680 Prof. B. M. Sen on the Kinetic Theory of Solids 



We now calculate the pressure at the surface due to the 

 molecular forces, the atmospheric pressure being of course 

 negligible. We take into account only seven of the fourteen 

 molecules lying on one side of the equatorial plane. The 

 potential energy in the displaced position, x being the 

 displacement from the mean position, 



. =7/(Z)-4*/'(Z). 

 Force along the normal 



= 4/'(/) = 4F, 



where F is the force between two molecules. 

 Pressure at the surface = 4N 2/3 . F. 



.'. ^=4F 



6a 



or a= 77T ( 2 > 



9. Compressibility. 



We proceed to find the simplest of the elastic constants, 

 viz. compressibility, on the basis of our hypothesis. The 

 work done against the molecular forces = /3 per molecule 

 for 1° rise of temperature. 



Now the pressure at the surface = 4F . N ; . 



Work done against the surface pressure = N . 12Fa l5 

 where a x is the coefficient of linear expansion. 



Work done against the inter-molecular forces per unit 

 volume = 7FSZ . N^TFc^N 2 ' 3 , there being fourteen mole- 

 cules arranged about each individual molecule and Ba = Bl. 



.-. X/3 = WFcc^ 3 . .-. F =r |^. ... (3) 



a0 19a0. ai l 



a= -7T 



i2F 12/3 



Now the surface pressure = 4F . N J/t5 = 



2/3 4N/3 



19V 



If the pressure be increased by one dyne without change 



19a 

 of temperature, it increases by ^ T * th part of itself. 



8a _ 1 9a ] 

 ""' ~a~~~W^' 



8l__a L 19«i 

 •'* I ~ I ' 4N/T 



