Mean photon energy ($⟨E_{\gamma }⟩=\frac{{\pi }^4}{30\zeta (3)}T\simeq 2.701T$)

The number and energy integrals of a zero-chemical-potential photon gas give $n=2\zeta (3)T^3/{\pi }^2$ and $\rho ={\pi }^2{T}^4/15$ in natural units. Their ratio is the mean energy per photon. It is useful for converting a relic number-density ratio into an energy-density ratio.