $x=h\nu/(k_BT)$ in the Planck distribution gives
$$
n=\alpha T^3,
\qquad
\rho=\xi T^4,
$$
where $\alpha$ and $\xi$ are temperature-independent constants.