Answer to Question #135516 in Optics for alfraid

Question

A cavity contains black body radiation in equilibrium at temperature T. The specific heat per unit volume of the photon gas in the cavity is of the form Cv=γT3,where γ is a constant. The cavity is expanded to twice its original volume and then allowed to equilibrate at the same temperature T. The new internal energy per unit volume is

Answer 1

$c_v=\gamma T^{3}$

also

$C_V=(\frac{du}{dT})_u$ ,therefore,

$\gamma T^{3}=(\frac{du}{dT})$

$\gamma T^3 dT=du$

Integrating both sides

$\int\gamma T^3 dT=\int du$

$\gamma \frac{T^4}{4}=u$ (Internal energy per unit volume)