(a) Which of the following is zero for an ideal gas?
(a) (∂U/∂T)V
(b) (∂U/∂V)T
(c) (∂H/∂T)P
(d) (∂P/∂V)T
(b) Using the equation Cp,m - Cv,m = [p + (∂U/∂V)T](∂V/∂T)p, show that for an ideal gas, Cp,m - Cv,m = R. Here Cp,m is the molar heat capacity of the gas at constant pressure.
(c) By suitable manipulation of the partial differential equation (∂U/∂V)T = 0, and H = U + PV, show that for an ideal gas (∂H/∂P)T = 0.