﻿14:4: Prof. A. W. Porter : Variation of Triple-Point 



must no longer be considered as a fixed point but as a point 

 which also varies with change in the hydrostatic pressure. 

 That this must be the case can be seen almost immediately. 

 Recall that the triple-point is the temperature at which the 

 vapour-pressure curves of the solid and liquid meet ; so that, 

 if this temperature is exceeded, we can only have liquid and 

 its vapour in equilibrium together ; and if it is not reached 

 we can only have solid and its vapour. Now the position of 

 the triple-point for ice-water-steam, as usually determined,. 

 is at 'OOTi C. Let the hydrostatic pressure, however, be 

 raised (for example) to one atmosphere : the melting-point 

 of ice becomes 0° C. If the triple-point is a fixed point we 

 shall, under these conditions, have a range of temperature 

 from 0° C. to '0074° C. for any point of which it may be 

 said that hoar-frost cannot form because the substance is 

 above the freezing-point, and dew cannot form because it is 

 below the triple-point. It is clear that this dilemma can be 

 resolved only by postulating that the triple-point must have 

 moved to the freezing-point, viz. C C, corresponding to the 

 hydrostatic pressure of one atmosphere. 



This can be proved by a more detailed examination in 

 which proper account is taken of the variation of vapour- 

 pressure with hydrostatic pressure. We will first of all 

 prove an auxiliary theorem. 



The slopes of the vapour-pressure curves 

 near the triple-point. 



In determining these slopes it is customary to take 

 Clapeyron's equation 



Li 2 =T(v 2 — v 0^f 



for the three possible variations, and by neglecting i\ v 2 , the 

 volumes of ice and water, in comparison with that of the 

 vapour, v 5 , to obtain the approximate equations : 



t t». d7r 2 2 



T, — TV?* —v \d]hl. 



whence, since at the triple-point 

 L 1?) = L 12 + L 23 



