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?
As an example, I found the equation of state (EOS) of gaseous and solid Helium is
$P/\rho kT= A+B\rho+C\rho^2+D\rho^3,$
where $A, B, C$ and $D$ are constants, $P, T$ and $\rho$ represent the pressure, temperature and helium atom density respectively, and $k$ is the Boltzmann constant.
Is there any way to calculate the Helmholtz free energy from the above EOS?