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U proportional to T^4 for photon gas

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Solution Preview

Substitute P = 1/3 u and E = u V in:

dE = T dS - P dV

to write it as:

dS = 1/T d(uV) + u/(3T) dV

Next use

d(uV) = V du + u dV to write it as:

dS = ...

Solution Summary

A detailed derivation is given.