# In which cases you use free energy to calculate pressure?

From thermodynamic identity you get: $$\left(\frac{\partial U}{\partial V}\right)_{S,N} = -P$$ But with Helmholtz free energy $$F = U-TS$$, we can also get pressure from this equation: $$\left(\frac{\partial F}{\partial V}\right)_{T,N} = -P.$$ In which cases should you use free energy version?

• Both of them are equivalent. You use the one which best suits your needs. Nov 28, 2021 at 15:58
• As indicated in the index of your function, the first identity apply for S=constant and N=constant while the second one apply for T=constant and N=constant Nov 28, 2021 at 16:25