120 Physical Properties [OH. vi 



have just collided with dS, and therefore over all values of v and w and over 

 all negative values of u. 



Substituting these values in equation (258), we obtain 



HO 



rrr 

 p = 2 m a (v a \ 1 1 lf a (u, v, w)u 2 dudvdw (284), 



where the integration now extends over all values of u, v and w. The 

 integral is the mean value of u 2 for all molecules of type a. If we denote 

 this by w a 2 we have, from equation (161) as before, 



m ^=l, 

 so that 



= 'S l m 



(zv)i 1 1 1 fa (u, v, w) u? dudvdw 



= Yh* Ml .......... ' .................................. (285)) 



and when there is only one kind of gas present, 



p=w> .................................... ( 286 >- 



Here v l is the "effective molecular density" at the nearest point to the 

 boundary at which it is possible for the centre of a molecule to lie. To 

 suggest the point at which v^ is measured, let us denote its value for this 

 point by v b , so that 



p = ^ = R Vb T ........................... (287). 



DEVIATIONS FROM THE LAWS OF DALTON, AVOGADRO, BOYLE, AND CHARLES. 



138. It will be clear both from Van der Waals' equation and the equation 

 just obtained that the various simple laws deduced from the former equation 

 (262), namely 



all require correction when we abandon the simplifying hypotheses upon 

 which this equation was deduced. 



Deviations from Avogadro's Law. 



139. If two gases are at the same temperature and pressure it follows 

 from equation (287) that i/ 6 must be the same for both. The correction 

 required for Avogadro's Law, therefore, consists simply in replacing v by j/ 6 . 



