THERMODYNAMICS OF CHANGE OF STATE, ETC. 311 



dd) _ L _ Lor ,. , 



39"3^~T 



%-&+*% (2) 



^-fe-^ <> 



or dividing by (2) 



(dot _ d<a\ _._ do/ _ L' x . v 

 d0~&) i5ff~T+i? 



These equations obviously apply to any substance at its triple point. In 

 the case of water at 



L = 606-5 from Regnault's formula (p. 180) 



L' = 80 ; Q = 4'60 - 4-26 = 0'34 mm. from Regnault's researches on 



vapour-pressure, 



cZw d<a 80 x-34 n 



---=' 



That is, the vapour-pressure of ice below falls down more rapidly than 

 Lhat of water by about 0*04 mm. 

 per degree. 



Then the line AT, if con- 



tinned beyond the triple point, [""" 



lies above TB; see the dotted 



line TB' in Fig. 174. FIG. 175. 



The difference in vapour- 

 pressures of ice and water just below is too small to measure accu- 

 rately, though Regnault's work on re-examination indicates its existence. 

 But if, instead of taking the difference of vapour-pressures for the same 

 temperature, we take the difference of temperatures for the same vapour- 

 pressure, we get a quantity large enough to be measured. For let T (Fig. 

 175) be the triple point on a pressure-temperature diagram. Let TA, 

 TA' represent the ice- vapour and water-vapour lines. Let A' AM be a 

 line of equal pressure. Then AA' is the difference of temperature of ice 

 and water in equilibrium with their vapours at that pressure. 



AA' A'N , . A , A'JST. AM 



But ~ and AA = =-= 



AM TM TM 



o> -a/ _ -040 

 = ~d^' ~ ~^4 



dd 



(where is the temperature of the water below the triple point) 



= 0-116x0 

 or 0'116 per degree below the triple point. 



