282-284J Calculation of Mean Free Path 233 



Maxwell's Free Path. 



284. From the formula just obtained we can also deduce Maxwell's 

 expression for the free path given in 30, and can extend it so that it applies 

 to a mixture of gases. 



For, from expression (536), the chance of a collision per unit time for 

 a molecule of the first kind moving with velocity c is Si, and out of all the 

 molecules of the first kind, a fraction 



//^ 



V 7T 3 



7T 3 



will be moving with velocity c. Hence the average chance of collision per 

 unit time, for all molecules of the first kind, is 



efc, 



and this again, by equation (535), is equal to 



7 hnii 

 where as before 



If we put 



c Vfim s = x, 

 expression (541) becomes 



* 4"A 2 



re-^cMc^hm^dc ................. (541), 



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xe~ x * + (2a- 2 + 1) t**?fa. 

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^[ e * x "'xty(x)dx (542). 



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The integral, upon substitution for -v/r (x), becomes the sum of the two 

 integrals 



I e x \ */ x^dx-^- 1 I x (2# 2 -\- 1) e v m * docdy (543). 



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The first integral has for its value 



1/7T 



3 



To evaluate the second we write y = Kx, so that dxdy = xdxdJK, and the 

 integral 



= f f l x* (2a? + 1) e~ x '( K ' + ^ dxdK 

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