34 MOLECULAR WEIGHT AND POLYMER1SM 



with a volume v of water, a process which, in the limiting 

 case in which V^ is infinite, is reversible, for under those 

 circumstances the water would not absorb any of the 

 infinitely dilute vapour X. Now let the piston be lowered 

 and so X be brought into solution, with an expenditure of 

 work 



Jo 

 Here, however, P 1 has not the value given by 



but a smaller value, because a part of the vapour has gone 

 into solution. This part is exactly i kilogram when the 

 pressure has risen to P, and consequently, if Henry's law of 

 absorption is true, when the pressure is P, amounts to 

 Pi/P kilograms; the undissolved part remaining is there- 

 fore i P! /P, and the pressure P may be calculated from 



so that 



RT 



"Vi+V 



Consequently the work done is 



-('"Pdv- RT[ VX ^ an<*! 

 Jo ^ K I- J y, 7, + y- V 



which, if V ^ is infinitely great, becomes 



Since the total work done in a reversible cyclic process 

 at constant temperature must be zero 



( + (2) + (3) + (4) = RT-pv + RT log ^f -RT log ^ = o 



or 



pv = RT. 

 By comparison with 



PV = RT, 



