 Thermodynamic derivation of blackbody radiation pressure

ID: 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

d E = T d S - P d V

gives

(\frac{\partial E}{\partial V})_{T} = T (\frac{\partial P}{\partial T})_{V} - P .

E = aV T^{4}

and

P = o (T)

T \to 0

, integration gives

P = a T^{4} /3 = E / (3 V)

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