712 EARNED ART. M 



by the system, we obtain 



de = (V - V")de + c?Q + dWa + dWp, (1) [691] 



in which de is the increment in internal energy of the cell, 

 de is the quantity of electricity which passed through the 

 cell, and V and V" the electrical potentials of leads of the 

 same kind of metal attached to the electrodes. Therefore, 

 {V — V")de is the electrical work necessary to charge the cell 

 reversibly, dQ is the heat absorbed from external bodies, 

 dW a is the work done by gravity upon the cell, and dWp, the 

 work done upon the cell when the volume changes. Since no 

 current is flowing, {V" — V) equals the electromotive force, 

 ±^, of the cell.* 



Since all changes are to be reversible, dQ will be transferred 

 to or from the cell under conditions of thermal reversibility, 

 that is to say, the cell at every instant must be at the same tem- 

 perature as the external source from which it receives the heat 

 or by which the heat is withdrawn. This is the only source of 

 change of entropy, and since the above condition of reversibility 

 prevails, the increment in entropy at constant temperature 

 will be 



dv = y • (2) [692] 



The first and second laws, therefore, lead to the equation for the 

 energy increment of the cell, 



de = (F' - V")de + tdtf + dWo + dWp, (3) [693] 



or the equation for the electromotive force, 



, „ „ de td-q dWo dWp , , , , 



* Two conventions regarding the sign of electromotive force are 

 in use. For a given direction of the current through the cell its elec- 

 tromotive force is V" — V or V — V" according to the convention 

 which we adopt. Since this is largely a matter of personal preference, 

 the adoption of one convention or the other will add nothing to the pres- 

 ent general development. Therefore, we shall write ±E for the electro- 

 motive force. 



