158 
DR. S. CHAPMAN ON THE KINETIC THEORY OF A COMPOSITE 
When the pressure, temperature, and composition of the gas are uniform, a steady 
motion of diffusion may be produced by equal and opposite forces ± (v 0 X' 0 , ^ 0 Y' 0 , v 0 Z' 0 ) 
per unit volume on the two components. This will be termed forced diffusion, and 
we define the coefficient of forced diffusion D' 12 by the equation 
(10-06) u\ = D' 12 v 0 X' 0 , 
so that, by comparison with (10’02), 
(10-07) D' 12 = - A 0 a' 0 = - D 12 . 
^0 Po 
From (l0'02) it is clear that diffusion will occur also when the relative proportion 
of the two gaseous components is uniform, and in the absence of external forces such 
as might produce diffusion, provided that the pressure or temperature varies. If we 
define coefficients of thermal diffusion D T and of pressure diffusion D p by the 
equation 
(10-08) = 
p a OX I ox 
we have, by comparison with (10"02) 
(10-09) D, = = — iAjRTct',, ^ = —D,j, 
v 0 m 0 m 0 w 0 
(10-10) D t = -lB 0 p' 0 T. 
( b) The Equation of Diffusion. 
If we now substitute the various coefficients of diffusion in the equation of diffusion 
(10‘02), this becomes 
(10-11) = -d 12 ^9 + DVX'.+D, - - d t i 
ox p 0 ox 1 ox 
In later sections, when we consider in detail the values of the four coefficients of 
diffusion, we shall see that they are all positive (the molecules 1 being the heavier— 
cf. § l). # Hence from (10" 11) we deduce that the direction of diffusion of the heavier 
component of a gas is (a) opposite to the direction of increasing concentration (b) in 
the direction of the diffusion-component of the external force ( c ) in the direction of 
increasing mean pressure and ( d) opposite to the direction of increasing temperature.* 
This is fairly evident as regards (a) and ( b ). In case (c), the sign of D p is the same 
as that of m' 0 (cf (10"09), D 12 being always positive), which is a multiple of 
the physical reason is also not difficult to grasp—under the influence of a difference 
of pressure both components will tend to flow in the direction of diminishing 
pressure, so as to render the pressure uniform. The lighter molecules will travel 
* This statement is modified, with regard to D T , in Note E, p. 197. 
