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 expansively b and isothermal compressibility a a dV/V = B dT- a dP 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.