THERMODYNAMICS OF CHANGE OF STATE, ETC. 33 J 



solution be under a semi-permeable piston A (Fig. 188), and let solvent 

 be above the piston, and let a movable piston B be above the solvent. 

 Allow volume v mass pv of the solvent to go through a one-temperature 

 cycle, thus 



(1) Let A be pushed down under pressure P till volume v of the 

 solvent has passed out of the solute, work Pv being done. 



(2) Let volume v, mass pv, of solvent evaporate at pressure <D, pushing 



B up, forming volume - of vapour and doing work t ^. 

 cr cr 



(3) Let the vapour expand isothermally from volume to , at 



pressure a/, doing work . pv ( , - ) approximately since w and u/ 



2 \cr cr/ 



are for dilute solutions not very different. 



(4) Let the vapour condense back on to the solution by some suitable 

 contrivance, the solution now being under pressure CD', the work done 



, . (a pv 

 being ?y- . 

 cr 



The cycle is now complete, and the total work is zero, or 



I ' /I 1 ^ 



or 2 \ 



But - = , by Boyle's law, whence 



<T cr' 



p _ O) + co' 



~2~' 



O) + 0>' 



or ft) ft)' = since o> + co' = 2o/ nearly. 



P 



If s be the density of the solute, and S its molecular weight, \Tan 

 t'Hoff's gas value of P gives 



P*^ . T> ft 

 ^ _rt(7. 



S 

 while if M be the molecular weight of the solvent . 



""M ' 



Hence, substituting for P and cr 



O) CD' _ 8 _._ p 



~~"g *a 



