Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/402

 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 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  of pure solvent; the function  will of course depend also on the temperature. Then when 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  gramme-molecules of liquid solvent, less the available energy of  gramme-molecules of the vapour of the solvent, together with  less nf{n/(V-vdn)}, where  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, if , denote the vapour-pressure of the solution at the temperature in question, and {{Wikimath|v&prime; denote the volume of one gramme-molecule of vapour. We have therefore Subtracting from this the equation obtained by making {{Wikimath|n}} zero, we have {{c|$$dn.(p_1 - p_0)(v^\prime - v) = nf(n/V) - nf\{n/(V-vdn)\}$$,}} where {{Wikimath|p{{sub|0}}}} denotes the vapour-pressure of the pure solvent at the temperature in question; so that {{c|$$(p_1 - p_0)(v^\prime - v) = -(n^2/V^2)f^\prime (n/V)v$$.}} 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