448 MR. S. CHAPMAN ON THE KINETIC THEORY OF A GAS 



9. The Coefficient of Diffusion. 



The general equation of transfer (l) is true for any system of molecules in a gas, 

 whether in the presence of other systems of molecules or not, provided that no 

 diffusion is taking place (this restriction arises in the elimination of the external 

 forces,* where it is assumed that AM = 0, which is true, of course, only when the 

 restriction just mentioned is satisfied). The form of the equation of transfer which 

 is applicable to the more general case now under consideration, where diffusion is 

 taking place, ist 



x.y,z 



cx m 



where X is the component of external force. If we put Q = u, and suppose that there 

 are no external forces, and that the motion has assumed a steady state, the equation 

 becomes 



where we have neglected products of u , v , iv as being small quantities of the second 

 order; similarly we have neglected such terms as UV, and have given j/mUQ its 

 proper value p. 



The equation just obtained applies to the first system of molecules, p being the 

 partial pressure due to this system ; there is a similar equation 



for the second system. Since the temperature is supposed to remain constant, we 

 have 



Now, from equation (31), it follows by symmetry that 

 so that 



|i = - = w > jB=^(*=rfr ,-i.jufc (?/u _ ?0 Fji . 



*"11* s-nr* /*v\ ..I. rt-^T ' \ /v\-i I /w-i' / \ V v/ j 



^ 



' .' cx 



Ihe total flow of molecules of the first kind per unit area per unit time is clearly 



vu , and also (by the definition of the coefficient of diffusion D J2 ) is equal to -D 12 . 



dx 



* See JEANH' treatise, p. 279. 

 t Ibid., p. 278 



