(a) Derive the following general relations
(i) (∂V∂T)U=−CV1[T(∂T∂p)V−p],
(ii) (∂V∂T)S=−CV1T(∂T∂p)V,
(iii) (∂p∂T)H=Cp1[T(∂T∂V)p−V].
In each case the quantity on the left-hand side is the appropriate thing to consider for a particular type of expansion. State what type of expansion each refers to.
(b) Using these relations, verify that for an ideal gas (∂T/∂V)U=0 and (∂T/∂p)H=0, and that (∂T/∂V)S leads to the familiar relation pVγ=constant along an isentrope.