THERMODYNAMICS OF CHANGE OF STATE, ETC. SJ9 



T, / 



whence * ~ v 



and 



Lt 



or the two vapour-pressures are equal at the new melting-point. 



The point T' is really above T, or as the melting-point falls by 

 pressure the vapour-pressure rises. For if we take the water vapour 

 pressure dd below T when the water is under pressure P, it is 



. d( T/1 T-, 



w = a) - 7a du + Per v z 

 do 



where to is the vapour- pressure at the triple-point 



d<a Ixr 



But ~ 



and 



<rdO/ L'v 8 T \ 

 then u> = a> + TP ( - Li ] 



e ^-v^ j 



, Lcr^fl/ L't> 2 - L(v t - v 2 ) \ 

 1F\ Lto-*,) / 



L' 80 , v, - v 9 Aft 



but T- = c7^-R and J - '~^ 



L 606'5 v 2 



then the second term on the right is positive, and o>' is greater than o>. 



The results just obtained enable us to give a molecular account of 

 the phenomena of melting under pressure. The vapour-pressure of a 

 substance depends on the number of molecules escaping from the surface 

 per second, or upon the " mobility " of the molecules, and we may take 

 the vapour-pressure as measuring this mobility. At the triple point the 

 three states are apparently in equilibrium ; but this is only a " mobile 

 equilibrium " due to the equality of the number of molecules passing in 

 each direction across each separating surface. In other words, the 

 mobility of each state is the same. Below the triple point the vapour- 

 pressures differ, and the mobilities differ also. Thus the liquid gives to 

 the solid more molecules than it receives in return and the solid grows. 

 The liquid evaporates more than the solid, and would distil over on to 

 the solid in the space above their surface. But if pressure is put on ,the 

 mobilities are increased, though not to the same extent, the denser state 

 being less increased than the less dense. Hence at the triple point 

 equilibrium is destroyed, the ice having a greater mobility than the 

 water, and the new point of equal mobility is below the triple point. 



We have applied the foregoing equations to the case of ice and 

 water ; but it is evident that they apply to any case of a substance 

 capable of existing in the three states or phases at the same time. 



