LEWIS. — THE LAW OF PHYSICO-CHEMICAL CHANGE. 53 



The total amouut of work gained, the sum of these terms, is equal to 

 the total amount of heat transformed into work, that is, 



W, ^ W, + W, + W, = d Q = ^d T, 

 from equation (3). Adding the terms we obtain, 



Q 



or writing so as to express the constancy of P, 



Q 



(9p\ _J 



T 



(7) 



This important result may be derived directly from equations (4) and 

 (6) and for solids as well as liquids. Since the vapor pressure is a func- 

 tion of the temperature, T, and the pressure on the surface, P, we may 

 write 



^9 T J p \9 P y T 



Now, in general, when only a pure substance and its vapor are present, 

 the change in pressure on the surface of the substance is merely the 

 change in vapor pressure, that is, 



dP=dp. 



Moreover, ( ^^ ) = — , from equation (6), therefore, 



dp. • / ,\ 



Substituting for -^ from equation (4), 



dT 





oritfe^ =A, 



9TL, v^T 



which is equation (7). "We have in this equation a marked simplifica- 

 tion of the Clausius formula with no loss of exactness. We could now, 

 by making the single assumption that the vapor obeys the gas law, throw 

 equation (7) into the form analogous to (5), namely. 



\9T )p~ RT-' 



