150 Partial Separation hy Thermal Diffusion of Gases. 



of the difference between the behaviour of real molecules at 

 collision, and of the elastic spherical molecules which have 

 formed the basis of our calculation. 



For corresponding gradients of \ogp and log T, pressure 

 diffusion is usually more powerful than thermal diffusion, 

 but the former vanishes altogether when the molecular 

 masses are equal. The equation of state for pressure 

 diffusion is 



dXi _ __ ~d^2 _ _ t. lb \ogp 



'bx ~d® p B-2*' 



where 



p X l m 1 + A 2^2 

 It is interesting to compare k p and k t in the above case, 

 where we have supposed m 1 = m 2 , a relation which is, however, 

 not quite exactly fulfilled. From the Smithsonian Physical 

 Tables (1910 ed.) the following exact values of the relative 

 atomic weights of hydrogen (1), carbon, and nitrogen are 

 taken : — 



Carbon 11-99, Nitrogen 13*90. 



Hence the molecular weight of C 2 H 4 is 27*98, and of N 2 

 is 27*80, so that for the proportions \ x and X 2 > already con- 

 sidered, the following are the calculated values of k p :— - 



Vi : v 2 1:3 1:1 3:1 



k* p ,. ... 0*00121 0*00161 0*00121 



In this case, therefore, k p is only about one eighth a3 great 

 as k t . If our atmosphere were composed of roughly equal 

 proportions of C 2 H| and N 2 , the settling out under the in- 

 fluence of gravity would only amount to 1 per cent, in about 

 100 kilometres, supposing there were no convection. 

 Thermal diffusion clearly gives much more control over the 

 mixture, in a case like this, than does pressure or forced 

 diffusion (under gravity). 



There are many pairs of gases of very nearly equal mole- 

 cular weight, but their diameters are usually less different 

 than in the above case, when the numbers of atoms in the 

 molecule are nearly alike. For instance, the diatomic 

 molecules CO and N 2 , of equal molecular weight, have 

 diameters 1*89 . 10~ 8 and 1*88 . 10" s cm. respectively. Simi- 

 larly, the triatomic molecules C0 2 and N 2 0, of equal mole- 

 cular weights 44, have diameters 2*27. 10" 8 and 2*30.10~ 8 cm. 

 respectively. The large difference of diameter in the case 

 of C 2 H 4 and N 2 " seems to be due to the large difference of 

 atomicity between them. Except in such cases the general 

 similarity between molecular diameters, just noted, seriously 



