﻿Attraction of Unlike Molecules. 3 



R 5.1-, and then any acceleration of the element of the first 

 gas is due to the force Bx (dp l /dx — 'R), but this acceleration 

 can be neglected in comparison with either 8x dp^jdx or 11 o\r, 

 and we have 



R=dpjdm (1) 



R has now to be evaluated ; it is the resistance offered by 

 the molecules of the two sets in unit volume at * to one 

 another's motion. Let v be the number of encounters per 

 second between n x molecules of the first set in unit volume 

 and n 2 of the second, and let /j, be the average value of the 

 momentum communicated when a molecule of the first set 

 with velocity * Y collides w T ith one of the second with velocity 

 a 2 in the opposite direction, then 



R = v/*. 

 If a x and a 2 are the radii of the molecules of the two sets 

 treated as spheres, and 3/^/2 and 3/c 2 2 /2 are their mean 

 square velocities, then (see for instance Tait, Trans. Roy. Soc. 

 Edin. xxxiii.) 



v= 2?i 1 n 2 (a 1 + a 2 yTr*(jc? + K 2 2 )i, 



2 m l m 2 . 



3m l + m 2 K ' z/ 



Now in diffusion the pressure remains constant, so that as 

 many molecules of one sort pass in one direction as of the 

 other in the other, or n 1 u 1 = n 2 a 2 , and accordingly 



R=|,W« x+ a,)M(» 1 » + ,,«)^i + 5)^; • (2) 



but n 1 m 1 = p 1 , the density of the first gas, and 



pi = n 1 m 1 Ki/ < '2=p 1 /Ci 2 /2, so that (1) becomes 



_ dpi 3 k{ 2 m, + m 2 1 ,„. 



PlUl " dx 8 [** + k 2 *)% m 2 7r*(«i + a 2 ) 2 {n, + n 2 ) ' ' [ } 



The coefficient of dpjdx is by definition the coefficient of 

 diffusion D ; remembering that Ki 2 //c 2 2 = m 2 /m 1 , we get 



3 ( m^mtf 1 m 



U ~S\ m 2 /7rt(a 1 + fl 2 ) s (w 1 + w 2 )" " ' [) 



Meyer's method of proceeding is quite different. He says 

 that as the density of one of the diffusing gases diminishes 

 in one direction, then, if a plane is drawn anywhere at right 

 angles to this direction, the density increases on one side and 

 diminishes on the other, so that more molecules cross the 



B2 



