256 



Free Path Phenomena 



[CH. XII 



309. A table expressing the variation of a- with the temperature will 

 give some information, although slight, as to the field of force surrounding 

 the molecules. For the calculated value of <r is, roughly speaking, the 

 average distance of closest approach of the centres of two molecules in 

 collision, so that the mutual potential energy of two molecules at a distance <r 

 is, on the average, equal to the kinetic energy of the velocities along the line 

 of centres before collision. 



As in formula (245), the average value of F 2 , the square of the relative 

 velocity before collision, is f c 2 . Thus the square of the velocity of each 

 molecule relatively to the centre of gravity of the two colliding molecules 

 will be, on the average, fc 2 . The probability that the direction of this 

 velocity makes an angle with the line of centres, which, lies between 6 and 

 4- d0, is 2 sin 9 cos 6d0, so that the average square of the relative velocity 

 along the line of centres is 



" 



The kinetic energy which has been destroyed by the intermolecular field of 

 force when the molecules are, on the average, at their point of closest approach 

 at distance a- apart is therefore 



= RT. 



Thus we may say that the mutual potential energy of two molecules at a 

 distance <r apart will be RT, where T is the temperature corresponding to the 



