Force and Osmotic Pressure. 379 



piston permeable to water but not to salt (whether dissociated 

 or not), and allow the solution to fall in concentration to the 

 original value C^. The work done by the solution is PiSVp 

 To evaluate hY x the change in volume, we have, 



BY, _ 80, 



Ti - 5 ' 



but since Y L = 1. 



sv 1 =«o 1 /c I . 



To evaluate Pj we will assume that the gaseous laws hold 

 for the solution : then 



P 1 =ETC 1 {H-(n-l) 7l }. 

 Hence the work done is 



BT{l+(n-l)7 1 }aC 1 . 



(3) In a similar manner, concentrate the cathode solution 

 reversibly till it recovers its original strength : the work done 

 by the cell is 



RT{I+(n-lJ7 S }50,= --ET{i+(n-l) 7s }SC 1 . 



We have now, however, more anode solution than was 

 originally present ; therefore we must — 



oC 



(4) Separate -^ cubic centimetres of the anode solution, 



1 

 concentrate them reversibly till they attain the strength of the 



cathode solution, and add them to the cathode solution. The 



work done by the solution in this process (negative) is 



$FdV, 



where 



7tt_ tt dO _ hC x dC 



and 



P = RTC{l+(n-l) 7 }; 

 therefore the work 



%) Cj 



Since the total work in the cycle must be zero, we find : — 



■^C 1 + BT{X+(n-l)7 1 }8Ci-aT.{I + (n-l)7 a [8C 1 



c sRT 



J^2 Kl 

 1T {l+(n-l)y}dC = 0, 



>r 



202 



