Question

Derivation for pressure dependence of molar enthalpy and entropy using maxwell's relation

Answer 1

From a Maxwell relation we known that:(∂S∂p)T=−(∂V∂T)pFor gases and most liquids, (∂V∂T)p>0, so indeed the entropy decreases as pressure increases.

Derivation: Starting with the Gibbs free energy relation:dG=VdP−SdT

dG=(∂G∂P)TdP+(∂G∂T)PdT

we find the thermodynamic definition of volume and entropy:V=(∂G∂P)TS=−(∂G∂T)P

since we know from calculus:

∂∂T(∂G∂P)T=∂∂P(∂G∂T)P

It follows that:(∂V∂T)P=−(∂S∂P)T