410 ELECTROCHEMICAL THERMODYNAMICS. 



Returning to equation (4), we may observe that if t under the 

 integral sign has a constant value, say t", the equation will reduce to 



V - V = f/ f -[Q] + [ W] + W P . (6) 



Such would be the case if we should suppose that at the tem- 

 perature t" the chemical processes to which the brackets relate take 

 place reversibly with evolution or absorption of heat, and that the 

 heat required to bring the substances from the temperature of the cell 

 to the temperature t", and that obtained in bringing them back again 

 to the temperature of the cell, may be neglected as counterbalancing 

 each other. This is the point of view of my former letter. I do not 

 know that it is necessary to discuss the question whether any such 

 case has a real existence. It appears to me that in supposing such a 

 case we do not exceed the liberty usually allowed in theoretical 

 discussions. But if this should appear doubtful, I would observe 

 that the equation (6) must hold in all cases if we give a slightly 

 different definition to t", viz., if t" be defined as a temperature deter- 

 mined so that 



t 



The temperature t", thus defined, will have an important physical 

 meaning. For by means of perfect thermo-dynamic engines we may 

 change a supply of heat [Q] at the constant temperature t" into a 

 supply distributed among the various temperatures represented by t 

 in the manner implied in the integral, or vice versa. We may, 

 therefore, while vastly complicating the experimental operations 

 involved, obtain a theoretical result which may be very simply stated 

 and discussed. For we now see that after the passage of the current 

 we may (theoretically) by reversible processes bring back the cell to 

 its original state simply by the expenditure of the heat [Q] supplied 

 at the temperature t", with perhaps a certain amount of work repre- 

 sented by [W], and that the electromotive force of the cell is 

 determined by these quantities in the manner indicated by equation 

 (6), which may sometimes be further simplified by the vanishing 

 of [W] and W P . 



If the current causes a separation of radicles, which are afterwards 

 united with evolution of heat, [Q] being in this case negative, t" 

 represents the highest temperature at which this heat can be obtained. 

 I do not mean the highest at which any part of the heat can be 

 obtained that would be quite indefinite but the highest at which 

 the whole can be obtained. I should add that if the effect of the 

 union of the radicles is obtained partly in work [W], and partly 

 in heat [Q], we may vary the proportion of work and heat; and t" 



