 Radiation-to-gas pressure boundary

For a nondegenerate fully ionized gas, equating $P_{\mathrm{gas}}=\rho k_{B}T/({\mu }_{\mathrm{mol}}{m}_u)$ with $P_{\gamma }=a_{\mathrm{rad}}{T}^4/3$ gives $T^3=3k_B\rho /(a_{\mathrm{rad}}{\mu }_{\mathrm{mol}}{m}_u)$. Radiation dominates at higher temperature for fixed density. A degenerate electron gas requires its degeneracy pressure instead of extrapolating this ideal-gas formula.