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
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Expert's answer
2020-10-01T09:58:39-0400
"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)
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