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



I 



and r 2 ==l— J^ + f.— 



••• M)=/(0 + (^+I t)/'(0+^ 2 /"(0, 



and fir,) =/(/) + (-** + ! j)/(0 + '4*V"(0- 



... /(n)+/(r 2 )=2/0) + f " r /'(0 + |.^./"(0- 



There are six pairs of such molecules. The total potential 

 energy 



It may be noted that the attractive force is/' (7)- And if, 

 as is only natural to assume, the force diminishes with the 

 distance, /"(/) is negative. And if the force varies as any 

 power of: the distance, the two terms of the variable part of 

 the potential energy are of the same order of magnitude. 



It is obvious, moreover, from general considerations that 

 the potential energy for any displacement x must be of the 



type A-f B<2? 2 -f- If the coefficient of x be not zero, there 



will be a permanent force independent of the displacement. 



The equation of energy, therefore, is 



MV 2 + ^IV_W +-5/"(0J= const. . . (1) 



The motion, therefore, is simple harmonic if the coefficient 

 of x 2 be positive. If the molecule can complete its oscil- 

 lation, the average potential energy would be equal to the 

 average kinetic energy. We assume that this is not the 

 case, so that the molecule comes into collision with its 

 neighbour as soon as it has described a small fraction of its 

 path *. 



5. Order of magnitude of the Kinetic and Potential Energy 

 terms. 

 In the equation (1) above, the first term 

 MY 2 = 2*6 



is of order 10~ 14 , for a = 2'02 X 10 -16 and 6 is the temperature. 

 From known values of the specific heat and the coefficient 

 of linear expansion, it will be proved that ,/'(/) is of order 

 10~ 5 and the maximum displacement of order 10" °. Now, 

 I being of order 10 ~ 8 , the potential energy term is of order 



* The reason for this assumption has heen given in the preface. 



