520 J. W. Gihhs — Eqtdlibrhtm. of Heterogeneous Substances. 



attect(^(l by the saiiu' dirteroiuH', viz., the liciit ol" fusion of an electro- 

 clicmical ('(juivalont oftlic metal. In fact, if such a diiferenee existed, 

 it would he easy to devise arranti;einents by which the heat yielded 

 by a iru'tal in |)assint>; from the licinid 1o the solid state could l)e 

 transfbiiiKMl into electromotive work (and therefore into mecrhanical 

 work) without otiier expendituic. 



The foretijoinn' examples will be snihcient, it is believed, to show 

 the lu'cessity of regardinjf other considerations in (h'termining- the 

 electronu)tive forct^ of a galvanic or electrolytic cell than the variation 

 of its energy aloiu' (when its temperature is supposed to remain con- 

 stant), or corrected only for the work which may be done by external 

 pressures or by gravity. Hut the relations expressed by (693), (694), 

 and (090) nniy be put in a briefer form. 



If we set, as on page 144, 



i/^=e — f //, 



we have, for any constant temperature, 



(///' =i de — t d }f ; 



and for any |>erfect electrochemical apparatus, the temperature of 

 which is maintained constant, 



V" - v =-'^ + -> + -^ ; (097) 



de de de 



and for any cell whatever, when the temperature is nniintained uni- 

 form and constant, 



( Y" — I ") dv ^ — df -f d Wa + dWy.. (098) 



In a cell of any ordinary dimensions, the work done by gravity, as 

 well as the inecpialities of pressure in diHerent parts of the cell may 

 be neglected. If the pressmc as wi'll as the temperature is main- 

 tained uniform and constant, and we set, as on [>age 147, 



K= f - f '/ + /> '\ 

 wliere )i> denotes the pressure in the (rell, and a its total voltinu' (in- 

 cbuling the products of electrolysis), we have 



dt. =z dh — t dii -\- p dv, 

 and for a. perfect electro-chemical apparatus, 



r"_ r'=- f^, (099) 



or lor any cell, 



( V^" — V')de'^ - <ft. (700) 



