Integrating this at constant temperature produces g ( p , T ) = g A ( T ) + ∫ ∫ p A p v ( p ¯ ¯ , T ) d p ¯ ¯ here g A is a constant of integration, but the constant is different for each isotherm hence it is written as a function of T . In order to evaluate g one must invert p = p ( v , T ) to obtain v = v ( p , T ) . However, it is the nature of the phase transition phenomenon that this inversion is not unique; for example the van der Waals quation written for v is, p v 3 − − ( p b + R T ) v 2 + a v − − a b = 0 ,