ELECTROCHEMICAL THERMODYNAMICS 713 



If the cell actually discharges at a finite rate, the conditions 

 of reversibility no longer prevail, and the cell is no longer a 

 thermodynamically useful "perfect electrochemical apparatus." 

 On the other hand, if the cell is maintained at constant tem- 

 perature, we have, in general, 



dO 

 dv^-J (5) [695] 



and, therefore, for the electrical work done by the cell, 



(7" - V')de ^ -de + tdr, + dWo + dWp. (6) [696] 



Before proceeding to further discussion of these equations, 

 we shall consider the relation of the reversible electrical work 

 to the work content function \p and the thermodynamic poten- 

 tial f (Gibbs, I, 349). The definition of \p is given by the 

 equation 



yP = e-tn, (7) [87] 



and, therefore, at constant temperature, 



dyp = de - tdr]. (8) 



If this value of {de — tdr]) be substituted in equations (4) and 

 (6), we obtain 



, „ ,s # dWo dWp , , , , 



for the electromotive force of a reversible cell and 



(V" - V')de ^- d^p + dWa + dWp (10) [698] 



for the electrical work of any cell at constant temperature. 



The value of the term due to gravity is extremely small, and 

 negligible in ordinary cells. Further, dWp is the reversible 

 work done on the cell corresponding to the volume contraction 

 or expansion against a pressure p, and is equal to — 'pdv. 

 Hence, for the reversible cell at constant temperature, 



(J" - V')de = -d^p - pdv, (11) 



