by the first law,
Although the property changes and are zero for each process, Q and W are path-dependent. Since the work for each of these mechanically reversible processes is given by , the work for each process is proportional to the total area below the paths on the PV diagram representing the process. The relative sizes of these areas correspond to the numerical values of W.
For application to the change of state described, equations require integration. Since enthalpy and entropy are state functions, the path of integration is arbitrary. Since the data indicate that CP is a weak function of T and that both V and β are weak functions of P, integration with arithmetic means is satisfactory. The integrated forms of Eqs that result are: