408 



ELECTROCHEMICAL THERMODYNAMICS. 



physicists. It has, however, received the unqualified commendation 

 of Professor Maxwell (although not with reference to this particular 

 application see his lecture on the "Equilibrium of Heterogeneous 

 Substances," in the science conferences at South Kensington, 1876); 

 and I do not see how we can do very well without the idea in certain 

 kinds of investigations. 



Hoping that the importance of the subject will excuse the length of 



this letter, 



I remain, 



Yours faithfully, 



J. WILLARD GIBBS. 



New Haven, November 21, 1887. 



Professor OLIVER J. LODGE, 



Dear Sir, As the letter which I wrote you some time since con- 

 cerning the rendement of a perfect or reversible galvanic cell seems to 

 have occasioned some discussion, I should like to express my views a 

 little more fully. 



It is easy to put the matter in the canonical form of a Carnot's 

 cycle. Let a unit of electricity pass through the cell producing 

 certain changes. We may suppose the cell brought back to its 

 original condition by some reversible chemical process, involving a 

 certain expenditure (positive or negative) of work and heat, but 

 involving no electrical current nor any permanent changes in other 

 bodies except the supply of this work and heat. 



Now the first law of thermodynamics requires that the algebraic 

 sum of all the work and, heat (measured in " equivalent " units) 

 supplied by external bodies during the passage of the electricity 

 through the cell, and the subsequent processes by which the cell is 

 restored to its original condition, shall be zero. 



And the second law requires that the algebraic sum of all the heat 

 received from external bodies, divided, each portion thereof, by the 

 absolute temperature at which it is received, shall be zero. 



Let us write W for the work and Q for the heat supplied by ex- 

 ternal bodies during the passage of the electricity, and [W], [Q] for 

 the work and heat supplied in the subsequent processes. 



Then 



and 



a) 



(2) 



where t under the integral sign denotes the temperature at which the 

 element of heat d[Q] is supplied, and tf the temperature of the cell, 

 which we may suppose constant. 



