408 The Thermodynamics of Cryohydrates. 



Then we have by (3) , 



Also 



$=E (TJ -tS)+pv, <E>!=E (U 1 -t BO+pvij 



where E is the mechanical equivalent of heat. 



Again, if the salt and ice be placed in contact with each 

 other, and the temperature kept slightly above the freezing- 

 point of the cryohydrate, the liquid cryohydrate will be 

 formed, and if Q is the heat absorbed during the process, we 

 must have, since <£> = <£>!, 



Q=«.(S-S 1 ) (4) 



If we move to a consecutive point (p + 8p, t + Bt) on the 

 freezing line, an indefinitely small quantity of ice (or salt) 

 may separate out from the cryohydrate ; but whether it does 

 so or not, the changes in d>, & x will be respectively 





S<I> =i-o.hp- 



-s.sn 





B^ 1 = v 1 .Sp- 



But by (3) 

 hence 



(i,-« 1 ).Sp=(S-S 1 ).S*, 



and, therefore, 



by (±), 



t v 



-«">•! 



(5) 



We may notice, generally, that the freezing-point of the 

 cryohydrate is depressed or raised by pressure, according as 

 the liquid employed expands or contracts in the act of 

 freezing. 



In particular, the freezing-point of the cryohydrate of an 

 aqueous solution of sodium chloride is lowered by pressure by 

 almost exactly the same amount as the freezing-point of pure 

 water. 



We will now give reasons for believing that the composi- 

 tion of a cryohydrate is independent of the pressure. For 

 suppose, if possible, that along the freezing line of the 

 cryohydrate, h increases with p. 



At any pressure p, let the temperature of the cryohydrate 

 be reduced below its freezing-point, and then let the pressure 



increase if J- is negative along the freezing line, but if 



j%- is positive, let the pressure decrease. 



Referring to the diagram we see that, sooner or later, the 



