1910-11.] Temperature Coefficient of Concentration Cells. 383 
when P W P S are the solution pressures of the metal in the two solvents, 
then if the partition ratio varies with temperature we must have a 
temperature coefficient as observed, because c w and c s at a higher or lower 
temperature are no longer the partition equilibrium concentrations. 
The temperature coefficient is therefore 
de 
Jt 
= R log 
since 
+ • 
RT dl\ 
dt 
RT<*P. =nT (J^dP w _J^dP I \ 
P s dt VP„ dt P s dt) * K h 
R (log log-^-^j = 0 by (1). 
\ ('w e s / 
The signs of the T.C. will therefore be positive or negative according 
.as i s greater or less than . 
P w dt 6 P s dt 
A simple concentration cell which is at zero E.M.F. at t will have no 
temperature coefficient, for in this case P w = P s , and therefore 
de _ r / 1 dV w _ 1 d?\_ 
dfi \n w dt P w dt) ' 
I prefer, however, to approach the matter in another way, which seems 
to me to lead us further into an understanding of these cells and their 
behaviour. 
The actual and only physical result of the passage of a current through 
the alcohol water cell with its silver silver iodide electrodes is the transfer 
of a certain quantity of potassium iodide from the one solvent to the other. 
JSlow we know that the solution of potassium iodide in water results in a 
large absorption of heat, and this absorption is not entirely due to the 
conversion of the potassium iodide from the solid to the fluid condition, 
as there is a further absorption of heat on diluting the solution. We do 
not know the latent heat of solution of KI in alcohol. It may be positive 
or negative, though doubtless small in amount. 
We are considering, here, not the latent heat involved in passing from 
the solid salt to the solvent, but the difference in latent heats involved in 
passing a molecule of the salt from the one solvent to the other solvent. 
This difference of latent heats is the only apparent source of energy 
.available to give us a voltaic cell from these materials which is both doing 
external work and producing heat. 
Let, then, A r be the latent heat due to the solution of one gramme 
molecule of potassium iodide in water (calling heat absorbed positive) and 
A the latent heat of solution of an equal quantity of salt in alcohol, then 
applying the Helmholtz equation (our unit quantity of electricity being 
still defined as that necessary to transfer a gramme molecule of the salt), 
