318 



HEAT. 



FIG. 180. 



At this temperature we may show that the two vapour-pressures of 

 solid and liquid are so changed by the pressure P that they are again 

 equal, or we have, as it were, another triple point. This may be proved 

 by imagining an arrangement to take the substance 

 through a one temperature reversible cycle. That used 

 on p. 309 for the ordinary triple point is no longer appli- 

 cable. Suppose that the two vapour-pressures at the 

 new equilibrium pressure are different, that of water say 

 being the greater, then if there be water in a vessel 

 (Fig. 180) containing air at pressure P, at the level of 

 the water surface the vapour in the air would be super- 

 saturated for ice. But if the vessel be sufficiently lofty, 

 then the pressure both of air and of water vapour will de- 

 crease from below upwards, and at some height A, ice will 

 be in equilibrium with the water vapour present. Then 

 arrange a side tube of this height containing a cylinder 

 of ice and supported a little above its base by upward 

 pulls T. If now the cylinder is slowly pulled up by 

 forces applied at the level C, evaporation will take place 

 at A, condensation will go on at the water surface, and 

 solidification at the base of the ice. Or if the cylinder 

 is slowly let down, doing work against T, everything is 

 reversed, and we have a one-temperature reversible 

 cycle from which work may be obtained. Our supposi- 

 tion of different vapour pressures must therefore be false. 

 It may be shown that the alteration given by the formula of p. 315 

 just accounts for this new equality of vapour-pressures. For if TA TA' 

 (Fig. 181) represent the vapour- 

 pressures of ice and water, re- 

 spectively, below the triple point 

 T, a pressure P on the surface 

 alters the ice vapour pressure by 



TI = = Po-y 1} where v^ is the 



Pi 

 specific volume of ice. That is, 



the new vapour-pressure line is 



IT 7 , P<rw, above TA. Similarly, 



the new water vapour pressure 



line is represented by WT', 



P<rv 2 above TA' where v 2 is the 



specific volume of water. W is 



lower than I, since u 2 is less 



than v v and IW = PO^VJ - f 2 )- If 



WT, IT' meet at T', and if r 



be dd below the triple point, 



evidently IW is equal to the 



difference of height of TA, TA' for the same temperature. 



p. 311 (3) this is 



LW0 

 W CD = g 



Temperature 

 FIG. 181. 



But by 



