348 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



as normal and which are to be rejected as involving secondary 

 processes.* 



If in any case secondary processes are excluded, we should expect 

 it to be when the ion is identical in substance with the electrode upon 

 which it is deposited, or from which it passes into the electrolyte. 

 But even in this case we do not escape the difficulty of the different 

 forms in which the substance may appear. If the temperature of the 

 experiment is at the melting point of a metal which forms the ion 

 and the electrode, a slight variation of temperature will cause the 

 ion to be deposited in the solid or in the liquid state, or, if the current 

 is in the opposite direction, to be taken up from a solid or from a 

 liquid body. Since this will make a considerable difference in the 

 variation of energy, we obtain different values for the electromotive 

 force above and below the melting point of the metal, unless we 

 also take account of the variations of entropy. Experiment does 

 not indicate the existence of any such difference,! and when we take 

 account of variations of entropy, as in equation (694), it is apparent 



Ci ( CM W 



that there ought not to be any, the terms -T- and t-^- being both 



affected by the same difference, viz., the heat of fusion of an electro- 

 chemical equivalent of the metal. In fact, if such a difference existed, 

 it would be easy to devise arrangements by which the heat yielded 

 by a metal in passing from the liquid to the solid state could be 

 transformed into electromotive work (and therefore into mechanical 

 work) without other expenditure. 



The foregoing examples will be sufficient, it is believed, to show 

 the necessity of regarding other considerations in determining the 

 electromotive force of a galvanic or electrolytic cell than the variation 

 of its energy alone (when its temperature is supposed to remain con- 

 stant), or corrected only for the work which may be done by external 



* It will be observed that in using the formulae (694) and (696) we do not have to 

 make any distinction between primary and secondary processes. The only limitation 

 to the generality of these formulae depends upon the reversibility of the processes, 

 and this limitation does not apply to (696). 



t M. Raoult has experimented with a galvanic element having an electrode of bis- 

 muth in contact with phosphoric acid containing phosphate of bismuth in solution. 

 (See Comptes J&ndus, t. Ixviii, p. 643.) Since this metal absorbs in melting 12*64 

 calories per kilogramme or 885 calories per equivalent (70 ki1 -), while a Daniell's cell 

 yields about 24000 calories of electromotive work per equivalent of metal, the solid or 

 liquid state of the bismuth ought to make a difference of electromotive force repre- 

 sented by '037 of a Daniell's cell, if the electromotive force depended simply upon the 

 energy of the cell. But in M. Raoult's experiments no sudden change of electromotive 

 force was manifested at the moment when the bismuth changed its state of aggrega- 

 tion. In fact, a change of temperature in the electrode from about fifteen degrees 

 above to about fifteen degrees below the temperature of fusion only occasioned a 

 variation of electromotive force equal to '002 of a Daniell's cell. 



Experiments upon lead and tin gave similar results. 



