THERMODYNAMICS OF THE YVOLTAIC CELL. 85 
Hence we have 
T.dpb—dU =E.dq+p.dv. 
Subtract d (pv) from both sides ; we obtain 
T.d¢dB—d U —d (pv) = E. dq—v. dp 
or, for constant temperature 
d(U—T q+ pv)* = —E.dq + v. dp. 
Since the left-hand member of this equation is a perfect differential, 
the right-hand member is also a perfect differential; hence we 
obtain at once 
dv 
— (= p q const. =(s)p const,” °°" + (9) 
From this equation we see that 
(1.) If the volume of a cell is altered by the passage of a 
current through it, the e. m. f. is a function of the 
external pressure. 
(2.) The e. m. f. increases with the pressure if the volume of 
the cell diminishes when it generates a current ; and the 
e. m. f. diminishes as the pressure rises if the volume of 
the cell increases while the cell generates a current. 
These laws were demonstrated—though by somewhat less direct 
reasoning than that employed here—by Duhem.; They were 
ae awards made the subject of an extended investigation by 
Gilbault,{ whose valuable memoir has hitherto received far less 
eeition eke it deserves. 
In accordance with Faraday’s law equation (9) becomes, for 
constant pressure, 
Sv _ Hy—Y ‘ 
Saaiesia (7-P-) 
where v, = initial volume of cell 
v,=final 5 
g =quantity of electrification which has traversed it 
Hence gq —=— 4 — v,. 
a) P 
This equation is easily integrated for solids and liquids, seeing 
that in them v, and v, are sensibly independent of the pressure ; 
the integration is equally easy for gas-cells, provided we assume 
Boyle’s law to hold good throughout the range of pressure 
employed. We may therefore write for solids and liquids, 
Bp Ey, ==) en eee oD) 
* The function U—T g + p v is termed by Duhem the ‘thermodynamic potential at 
constant pressure.” 
+ Duhem ; ‘‘ Le Potential Thermodynamique et ses Applications,” p. 117. 
t Ann. de la Fac. des Sci. de Toulouse, Vol. V, p. A5; C.R, 1891, p. 465. 
