﻿242 Mr. Bernard Cavanagh on 



to the expansions of U and Y, the total energy and volume 

 o£ the solution. (Fuller consideration is postponed, as this 

 paper is already rather long.) 

 In " perfect " solution we have 



U = %n 0l u 01 -f %n s u 

 and 



■„ } • • • ■ (39) 



+ 2<n s v s J 



V = %n 0l v 0l 



Q = %n 01 q 01 + %n s q s , (40) 



where, according to the usage of the previous paper, Q is 

 (U+joV), q s is (iis+pvs), etc., and we can write this 



Q = M 2coi?oi+2w,ft (41) 



2coi#oi> however, depends (through c 01 , c 02 ; . . . .) upon the 

 concentrations of solutes present, but has, in the pure 

 solvent, a limiting value <^m depending only on T and p, and 



tc 01 q 01 = q M +%qoi\ dcoi . • • • (42) 



Jc=o 



= q M + %q 01 Ac 01 (43) 



And so 



Q = M ? M +2w^ + M SgoiAc i. . • ■ ( u ) 



Dilute now such a solution "infinitely" by adding a large 

 mass M(/ of pure solvent at the same T and jo, for which 



Q' = M '^M. 



The united heat will be 



(Q+Q') = (Mo + MoO^M + Sw^ + MoSgoiAcoi. 



But since the solution is now " infinitely " dilute, we shall 

 have on bringing it to the original temperature and pressure 



Q"= (Mo + M ')?m+2m^= (Q 4 Q / )-M 2?oiAc i. 



In other words, MqX^oi^^oi was the heat developed (evolved) 

 on diluting the %n 8 molecules of solute. 

 That is, there is a heat of dilution of 



ytq 01 Ac 0l (45) 



per gram-molecule of solute, in " perfect " solution in a 

 " complex " solvent. The explanation of this apparent 



