Thermal Diffusion of Gases of Equal Molecular Weight. 149 



if <Ti >(j 2 , it follows that, as above stated, the larger molecules 

 diffuse towards the regions of lower temperature. 



As a numerical example, let us consider a mixture of 

 ethylene (C 2 H 4 ) and nitrogen (N 3 ) : the atomic weights 

 of hydrogen, carbon, and nitrogen being approximately 1, 

 12, and 14, the molecular weights of these two gases are 

 approximately equal, viz. 28. The molecular radii, deduced 

 from the coefficients of viscosity on the hypothesis that the 

 molecules are rigid elastic spheres, are* 2*39 . 10 -8 cm. (C2H4) 

 and 1*84. 10" 8 cm. (N 2 ). On substituting these values into 

 the above expression for k t , we find that in this case (the 

 gas 1 being taken as ethylene) 



_4 -64 + 0'302(X 1 -X 2 ) 



a/ — . 



157 - 1 + 130 + 93^ 



This has its maximum value when v 2 and v 2 are nearly equal. 

 The following are three typical values of k t for various 

 relative proportions of the two gases : — 



Vl :v 2 1:3 1:1 3:1 



k t 0-0094 0-0122 0-0078 



In order to understand the physical significance of these 

 numbers, we may consider the steady state of the mixture 

 when placed, in originally equal proportions (say) by volume, 

 in a tube in which a permanent temperature gradient is 

 maintained from T at one end to T ' at the other. The 

 equation of steady state (I. c.) is 



dAq _ BX 2 _ h d log.T 

 ~dx B^ d^ 



We may assume h t to be nearly constant, so that the 

 change in \ x or X 2 between the two ends (due to the balance 

 of influence between thermal diffusion, which tends to 

 separate the two sets of molecules, and ordinary diffusion, 

 which tends to restore uniformity of composition) is equal 

 to A, log. To/To'. If, for instance, T ' = «T (say T = 200° abs., 

 and T / =544° abs.), the percentage difference of compo- 

 sition between the two ends would be 100^, or 1'22 per cent, 

 in the case suggested. The separating action is clearly not 

 at all powerful, although by successive operations of thermal 

 diffusion a very appreciable difference of relative proportions 

 could be produced in the mixture. It should be added, 

 however, that the effect would in fact probably be only 

 one half or one third of this calculated amount, on account 

 * Cf. Phil. Trans. A. ccxi. p. 476 (1912), 



