Thermal radiation can be treated thermodynamically as a gas of photons with internal energy U = u(T) V and pressure p = u(T)/3 where u(T) is the energy density. Show that
(a) entropy density s is given by s = 4p/T
(b) Gibbs function = 0
(c) heat capacity at constant volume Cv = 3s per unit volume
(d) heat capacity at constant pressure Cp is infinite.
I've done (a), (b), but am having trouble on (c). I guess im trying to find T(Ds/DT) where capital D is partial.. but Im having touble arriving at 3s..
any hints? Thanks!
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