Calculus dictates that
(∂U/∂V) T,Ni = T(∂S/∂V)T,Ni – p = T(∂p/∂T)V,Ni – p
(a) Calculate (∂U/∂V) T,N for an ideal gas [ for which p = nRT/V
]
(b) Calculate (∂U/∂V) T,N for a van der Waals gas
[ for which p = nRT/(V–nb) – a (n/V)2 ]
(c) Give a physical explanation for the difference between the
two.
(Note: Since the mole number n is just the particle number N
divided by Avogadro’s number, holding one constant is equivalent...