1.V2 MR. S. CHAPMAN ON THE KINETIC THEORY OF A (IAS 



Since q = l/2//m, so that mq = m'q', on solving for U(U 2 + V 2 + W 2 ),, we obtain 



(AD-BC) U(U 2 + V 2 +W 2 ) = 51 



\yi ffftj 



(AD-BC) U'(U' 2 +V' 2 +W' 2 ) = 5 A-_c. 



\m m / da; 



If we multiply equation (9) by m, and add the corresponding equation for the 

 second system of molecules, we get 



3 (+') ^ = _ 2 {*m U(U 2 +V 2 + W 2 ) u + /m' U' 



z,y, i 



since the sum of the remaining terms 



m A 12 (?t a + v 2 + W 2 ) + m' A 12 (?t' 2 



vanishes. This follows from the principle of conservation of energy, for the last 

 expression represents twice the rate of change of the combined energy of the two 

 systems of molecules due to their mutual collisions, which is evidently zero. 



We substitute the values already obtained for U (U 2 + V 2 + W 2 ),, and 



U'(tJ'"+V"+W'*) in the last equation, and compare the resulting equation with 

 the equation of conduction of heat in a medium at rest. As in the case of a simple 

 gas ( 8) we obtain the following expression for the thermal conductivity 3- 12 : 



m 



. 



AD-BC 



In this equation we must substitute the proper values for A, B, C, D. I shall not 

 enter into the details of the calculation, which is rather long and complicated, but 

 will simply quote the result in the simplest form. It must first be mentioned that 

 (Cv)i2, the specific heat of the compound gas at constant volume, is connected with 

 the same constants for the component gases, viz., C,, and C' r , by the following 

 relation : 



(39 A) (c.) u =-p t< - + pyp' 



pw+pw 

 using the notation of 10. 



The formula finally obtained is 



(40) 



= 



M 



