AND OF THE SECOND LAW 77 



OF THE DIFFUSION OF GASES 



This case of an irreversible process comes under group d. 

 Concerning this phenomenon J. W. GIBBS established the follow- 

 ing proposition: 



" The entropy of a mixture of gases is the sum of the entropies 

 which the individual gases would have, if each at the same temper- 

 ature occupied a volume equal to the total volume of the mixture." 



That the total entropy will be larger as a result of the mixing 

 detailed under d, p. 73, maybe inferred from the following consid- 

 eration: When two gases are thus brought together, it is more 

 probable that in any part of the total space available for this 

 mixture there will be found both kinds of molecules than only 

 one kind of these molecules. 



But this irreversible process can be explained in a more dis- 

 tinctly physical way. The two gases are originally at the same 

 pressure and temperature; they mix without other changes 

 occurring in surrounding bodies; the mixture (when diffusion is 

 completed) is at the same pressure and temperature as the 

 original gaseous constituents. Considering each gas by itself, 

 what has happened as the result of diffusion is that each gas in 

 its final state occupies a larger volume than in its initial, unmixed, 

 state. The presence of the other gas in the mixture in no wise 

 changes this fact. Of course this increment in volume is accom- 

 panied by a corresponding decrement in its pressure, without 

 change in temperature. A sort of isothermal change of state 

 has taken place in the passage from one condition of thermal 

 equilibrium to the other. We have already seen that then the 

 number of complexions of the gas increases and consequently 

 also its entropy. The sum of the increments of the number of 

 complexions separately experienced by the two diffusing gases 

 constitutes an increase in the total number of complexions over 

 and above the total number of complexions existing in both gases 



