LOWERING OF FREEZING POINT 55 



effected at the constant temperature TAt if the mass of 

 solution is so great that the separation in question makes 

 but an inappreciable change in the concentration. Then the 

 solution and solid solvent are to be separated and warmed 

 to T, the solvent melted and mixed with the solution in 

 an osmotic reversible manner (with cylinder, piston, and 

 semipermeable membrane), a certain amount of work being 

 gained. If A t is very small (df) a quantity of heat Q has 

 in the cyclic process fallen in temperature by A, which 

 implies a production of work 



If the solution contains a per cent, and so much of ,the 

 solvent is frozen out as contains one kilogram-molecule m of 



, , , . loom ., 

 the dissolved body, i. e. - ? then 



where W is the latent heat of fusion of ttie solvent 

 per kilogram. The work gained is, according t to the 

 previous argument, 



so that 



.a T 



or 



A t 0-02 T 2 



m = 



- ^ 



a W 



Here, however, the first term is the so-called molecular 

 lowering of the freezing point f, i.e. the lowering for 



a one per cent, solution , multiplied by the molecular 



CL 



weight m. 



Thus for water, from T = 273 and W = 80 we may 

 calculate 



t= 18-6 



