# Rotating molecules of a gas

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 \(k = 1.38 \times 10^{-23} J/K\)