338 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



General Properties of a Perfect Electro-chemical Apparatus. 



When an electrical current passes through a galvanic or electro- 

 lytic cell, the state of the cell is altered. If no changes take place in 

 the cell except during the passage of the current, and all changes 

 which accompany the current can be reversed by reversing the 

 current, the cell may be called a perfect electro-chemical apparatus. 

 The electromotive force of the cell may be determined by the 

 equations which have just been given. But some of the general 

 relations to which such an apparatus is subject may be conveniently 

 stated in a form in which the ions are not explicitly mentioned. 



In the most general case, we may regard the cell as subject to 

 external action of four different kinds. (1) The supply of electricity 

 at one electrode and the withdrawal of the same quantity at the 

 other. (2) The supply or withdrawal of a certain quantity of heat. 

 (3) The action of gravity. (4) The motion of the surfaces enclosing 

 the apparatus, as when its volume is increased by the liberation of 

 gases. 



The increase of the energy in the cell is necessarily equal to that 

 which it receives from external sources. We may express this by the 

 equation 



de = (V- W'yde+dQ+dWe+dWf, (691) 



in which de denotes the increment of the intrinsic energy of the cell, 

 de the quantity of electricity which passes through it, V and V" 

 the electrical potentials in masses of the same kind of metal con- 

 nected with the anode and cathode respectively, dQ the heat received 

 from external bodies, dW G the work done by gravity, and dW P the 

 work done by the pressures which act on the external surface of the 

 apparatus. 



The conditions under which we suppose the processes to take 

 place are such that the increase of the entropy of the apparatus is 

 equal to the entropy which it receives from external sources. The 

 only external source of entropy is the heat which is communicated 

 to the cell by the surrounding bodies. If we write drj for the 

 increment of entropy in the cell, and t for the temperature, we have 



(692) 

 Eliminating dQ, we obtain 



(693) 



or 



v ,, v ,_ de dr\ dW G f 

 v v = -j--\-t -j-H j -- -j . (toy4) 



de de de de 



It is worth while to notice that if we give up the condition of the 

 reversibility of the processes, so that the cell is no longer supposed 



