A gas consisting of `N-`atomic molecules has the temperature `T` at which all degrees of freedom (translational, rotational, and vibrational) are excited. Find the mean energy of molecules in such a gas. What fraction of this energy corresponds to that of translational motion ?

Explanation

For a general noncollinear, nonplaner molecule
mean energy `= (3)/(2) kT ("translational")+(3)/(2) kT("rotational") + (3 N - 6) kT("vibrational")`
=`(3 N - 3) kT` per molecule
For linear molecules, mean energy `= (3)/(2) kT` (translational)
`+ kT("rotational")+(3 N - 5) kT("vibrational")`
=`(3 N - (5)/(2)) kT` per molecule
Translational energy is a fraction `(1)/(2(N - 1))` and `(1)/(2 N - (5)/(3))` in the two cases.