ON THE SPECIFIC HEAT OF AQUEOUS SOLUTIONS. 
141 
is the value of x when H = o, v 0 being the specific volume of the liquid solute. To 
apply this to the case of a solid solute the specific volume of the liquefied solute 
as it exists in the solution must be deduced by the help of the data above-mentioned. 
It will be shown later that for NaCl solutions the value of En 0 (a gramme molecule 
of the liquefied solute) at 20 C. may be taken as 25'053 c.c. 
If w M is the mean specific volume of all the water in the solution, both free and 
combined, then 
(E + H)v = Ei; 0 + H %, 
and therefore 
Hw M = Hw + E (w—v 0 ) — (E + H) (w—v), 
and since 
X = (E + H)(w-v) and Xu = E (w—v 0 ), 
we have 
H {w-wf) = x-Xo, 
or writing iv—w u = A%, the change in the mean specific volume of the water, we 
have 
Aw u = A X JH, 
which also obviously follows from the mere fact that we treat Ev 0 as a constant, 
considering the whole contraction on dilution as due to changes in the density of the 
water. 
Either of the quantities A% or A xo/H is the contraction per gramme (or the 
specific contraction) of the water of the solution. 
18. Relation of Specific Heat Lowering to Specific Contraction of the Water. —In 
the search for the true relation between specific heat and specific volume changes the 
values of As 20 were plotted on the specific contraction of the water. The values 
of Ay 0 at 20° C., taking E-y 0 = 25'053, are set out in Table XIY. together with the 
values of As 20 and of the specific contraction. They are plotted in fig. 5. 
Table XIY. —NaCl Solutions at 20° C. 
No. of 
solution. 
ASoq. 
A Xo- 
Axo/#. 
As'20, 
calculated. 
Difference. 
I. 
0-881 
■ 
4-04 
0-02304 
0-880 
- 1 
II. 
0-735 
4-82 
0-01927 
0-736 
+ 1 
III. 
0-575 
5-66 
0-01513 
0-578 
+ 3 
IV. 
0-449 
6-23 
0-01185 
0-453 
+ 4 
V. 
0-268 
6-93 
0-00707 
0-270 
+ 2 
VI. 
0-145 
7-60 
0-00384 
0-147 
+ 2 
VII. 
0-076 
8-00 
0-00201 
0-077 
+ 1 
The graph shown in fig. 5 looks an excellent straight line which may be represented 
b y 
A.s- 20 = 38'2 A X JH. 
