164 THE REALITIES OF MODERN SCIENCE 



Let v represent the average velocity of the mole- 

 cules in the direction of the dimension a of the box. 

 So far as concerns the impacts of any of these mole- 

 cules on the end be it is evident that there will be one 

 impact for every time a molecule, moving with this 

 velocity, would make one round trip 1 between this 

 end and the opposite one That is, for every 2a cm. 

 which it travels in the a direction it will strike the end 

 be. Since it travels v cm. per second it will make 

 v/2a impacts per second. Since there are N/3 mole- 

 cules which are in effect traveling in this direction 

 there will be a total of Nv/Qa impacts per second. 

 The force exerted on be is therefore 



fe > 

 _(2m,)or 



Dividing by the area be gives the pressure, P, as 



p _W_fmtf\ 

 3abc\ 2 ) 



in which the product abc is the volume V of the con- 

 tainer. Hence 



We have thus obtained a relation which indicates that, 

 provided the average kinetic energy of translation, 

 7V(mt; 2 /2), of a group of TV molecules is not altered, the 

 product of the pressure and volume is constant. In 



1 Actually, of course, any particular molecule may collide with 

 another and bounce back. The other molecule also bounces back. 

 The net effect so far as concerns impacts on the walls is just the 

 same as if the molecules had passed by or through each other. 



