 Thermodynamic derivation of blackbody radiation pressure (source code)

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= Thermodynamic derivation of blackbody radiation pressure

For an equilibrium system with energy $E(T,V)$ and no conserved particle number, exactness of the entropy differential obtained from $dE=T\,dS-P\,dV$ gives
$$
\left(\frac{\partial E}{\partial V}\right)_T
=T\left(\frac{\partial P}{\partial T}\right)_V-P.
$$
If $E=aVT^4$ and $P=o(T)$ as $T\to0$, integration gives $P=aT^4/3=E/(3V)$.

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