Why are there only 2 rotational degree of freedom for diatomic gases?
Dear Student , 
There is one principal axis passing through the middle of the rod in the direction perpendicular to the plane where it situated ( in case of three different axes x,y and z axes) .
Now we have contributions from z axis and y axis but moment of inertia is zero in case of x axis as those masses are point like mass and thus the distance of these masses from the axis is zero. So no rotational energy as well since rotational energy is (1/2) Iw2 .
Thus hence there are 2 rotational degrees of freedom for diatomic gases.
Hope this explanation helps you.
Regards
As we know diatomic gas is like two masses constrained by a rod. Rotational degrees of freedom comes from rotation about principal axis contributing to the energy of the system.
There is one principal axis passing through the middle of the rod in the direction perpendicular to the plane where it situated ( in case of three different axes x,y and z axes) .
Now we have contributions from z axis and y axis but moment of inertia is zero in case of x axis as those masses are point like mass and thus the distance of these masses from the axis is zero. So no rotational energy as well since rotational energy is (1/2) Iw2 .
Thus hence there are 2 rotational degrees of freedom for diatomic gases.
Hope this explanation helps you.
Regards