104 



BUTLER 



ART. D 



Gibbs points out that these conditions do not depend on the 

 supposition that the volume of each fluid mass is kept constant. 

 The same conditions of equiUbrium can easily be obtained, if we 

 suppose the volumes variable. In this case the equilibrium 

 must be preserved by external pressures P', P" acting on the 

 external surfaces of the fluids, equal to the internal hydrostatic 

 pressures of the liquids p', p". Suppose that external pressures 

 P' and P" are appUed to the two fluids, which are separated by 

 an immovable diaphragm, in some such arrangement as Figure 1. 

 When the volume of the fluid (/) increases by 8v' work is done 

 against the external pressure P' and the energy of the source of 

 this pressure is increased by P'8v'. Similarly when the volume 

 of fluid (//) is increased by 8v", the energy of the source of the 



Fig. 1 



pressure P" is increased by P"hv". These energy changes 

 must be added to the energy change of the fluids in order to 

 find the conditions of equilibrium. The general condition of 

 equilibrium for constant entropy thus becomes 



5e' + Se" + P'y + P"hv" ^ 0. 



(93) [79] 



From this equation we can derive the same internal conditions 

 of equilibrium as before, and in addition, the external conditions : 



p' = P', p" = P". 



When we have a pure solvent Si and a solution of a sub- 

 stance S2 in Si separated by a membrane which is permeable to 



