FUNDAMENTAL EQUATIONS OF IDEAL GASES 377 



The generalization of the above result follows easily, and if 

 Xi, Xi, ... Xi are the mol fractions we find 



^ 



- V 



1 



= r^-iV 



Sri 



2J (vi - vx) = 2j «i^i ^°g - = C'-i Zy '' l^s ' ^^^^^ ^^^^1 



Xi 



Ti 



where C~^ in Gibbs' notation is equal to the universal gas 

 constant, usually designated by R. The discussion following 

 equation [297] is too complete to require comment other than to 

 draw attention to the remark which admirably sums up the 

 import of the Gibbs theorem on entropies: "the impossibility 

 of an uncompensated decrease of entropy seems to be reduced to 

 improbability" (15th line from bottom p. 167). It is of addi- 

 tional interest to note that an entirely analogous theorem may 



P/STOf^ 1 PERMEABLE TO &AS1 



GASl 



V 



z 



GAS 1 



a/x/ 



GAS Z 



V 



A 



GAS a 



P/STOA/Z PERMEABLE TO GASZ 



Fig. 1 



be deduced by starting with equation [92] of Gibbs' Statistical 

 Mechanics (Gibbs, II, Part I, 33) and extending the equation 

 to include two or more molecular species. 



IV. The Phases of Dissipated Energy of an Ideal Gas Mixture 



with Components Which Are Chemically Related 



(Gihhs, I, 168-172) 



Before reading this section, the section on "Certain Points 

 relating to the Molecular Constitution of Bodies," pp. 138-144, 

 should be consulted. The immediate goal is to provide the 

 basis for treating the phenomena exhibited by mixtures of gases 

 which are capable of chemical interaction. What is sought is a 

 scheme whereby the equilibrium amounts of the different 

 distinct molecular species may be correlated as a function of 



