69 MOLECULAR FREE PATHS 163 



contained in unit volume which is given by ^X 3 = 1, we 

 find that the molecular path-volume is determined by the 

 expressions 



^L = \ 3 I V2 = l/4yW, 



which show that its value is the same for all gases, since, 

 according to Avogadro's law, the number N has the same 

 value for all kinds of gas. 



7O. Frequency of Collisions 



From the value of the free path and of the known 

 magnitude of the molecular speed we can without difficulty 

 determine the frequency of the collision of any particle with 

 others, and the time which on an average elapses between 

 two successive collisions. We need only remember that the 

 speed is simply measured by the length of path traversed in 

 the unit of time. 



If now a particle traverses on an average in unit time 

 the path O, which in general is zigzag-shaped, and between 

 two successive collisions passes over the average length L in 

 a straight line, the time required on an average for the 

 particle to move over the length L is 



From this interval between successive collisions we obtain 

 the frequency of collision or the number of collisions 

 particle undergoes in unit time, viz. 



If we put for the speed in these formulae the aritl 

 mean H calculated by Maxwell's theory, we must also put 

 for the free path L the value 



as calculated ( 68) on the same theory. 



If, on the contrary, in accordance with Glaus ius' theory, 

 we assign to all the molecules the same mean energy and 

 the same value G of the speed which corresponds to it, the 

 interval between successive collisions in this case would be 



T' = L'/G, 



M 2 



