91Ó°ÊÓ

$P=-{\left(\frac{∂F}{∂V}\right)}_{T,N}$

From thermodynamics Helmholtz free energy is given by

$P=-{\left(\frac{∂F}{∂V}\right)}_{T,N}$

Here, P is the pressure, F is Helmholtz free energy, V s the volume, T is the temperature and N is the number of molecules.

Write the expression for Helmholtz free energy: F=U-T S
Where, U is the internal energy and S is the entropy of the system.
The equilibrium state occurs when the energy of the system is the minimum and when the overall entropy is maximum.

For a given number of molecules and given temperature, the increase in the volume yields an increase in the entropy and decrease in the Helmholtz free energy.
Draw a graph to show the variation of F with V.
Conclusion:
So, the equilibrium condition occurs when the slope of a curve of F verses V is equal