LEWIS. — A NEW SYSTEM OF THERMODYNAMIC CHEMISTRY. 273 



The surface C does not change its position during these operations 

 (according to the definition of the ideal solvent). The total work 

 done by the system is therefore equal to the sum of Ai, A 3 , A s , and 

 A 4 , and since the cycle is isothermal and reversible this sum is equal 

 to zero, by the second law of thermodynamics. Equating the terms to 

 zero and simplifying gives, 



vdP — v'dll = 0. 



T> r p 



v' , the molecular volume in the ideal solution, is equal to — - . Sub- 

 stituting this value in the last equation gives, 



d\nU v 

 dP ~lif' 



The activity of Xi , £, is the same in the mixture A and the solution B 

 and its value in terms of II is given by equation III. Substituting for 

 IT and expressing in the equation the constancy of temperature and com- 

 position, 9 we have, 



(d In A 



V cP ) T ,N 



BT (IX) 



This is the general equation for the influence of pressure upon the 

 activity of one constituent of a binary mixture. The quantity v is of 

 very great importance in the thermodynamics of mixtures. It is the 

 increase in volume of an infinite quantity of a mixture when one mol 

 of the constituent in question is added to it. We will call v the par- 

 tial molecular volume of that constituent. 



Similarly we may define the partial molecular energy, entropy, etc., 

 and these quantities play the same role in the thermodynamics of 

 mixtures that the molecular volume, energy, entropy, etc., do in the 

 treatment of pure substances. 



An important difference between the partial molecular volume in a 

 mixture and the molecular volume of a pure substance is that while 

 the latter is always positive the former need not be. Therefore the 

 activity of one of the constituents of a mixture may either be increased 

 or diminished by increase of pressure on the mixture. 



9 We will use the subscript N with the partial differential coefficient to denote 

 constancy of composition in the mixture. 

 vol. xmi. — 18 



