Explaining Photon Entropy: G=<E>-TS+pV

[blueyellow]

i have been revising but in my notes it says this about photon entropy:

G=<E>-TS+pV
=<E>-(4/3)<E>+(1/3)<E>=0

how did they go from 'TS' to (4/3)<E>
and pV to (1/3)<E>?

 

[Bill_K]

Don't know what information you're starting with. Actually it's much easier to argue G = 0 from the beginning! (because photons have zero mass). Otherwise you might get everything by integrating over the Planck distribution. pV = U/3 is often hand-waved (1/3 of the photons hit each wall), and S = 4/3 U/T usually comes from deriving Stefan's law U ~ T⁴ and then integrating dS = dU/T.