When evaluating the thermodynamic properties of a pure substance, when are T and P independent of one another? When evaluating the thermodynamic properties of a pure substance, when are T and P independent of one another? Solution at liquid phase only both are independent to each other according to Gibbs phase rule for pure substance independent intrinsic properties are 2 for example water 0o C to 100o C, T and p are independent to each other for any substance after boiling point T and P dependent to each other at liquid phase ,liquid is incompressible ,after getting vapor phase variations are high.