ON I N D I F F E R E N T POINTS BYPAULSAUREL
The following properties of an indifferent point of a bivariant or multivariant system are well known : The temperature of the indifferent point which corresponds to a given pressure is a maximum or a minimum of the temperatures at which the system can be in equilibrium under the given pressure ; the pressure of the indifferent point which corresponds to a given temperature is a maximum or a minimum of the pressures under which the system can be in equilibrium at the given temperature. In certain cases, however, it is possible to assert that the temperature of the indifferent point is a maximum and again in other cases it is possible to assert that the pressure of the indifferent point is a minimum. Let us consider first a bivariant or multivariant system consisting of a liquid phase of variable composition and of solid phases of invariable composition, and let us suppose that in a reversible change at the temperature and under the pressure of the indifferent point an increase of entropy is accompanied by an increase in the mass of the liquid phase. It follows from this supposition’ that the system formed by removing the liquid phase cannot be in equilibrium at temperatures higher than that of the indifferent point. It follows, further, that the original system cannot be in equilibrium at temperatures higher than that of the indifferent point, for if it could be in equilibrium, this equilibrium would not be destroyed by the removal of the liquid phase. Thus, in the case under consideration, the temperature of the indifferent point is a maximum. It is to be noticed that if the solid phases were of variable composition the above conclusion could not be drawn. Let us next consider a bivariant or multivariant system consisting of a vapor phase of variable composition and of solid Jour. Phys. Chem. 8,488 (1904).
phases of invariable composition, and let us suppose that in a reversible change at the temperature and under the pressure of the indifferent point an increase of volume is accompanied by an increase in the mass of the vapor phase. It follows from this supposition that the system formed by removing the vapor phase cannot be in equilibrium under pressures lower than that of the indifferent point. It follows, further, that the original system cannot be in equilibrium under pressures lower than that of the indifferent point, for if it could be in equilibrium, the equilibrium would not be destroyed by the removal of the vapor phase. Thus, in the case under consideration, the pressure of the indifferent point is a minimum. I t is to be noticed that if the solid phases were of variable composition the above conclusion could not be drawn. New Yo&, May r5,r904.
