Let us consider a diatomic gas whose molecules have the shape of a dumbell. In this model, the center of mass of the molecule can translate in the `x,y` and `z` directions. In addition, the molecule can rotate about three mutually perpendicular axes. We can neglect the rotation about the `y` -axis because the moment of inertia `I_(y)` and the rotational energy `1/2 I_(y)omega^(2)` about this axis are negligible compared with those associated with the `x` and `z` axes. (If the two atoms are taken to the point masses, then `I_(y)` is identically zero). Thus, there are five degrees of freedom: three associated with the translation motion and two associated with the rotational motion. Because each degree of freedom contributes, on average, `1/2k_(B)T` of energy per molecule, the total internal energy for a system of `N` molecules is:
`E_("int")=3N(1/2k_(B)T)+2N(1/2k_(B)T)=5/2NK_(B)T=5/2nRT`...........(i)
We can use this result to find the molar specific heat at constant volume:
`C_(v)=1/n (dE_("int"))/(dT)=1/n d/(dT)(5/2nRT)=5/2R`................(ii)
From equation (i) and (ii) we find that
`C_(P)=C_(V)+R=7/2R`
`gamma=(C_(P))/(C_(V))=(7//2R)/(5//2r)=7/5=1.40`
In the vibratory model, the two atoms are joined by an imaginary spring. The vibrational motion adds two more degrees of freedom, which correspond to the kinetic energy and the potential associated with vibrations along the length of the molecule about its centre of mass.

A diatomic molecule is moving without rotation or vibration with velocity `v_(rms)` such that it is oriented along `x`- axis. It strikes a wall in `yz`- plane while moving in +ve `x` direction. The spring constant can be assumed to be `K` and time of collision is negligible. After all collision are over:

Options

A. The molecule is moving along -ve x-direction and oscillating about its centre of mass
B. The molecule is moving along -ve `x`-direction but not oscillating about its centre of mass
C. The molecule is oscillating about it centre of mass but not moving at all
D. The molecule is neither rotating nor moving at all

Answer

B

Explanation

NA