270 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 

 The increase of the volume of liquid will be 



' (589) 



and the diminution of the volume of vapor 



a/ *; (1) TV (590) 



*%/ I 77 ff 1 



Hence, for the work done (per unit of surface formed) by the 

 external bodies which maintain the pressure, we shall have 



(591) 



'/M '/M vjr Y ' 



and, by (514) and (131), 



-rrr_ d<T dt d(T _ d<T /KQO\ 



^ c cp -*a_p dlogp' 



The work expended directly in extending the film will of course 

 be equal to cr. 



Let us now consider the case in which there are two component 

 substances, neither of which is confined to the surface. Since we 

 cannot make the superficial density of both these substances vanish 

 by any dividing surface, it will be best to regard the surface of 

 tension as the dividing surface. We may, however, simplify the 

 formula by choosing such substances for components that each homo- 

 geneous mass shall consist of a single component. Quantities relating 

 to these components will be distinguished as on page 266. If the 

 surface is extended until its area is increased by unity, while heat 

 is added at the surface so as to keep the temperature constant, and 

 the pressure of the homogeneous masses is also kept constant, the 

 phase of these masses will necessarily remain unchanged, but the 

 quantity of one will be diminished by F, , and that of the other by r,,. 



r r 



Their entropies will therefore be diminished by ,?]? and jfrjy', 



respectively. Hence, since the surface receives the increment of 

 entropy q a , the total quantity of entropy will be increased by 



_r, ,_r, 

 7/8 y' ^ 7" nv ' 



which by equation (580) is equal to 



\dt/ p ' 



Therefore, for the quantity of heat Q imparted to the surface, we 

 shall have 



Q= _(?) =_(*!_). (593) 



\dt/ n \dLOt/ n 



