cv=γT3c_v=\gamma T^{3}cv=γT3
also
CV=(dudT)uC_V=(\frac{du}{dT})_uCV=(dTdu)u ,therefore,
γT3=(dudT)\gamma T^{3}=(\frac{du}{dT})γT3=(dTdu)
γT3dT=du\gamma T^3 dT=duγT3dT=du
Integrating both sides
∫γT3dT=∫du\int\gamma T^3 dT=\int du∫γT3dT=∫du
γT44=u\gamma \frac{T^4}{4}=uγ4T4=u (Internal energy per unit volume)
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