448 MEASUREMENT OF ELECTROMOTIVE FORCES. 



We may consider the state of an element as defined by three 

 independent variables the temperature T, the quantity x of elec- 

 tricity which has traversed it starting from a certain initial condition, 

 and the degree of concentration of the solutions. In order to 

 allow for this latter variable, suppose the system contained in the 

 barrel of a pump in which is water in a state of saturation. By 

 raising or lowering the piston, the concentration can be varied at 

 pleasure, and the volume v of the system taken as a third inde- 

 pendent variable. If the couple can be regenerated by the current, 

 we may make it traverse a closed cycle. In this case the work 

 produced -W is equivalent to the thermal energy absorbed JQ. 

 Let / be the maximum elastic force for the temperature T, E the 

 electromotive force of the couple, U the internal energy of the 

 system ; generalising the reasoning used in 645 and 646, we see 

 that the expression 



should be an exact differential. We have further 



c being the thermal capacity of the couple, l^ and / 2 the coefficients 

 defined by the equation itself. 



If the external resistance is so great that the heat disengaged 

 in virtue of Joule's law may be neglected, we may consider the 

 cycle as reversible, and apply Carnot's principle. 



The influence of the concentration of the liquid may be studied 

 by the properties of the coefficient / 2 . Consider only the inde- 

 pendent variables T and x ; observing that in the present case 



equation (5) of 646 gives 



From this follows the important fact that to keep an element 

 of a given concentration at a constant temperature, a thermal 

 energy must be imparted to it of T for each unit of electricity 



