THERMODYNAMICS OF THE VOLTAIC CELL. 75 
Differentiating with respect to g we obtain 
oe 6 UL T oe Gz 
Sa. OD 
= OF ONS. 
== 7 (7) since F depends only 
on the state of the system 
but sa =—E 
dE 6U : 
-E—TSa a : seen (Oo) 
In accordance with Faraday’s law — ae simply the algebraic 
q 
sum of the heats of formation of one electrochemical equivalent 
of each of the active substances produced in the cell. Since the 
heat evolved in any chemical reaction is, for a given temperature, 
simply proportional to the amount of new substance produced, we 
may write (5) thus 
H = E—T 5 Be a ey (2), 
where H denotes the net heat evolved by the formation of one 
electrochemical equivalent of each of the active substances. H 
is of course reckoned here in ergs. If now we denote by o the 
electrochemical equivalent of hydrogen, and by J the mechanical 
equivalent of heat, (C) paras 
ee eS eee 
Sr 
where H' denotes the ee sum of the “heats of formation” — 
as ordinarily tabulated—of the solutions in the cell. This calcu- 
lation enables us to deduce thermochemical constants from 
electrical data. 
The equation (C) was established by Helmholtz* in the first 
of the memoirs cited above, and is now well known as ‘“Helmholtz’s 
Law.” It has been verified in a large number of cases, and now 
takes rank as a well-attested physicallaw. The first experiments 
on the subject are those of Czapskiy; these, however, did little 
more than indicate the superiority of Helmholtz’s law over the 
relation advanced by Lord Kelvin ; they cannot be looked on as 
affording a rigorous verification. This has since been supplied by 
Gockelt and Jahn§ ; the lastnamed observer determined by means 
* Helmholtz’s method of investigation differs from that given here; but it seemed 
advisable to show that the law is directly deducible from the properties of the function F, 
7 Wied. Ann. xxi, p. 209. 
¢ Wied. Ann. xxiv, p. 618. 
§ Wied. Ann. xxviii, p. 21. 
