Question

Obtain an expression for the entropy of an assembly of photons. Using this expression, show that the equation for the adiabate of a photon gas is given by pV4/3= constant.

Answer 1

Enthalpy : $H = U+P\times V$

$S = \frac {4}{3} (\frac{U}{T})$

$S = \frac {4}{3}T^3 \alpha V = constraint$

Thus $V\times T^3= C$

since $P = \frac{1}{3}T^4 \alpha V , V\times T^3 = V\times P^ { \frac {3}{4}} or PV^{\frac {4}{3}}=C.$