268 proceedings of the american academy. 



Applications of the Preceding Equations. 



A few examples will serve to illustrate the raode of application of 

 equations V and VIII. 



Two phases of the same substance, ice and water, for example, are in 

 equilibrium at a given temperature and pressure. If the pressure on 

 either phase alone is increased, the activity in that phase is increased, 

 and the phase must disappear. If the pressure upon both phases is 

 increased by the same amount, the activity is increased more in the 

 phase of largest molecular volume, namely the ice, and it will disappear. 

 By increasing the pressure on the ice by the amount dP, and that on 

 the water by a greater amount, dP', it is possible to maintain equilib- 

 rium. Let us see what relation these two increments of pressure 

 must bear to each other. Let $, P, v, and $', P', v', represent the 

 activity, pressure, and molecular volume of the ice and the water, re- 

 spectively. From equation V, 



c? In f = -jT77,dP, and d In ^' = -^4P'. 

 lb 1 li, 1 



In order to maintain equilibrium we must always keep I equal to ^'. 

 Hence, 



d^ = di', or d\a^ = d In i'. 



Therefore the condition of continued equilibrium is, 



^dP — -jyyj^dP' and 



MT RT dP' V 



In order to maintain equilibrium the increments of pressure on the 

 two phases must be inversely proportional to the molecular volumes.^ 



As a second illustration let us consider the same system of ice and 

 water subject to a simultaneous change of pressure and temperature. 

 The effect of increasing the pressure equally on both phases is to in- 

 crease the activity of the ice more than that of the water. An increase 

 of temperature has the same effect. By increasing the pressure and at 

 the same time lowering the temperature, equilibrium may be maintained. 

 The condition of equilibrium, as in the preceding case, is, 



dhi^ = d\n^>, 



but in this case the change in t and in i' is due in part to change in 

 temperature, in part to change in pressure, that is, 



8 For a proof of this equation by otlier metho'ds, see Lewis, Z. physik. Chem., 

 35, 343 (1900) ; These Proceedings, 36, 115 (1900). 



