# Finding a Helmholtz free energy from the equation of state

Finding a Helmholtz free energy from the equation of state
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Momellaxi
The Helmholtz free energy per particle $f=F/N$, is related to the pressure P by the relation:
$P={\rho }^{2}{\frac{\mathrm{\partial }f}{\mathrm{\partial }\rho }|}_{T}$
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 $\rho$ and T dependence.