Sometimes it is useful to know the free energy of a photon gas.Calculate the (Helmholtz) free energy directly from the definition F =U - TS. (Express the answer in terms of T and V.)

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cegielnikmzjkf · Accepted Answer

Total electromagnetic energy for all frequencies of light is expressed as follows:  U  =            8              π        5            (      k              T        4            )              15      (      h      c              )        3              VThe absolute entropy of the photon gas is  S  =      32    45        π    5    V            (      k      T              )        3                    (      h      c              )        3              kSubstitute:  F  =  U  −  T  S    U  =            8              π        5            (      k      T              )        4                    15      (      h      c              )        3              V    F  =            8              π        5            (      k      T              )        4                    15      (      h      c              )        3              V  −            32              π        5            V        45              (      k      T              )        3                    (      h      c              )        3              k  T    =            8              π        5            (      k      T              )        4                    15      (      h      c              )        3              V  [  1  −      4    3    ]    =            8              π        5            (      k      T              )        4                    15      (      h      c              )        3              V  [  −      1    3    ]    F  =  −      1    3    UHence, the free energy becomes F = -1/3 U

Sometimes it is useful to know the free energy of

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