Is there a way to calculate the coefficient of thermal expansion ( α) from Helmholtz free energy (A) ?

Question

Is there a way to calculate the coefficient of thermal expansion (  α) from Helmholtz free energy (A) ?

Gaige Burton · Accepted Answer

Kind of, in differential form we have:  d  A  =  −  S  d  T  −  p  d  VIf we Sub in:  d  V  =  (            ∂      V              ∂      T            )    p    d  T  +  (            ∂      V              ∂      p            )    T    d  pWe get:  d  A  =  −  S  d  T  −  p  [  (            ∂      V              ∂      T            )    p    d  T  +  (            ∂      V              ∂      p            )    T    d  p  ]So  (            ∂      A              ∂      T            )    p    =  −  S  −  p  (            ∂      V              ∂      T            )    p  So:      1    V    (            ∂      V              ∂      T            )    p    =  −      1          p      V        [  S  +  (            ∂      A              ∂      T            )    p    ]

Is there a way to calculate the coefficient of thermal expansion (alpha) from Helmholtz free energy (A) ?

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