Is it possible to create an explicit function of entropy S(E,V,N) starting from Helmholtz free energy given as F(T,V,N)?

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Kason Gonzales · Accepted Answer

The expression can easily be derived from knowing the differential form. Since we know that  d  E  =  T  d  S  −  p  d  V  +  μ  d  Nand we know as well that  F  =  E  −  T  Sthen differentiating that later  d  F  =  d  E  −  T  d  S  −  S  d  Tand using the first expression for dE you obtain the differential expression desired  d  F  =  −  S  d  T  −  p  d  V  +  μ  d  NThis expression above tells you that F is a potential function (its integral is independent of path, or its values are uniquely determined by its independent variables) when is expressed in terms of T,V,N as you are asking F(T,V,N). It also tells you that  S  =  −            ∂      F              ∂      T      as desired, where entropy will be a function of the same variables   S  =  S  (  T  ,  V  ,  N  )

Is it possible to create an explicit function of entropy S(E,V,N) starting from Helmholtz free energy given as F(T,V,N)?

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