Sometimes it is useful to know the free energy of a photon
Chapter 7, Problem 46P(choose chapter or problem)
Problem 46P
Sometimes it is useful to know the free energy of a photon gas.
(a) Calculate the (Helmholtz) free energy directly from the definition F = U − TS. (Express the answer in terms of T and V.)
(b) Check the formula for this system.
(c) Differentiate F with respect to V to obtain the pressure of a photon gas. Check that your result agrees with that of the previous problem.
(d) A more interesting way to calculate F is to apply the formula F = –kT In Z separately to each mode (that is, each effective oscillator), then sum over all modes Carry out this calculation, to obtain
Integrate by parts, and check that your answer agrees with part (a).
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