382 Conduction in Solutions and Gases , 



of salt, in passing from a high to a low concentration, are 

 therefore capable of supplying energy, just as a compressed gas 

 is capable of supplying energy when its degree of compression 

 is reduced. To examine the matter quantitatively, let nf(nf V) 

 denote the term in the available energy of a solution, which is 

 due to the dissolution of n gramme-molecules of salt in a volume 

 V of pure solvent ; the function / will of course depend also on 

 the temperature. Then when dn gramme-molecules of solvent 

 are evaporated from the solution, the decrease in the available 

 energy of the system is evidently equal to the available energy of 

 dn gramme-molecules of liquid solvent, less the available energy 

 of dn gramme-molecules of the vapour of the solvent, together 

 with nf(n/ V) less nf{n/(V-v dn) } , where v denotes the volume 

 of one gramme-molecule of the liquid. But this decrease in 

 available energy must be equal to the mechanical work supplied 

 to the external world, which is dn . p (v - v), if p l denote the 

 vapour-pressure of the solution at the temperature in question, 

 and v denote the volume of one gramme-molecule of vapour. 

 We have therefore 



dn . pi (v' - v) = available energy of dn gramme-molecules of 



solvent vapour 

 + available energy of dn gramme-molecules of 



liquid solvent 

 + nf(n/ V) - nf {n/( V-v dn) \ . 



Subtracting from this the equation obtained by making n zero, 

 we have 



dn . (Pi - p ) (v - v) = nf(n/ V) - nf( n/( V - v dn) } , 



where p Q denotes the vapour-pressure of the pure solvent at the 

 temperature in question ; so that 



(Pi -Po) <>' - v) = - (n'/V*)f(n/V)v. 



Now, it is known that when a salt is dissolved in water, the 

 vapour-pressure is lowered in proportion to the concentration 

 of the salt at any rate when the concentration is small : in 



