119-1-23] Boyle's Law 107 



The integration is therefore over all values of v and w, and over all negative 

 values of u. 



By addition of the two results just obtained, and comparison with equation 



(258) we obtain 



+ 



p f f 



(u, v, w)u*dudvdw (261), 



the integration now extending over all possible values of the velocity com- 

 ponents. 



The integral is equal to the mean value of w 2 throughout the gas. If, as 

 before, we denote this by u? } we have from equation (161), 



mw 2 = ^, 



in which we now introduce the supposition that the gas is in the normal 

 state. Hence we have the pressure in the forms 



p = mvu 2 = ~ (262), 



or again, if we use the relation mv = p, we have 



p = piC 1 = ^pc 2 ,(263). 



This last result can be conveniently stated in words in the form : 



The pressure per unit area of surface is equal to two-thirds of the Icinetic 

 energy of translational motion per unit volume of the gas. 



Boyle's Law. 



122. Since the heat of a gas, on the hypothesis of the Kinetic Theory, 

 represents the energy of motion of the molecules of the gas, we must suppose 

 that c- remains the same so long as the temperature of the gas remains the 

 same. Hence from equation (263) we can deduce Boyle's Law : 



The pressure of a gas is proportional to its density so long as the tem- 

 perature remains unaltered. 



The exact relation between the temperature and the value of c 2 , must 

 however be the subject of more careful discussion later. 



Pressure in a Mixture of Oases. 



123. If there are present in the gas molecules of different types a, /3 . . . , 

 equation (261) must be replaced by 



00 



p = X m a v a 1 1 1 f a (u, v, w) u?dudvdw, 



