1/54 HEAT. 



In place of 



we shall, therefore, put jo 



V 

 where .v is the number of collisions per second. 



But v = 



whence ** 



N7TS 3 



Here - = total volume of the molecular systems per c.c., and since this 



is small we may put 



V 2 



where v = - is the volume of unit mass. 



P 

 If we put 



,N7TS 3 , , , x V 2 



4- w = o we get p (v - 6) = _. 



O o 



Now let us turn to the second consideration, that of time lost in 

 collision. We may think of a slackening of the velocity on close approach 

 and then an acceleration, so that in each collision there is a time greater 

 on the average by r than if one free path had instantaneously changed 

 to the next. If v is the number of collisions in one second, the time 

 occupied in traversing a given path will be greater than that obtained 

 on the supposition of instantaneous change in the ratio 



l+vrrl, 



and a molecule or its representative will return less often to a face of 

 the containing vessel in the ratio 1 : 1 + VT. On this account then, the 

 pressure will be reduced to 



J_ Z? _L 



P v-b 3 I+VT 

 or, instead of p, we must 



Now v = =- = VNvrs 2 and Nwi = p where m = mass of a molecule. 

 L 



therefore v = V/> . 



m 



