358 Prof. G. W. Todd on the Variation of the 



The translational energy of these molecules is therefore 



y /^ SSm \2U0j e 



So that the kinetic energy of molecules in 1 c.c. having 

 velocities greater than a critical value c is 



9 , v 3/2 >oo _ »JC2 



The total energy of these molecules is 



3 + ? 2 AT / m \ 32 f°° , , 



Vt? Ni,i W J. *'*■ 



The translational energy of molecules in 1 c.c. with 

 velocities less than c is 



M^)T^ 



_2_ 



and since by hypothesis these have only three degrees of 

 freedom, this is also their total energy. 



Hence the total energy of 1 c.c. of the gas is 



w-£*-<ft)*M"*-H.v*}- <' 



It follows that the Specific Heat at Constant Volume will 

 be given by 



2 

 When 2 = 0, the equation becomes 



r&KAm'f ♦■*♦!>*)■}•• » 



_ _ JL d f 2R0 3 ./it \ = 3R 



which is the usual expression for a monatomic gas. 

 Now the integral 



( * • <* c== Ur; J * ^ where x=c V «!?• 



