Transformations of thermodynamic systems with the retention of projective invariants

Equations that determined the transformations of thermodynamic properties with the retention of projective invariants and had a solution for thermodynamic systems whose fundamental equation satisfied a certain phenomenological condition were obtained. (The geometric meaning of this condition is the possibility of projective bending of the surface described by the fundamental equation.) It was shown that, for a mixture of ideal gases, there were three sets of solutions, and, for a mixture of real gases in the region of convergence of the virial expansion (with an accuracy to at least the forth virial coefficient inclusive), there was one solution. A second solution appeared if the virial coefficients of intermolecular interactions were related by an additional equation.