94 DIFFUSION OF GASES 251 



The proof that the shortness of the molecular paths 

 must cause an equal slowness in the mixing or diffusion of 

 two gases may be deduced in an exactly corresponding way. 

 This is just the point on which Clausius 1 laid special 

 stress in his celebrated memoir on the free paths of mole- 

 cules. Into a space already filled with one gas the mole- 

 cules of a second gas penetrate only slowly, because by their 

 frequent collisions with the molecules of the first gas they 

 are driven hither and thither, so that it is impossible for 

 them, even with their enormous speed, to penetrate into the 

 interior of the other mass in straight lines. 



The velocity of diffusion therefore depends not only on 

 the speeds with which the molecules of the diffusing gases 

 move, but also no less on the length of the free path which 

 a molecule of one sort traverses among molecules of the 

 other sort. It is thus conditioned by the same elements as 

 the friction of gases, viz. molecular speed and free path. 



A closer examination of the way in which these two 

 elements are connected together leads to a knowledge of the 

 value of the coefficient of diffusion and teaches us to see its 

 meaning and its relations to other magnitudes. 



95. Theoretical Value of the Coefficient of 

 Viscosity 



At each moment during the interval occupied by an 

 experiment the diffusing gases may be in such a state of 

 motion that the equilibrium of the total pressure exerted by 

 the mixture is nowhere disturbed ; there is then at every 

 point the same pressure p, and this is the sum of the partial 

 pressures p 1 and p 2 which each of the two gases would exert 

 by itself, or 



P = Pi + Pr 



Similarly, by Avogadro's law, there is the same number 

 of molecules in each unit volume, which we will repre- 

 sent by 



1 Pogg. Ann. 1858, cv. p. 239 ; Abhandlungen, Abth. 2, 1867, p. 260 ; Phil 

 Mag. 1858 [4] xvii. p. 81. 



