A RIGOROUS TREATMENT OF THE PHASE RULE

After a critical analysis of the literature, the traditional formulati on of the phase rule proposed by Gibbs is stated in a different form a nd is proved rigorously, together with Gibbs' conjecture on the maximu m number of coexisting phases. A new statement of Gibbs' phase rule is proved for closed systems. Then, Hatsopoulos-Keenan's formulation of the phase rule is restated and proved, both for open and for closed sy stems. The whole treatment of the phase rule presented in this paper h olds both in the presence and in the absence of chemical reactions.