Change of State : Solid-Liquid. 41 



But T is constant ; then 



JdQ=0, 



and the external work is, on the whole, zero. This gives us 

 (v+^Ftcv + (co + F)v(l-F K v)--pY'-->cTYhg£- 



+ wfV—v) = 0. . . (7) 



But since, at low temperatures such as we are here considering, 

 Boyle's law is almost exact, we have 



Then, neglecting terms containing ztk } 



or 



jl = M i -t). 



(8) 



For ordinary values of P this gives 



?v Pa- 



P-»=Y = T' W 



which agrees with Sir W. Thomson's result in equation (6). 



It may be worth while to point out the following result of 

 the reasoning on which the above proof is based. 



In a quantity of liquid at a uniform temperature, the num- 

 ber of molecules interchanged across a surface will increase as 

 we descend, owing to the increase of pressure. If near the 

 surface the number be proportional to the vapour-tension at 

 the surface, then at any depth the number will be proportional 

 to the pressure in an atmosphere of vapour at that level which, 

 at the level of the surface, has the pressure of the vapour in 

 equilibrium ; that is, the liquid will behave as a non-vapori- 

 zing solid through whose interspaces the vapour can move 

 freely. 



Assuming, then, that equation (9) holds both for solids 

 and liquids, let us apply it to the case of ice and water in con- 

 tact with each other at a temperature —t° and at a pressure P, 

 such that — 1° is the melting-point. 



Let -sr be the normal vapour-tension of water at — 1°, 

 vr' „ „ „ _ ice at -/ c , 



p be the altered vapour-tension of water, 

 P v jj 5; t lce j 



p the density of water, v its specific volume, 



p f „ „ ice, xf 



their vapour, V its specific volume. 



