Chapter 12.6, Problem 88RP

For a homogeneous (single-phase) 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 β and isothermal compressibility α as

$\frac{dv}{v}=\beta dT=\alpha dP$

Also, assuming constant average values for β and α, 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.