Gas-liquid phase transition and singularities

A new model for the space of undercritical states of a gas-liquid system is proposed. Simple, physically motivated mathematical hypotheses among which stsbility plays an essential role, determine differential types of germs of pressure and temperature at the critical point. They are connected with the class D⁺₄ of Arnold's classification. The general configuration of vaporization and condensation curves is examined. As a result, Guggenheim's one-third law is obtained.