QuestionThermodynamics / equations of state
Which one of the following is the correct thermodynamic equation of state?
- (a) dG = \((\partial G/\partial P)_T\,dP + (\partial G/\partial T)_P\,dT\)
- (b) \((\partial U/\partial V)_T = P + T(\partial P/\partial T)_V\)
- (c) dU = \((\partial U/\partial V)_S\,dV + (\partial U/\partial S)_V\,dS\)
- (d) \((\partial H/\partial P)_T = V - T(\partial V/\partial T)_{P,n}\)
Answer: (d) \((\partial H/\partial P)_T = V - T(\partial V/\partial T)_{P,n}\)
The thermodynamic equations of state: (∂U/∂V)T = T(∂P/∂T)V − P and (∂H/∂P)T = V − T(∂V/∂T)P → (d). (b) has the wrong sign. (a) and (c) are just total differentials, not equations of state.