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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...

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Physics

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 thetwo.

(Note: Since the mole number n is just the particle number Ndivided by Avogadro’s number, holding one constant is equivalent toholding the other constant.)

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