Rotating molecules of a gas

Level pending

Consider a thermally insulated cylinder containing ideal gas having triatomic rigid molecules having moment of inertia about center of mass $$I = 3 \times 10^{-46} \text{ Kg} m^2$$ each. The initial temperature is $$T_{0} = 400K$$. Now , the gas is compressed by a factor of $$n=4$$, such that in the time of compression, volume $$V$$ decreases linearly with time $$t$$. Clearly, over this time the root mean square angular velocity, $$\Omega = \sqrt{<\omega^2>}$$ of particles would change . Find the value of $$\sqrt{<\Omega^2>}$$ (in m/s) over the course of the time of compression .

Details and assumptions

Boltzmann constant $$k = 1.38 \times 10^{-23} J/K$$

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