When we try to find the heat capacity which will be used to calculate the inner energy, it would not be very hard when neglecting the force interactions between atoms, such as ideal gas. But if we consider the interactions, is it possible to find out the expression of Helmholtz free energy from the EOS?

Sandra Terrell

Sandra Terrell

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2022-08-19

When we try to find the heat capacity which will be used to calculate the inner energy, it would not be very hard when neglecting the force interactions between atoms, such as ideal gas. But if we consider the interactions, is it possible to find out the expression of Helmholtz free energy from the EOS?

Answer & Explanation

Makai Lang

Makai Lang

Beginner2022-08-20Added 11 answers

No way, without additional information. The Helmholtz free energy per particle f = F / N, is related to the pressure P by the relation:
P = ρ 2 f ρ | T
Since the partial derivative is taken at constant T, it could be integrated only within an unknown function of T.
Additional information, like the specific heat, has to be used in order to find the full ρ and T dependence.

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