Blackbody radiation

Blackbody radiation is a thermal equilibrium gas of photons. In units with $k_B=1$, its energy density isand its isotropic radiation pressure is $p=u/3$.

In a large periodic box of volume $V$, one polarization has $V/(2\pi {)}^3$ wavevector modes per unit $d^{3}k$. The two transverse photon polarizations therefore giveafter integration over directions.

For an equilibrium system with energy $E(T,V)$ and no conserved particle number, exactness of the entropy differential obtained from $dE=TdS-PdV$ givesIf $E=aV{T}^4$ and $P=o(T)$ as $T\to 0$, integration gives $P=a{T}^4/3=E/(3V)$.