12-83 For a homogeneous (single-phas
e) simple pure substance, the pressure and temperature are independent properties, and any property can be expressed as a function of these two properties. Taking v = v(P, T), show that the change in specific volume can be expressed in terms of the volume expansivity b and isothermal compressibility a as
Also, assuming constant average values for b and a, obtain a relation for the ratio of the specific volumes v2/v1 as a homogeneous system undergoes a process from state 1 to state 2.