ON THE SPECIFIC HEAT OF AQUEOUS SOLUTIONS. 
147 
and therefore 
Qt Q t _ 
T—t 
h 2 -h/ 
whence 
( dQ\ _ 
(d±\. 
\ dt / a 
\dRjt 
From the preceding section it follows that 
d\js _ j dx 
dR dll ’ 
and hence we get the result 
Since dx/dR is the contraction which takes place when 1 gr. of water is added to 
an infinite quantity of the solution we get a direct relation between heat of dilution 
and contraction which has been arrived at indirectly through the law developed for 
the specific heats. 
21. Specific Heat in Relation to Free and Combined Water .—In Section 18 the 
specific heat of the solution was considered in relation to the mean specific heat of all 
the water both free and combined. It may now be considered in relation to the 
separate specific heats of the free and combined water, for which purpose we must 
have recourse to the number of molecules of combined water at different dilutions as 
determined in a former paper (Bousfield, ‘Trans. Chem. Soc.,’ vol. 105, p. 1821, 
Table X., 1914). 
Let us examine the matter on the hypothesis 
(1) That the specific heat of the combined water is constant for all dilutions, and 
(2) That the specific heat of the free water is lowered by an amount which is 
proportional to the percentage of the solute. 
The first assumption is probably sufficiently accurate for concentrated solutions, 
where the combined water molecules are few. The second suggested itself as the 
result of an enquiry into the changes which take place in the free water in relation to 
viscosity changes. 
Let ' 
n = molecules of combined water per molecule of solute, 
h—n = molecules of free water per molecule of solute, 
s c = specific heat of combined water (assumed a constant), 
= specific heat of uncombined or free water for which we assume 
= s w —CP, where C is a constant. 
Then we must have 
(he + R) s = Es s + nes c + ( h—n)es F , 
dQ\ 
dt in 
= li Jr 
