Find the fundamental equation of a monoatomic ideal gas in Helmholtz Representation, where F = U − T S

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Find the fundamental equation of a monoatomic ideal gas in Helmholtz Representation, where  F  =  U  −  T  S

Javier Mathis · Accepted Answer

F    0   is the Helmholtz free energy at   T  =      T    0  ,   V  =      V    0  ,   N  =      N    0  . So       F    0    =      3    2        N    0    R      T    0    −      T    0        N    0        s    0   and             F      0                      N        0            R              T        0              =      3    2    −            s      0        R  . You can show  F  =  N  R  T  {            F      0                      N        0            R              T        0              −  ln  ⁡  [  (      T          T      0            )          3              /            2        (      V          V      0        )  (            N      0        N        )          −      1        ]  }  =  N  R  T  (      3    2    −            s      0        R    )  +  N  R  ln  ⁡  [  (      T          T      0            )          3              /            2        (      V          V      0        )  (            N      0        N        )          −      1        ]  =      3    2    N  R  T  −  T  (  N      s    0    +  N  R  ln  ⁡  [  (      T          T      0            )          3              /            2        (      V          V      0        )  (            N      0        N        )          −      1        ]  )and you derived the formula correctly.

Find the fundamental equation of a monoatomic ideal gas in Helmholtz Representation, where F=U−TS

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