FOUNDATIONS OF THE KINETIC THEORY OF GASES. 83 



formula referred to, we put (M) 3/2 for h 3 , and also put k for h in the exponentials 

 where the integration is with respect to v ly it becomes 



8ns 2 (hk)%/3 , 



according to the notation of § 21. This is the average number of impacts per 

 second which a P has with Qs. 



Hence, if •& be the whole energy of the Ps, p that of the Qs, per unit volume, 

 the equations of § 19 become 



16 PQ . /irQi+k), > 



from which we obtain, on the supposition (approximate enough for our purpose) 

 that we may treat ljh + l/k as constant, 



where 



1_1_6_2Q_ / ! r(A+i). 



T~3 (P + Q)*^ W + w;V hk 



The quantity 



tits — mp = mn(m/m — p/n) , 



is mn times the difference of the average energies of a P and a Q, and (since 

 g 4 - 6 r= 100 nearly) we see that it is reduced to one per cent, of its amount in the 



time 



t ,__ 13.8 (P + Q) 2 / hk , 



t x = 4.6T = TX - — — -. v V( ?' V n , 7 , seconds. 



24. For a mixture, in equal volumes, of two gases in which the masses of 

 the particles are not very different, say oxygen and nitrogen, we may assume as 

 near enough for the purposes of a rough approximation 



m = % = |xl0 20 , 



whence m + n (per cubic inch) is double of this, 



^ = 27, = (12 x 1600 inch sec.) 2 , 



s = 3x 10 -8 inch, 



so that 



13.8xl0 16 x4 /3 1 , . 



h = T7r — 7{ — r, — TKSTi — tt; — tt^t^V r~ = rr— --,-r.a seconds, nearly: 

 16x9x3x 10 20 x 12x1600 4tt 3 x 10 9 ' ' 



and the difference has fallen to 1 per cent, of its original amount in this period, 

 i.e., after each P has had, on the average, about four collisions with Qs. This 

 calculation has no pretensions to accuracy, but it is excessively useful as showing 

 the nature of the warrant which we have for some of the necessary assump- 



