7.10 A polyatomic molecule consists of n atoms, each possessing three degrees of freedom (i.e. we treat each atom as a point mass neglecting its internal degrees of freedom). Divide the degrees of freedom of the molecule into translational, rotational and vibrational degrees: (i) for a nonlinear molecule, (ii) for a linear molecule. (Note that a nonlinear molecule, like a rigid body, possesses three rotational degrees of freedom, e.g. two angles to fix an axis of rotation and a third angle to fix the extent of the rotation about this axis relative to some standard position. On the other hand a linear molecule possesses only two rotational degrees of freedom.

We need two angles to fix the interatomic axis but do not now have rotations about this axis. See the previous problem where the diatomic molecule was considered in detail.)

Use your results to discuss the heat capacity of a polyatomic perfect gas.