(*) 



Fig. 5. 



(2) 



A 



— > [ p/ 



P/|<— 







-+|k 



P/,%< 



t 



i 



hi the Analogy between Solutions and Gases. 97 



Let there be two systems of gaseous or dissolved substances 

 in equilibrium, which may be expressed by the following 

 symbols : — 



a/M/ + a,"M," + &c. ^r a tt 'M w '+a/M,/' + &c.> 



where a denotes the number of molecules, and M the formula. 

 This equilibrium exists in two different vessels, A and B, at 

 the same temperature but at different concentrations, shown 

 by the partial pressure, or by the osmotic pressure which each 

 of the bodies exerts. Let these pressures be in vessel A, 

 P/P/'...P,/P,/'&c; and in B greater than these by dP/ 

 dF t ". . . dFJ dP Jt ". . . &c. 



The reversible cycle consists in introducing into A that 

 amount in kilograms expressed by the first symbol of the first 

 system, while the second is removed in equivalent amount : 

 both systems have here the concentrations which exist in A 

 (fig. 5). This change is accom- 

 plished by causing the entry or 

 exit of each of the substances in 

 question by means of its own 

 cylinder and piston, which is se- 

 parated from A by a diaphragm 

 permeable to that body alone. etc 

 If they are in solution, then the {&) 

 cylinders possess a semiperme- 

 able wall, and are surrounded 

 by the solvent. 



When this has been done, each 

 constituent of the two systems has 

 undergone such a change of concentration that it is now equal 

 to that in B ; and, as before, the work done per kilogram - 

 molecule equals 2AT, where A represents a minute fraction 



of the pressure, and is here =p- ; for the amounts here in 



dP 

 question it is 2aT-p-. 



By making use of the vessel B, the second system, which 

 lias just been evolved, is now converted into the first, but of 

 concentration as in B, proceeding as just described ; and by 

 suitable alteration of volume it is finally changed into its 

 original state, as it at first existed in A. 



As no change of temperature; has occurred, the algebraic 

 sum of all these operations is zero, ns is Been from the num- 

 bers ; it is thought unnecessary to interpret them, as they 

 refer to the operations in the order in which they were earned 

 °** : — (i)+(2) + (3) + (4) + (5) l-(6)=0. 



Phil. Mag. S. 5. Vol. 26. No. 159. Aug. 1888. H 



(5) 



