An adiabatic vessel contains n_ 1 =3 mole of a diatomic gas. Moment of inertia of each…

An adiabatic vessel contains \(n_{1}=3\) mole of a diatomic gas. Moment of inertia of each molecule is \(I=2.76 \times 10^{-45} \mathrm{~kg} \mathrm{~m}^{2}\) and root mean square angular velocity is \(\omega_{g}=5 \times 10^{12} \mathrm{rad} / \mathrm{sec}^{\circ}\). Another adiabatic vessel contains \(n_{2}=5\) mole of a monatomic gas at temperature \(T_{\square}=470 \mathrm{~K}\). Assuming gases to be ideal, calculate root mean square angular velocity of diatomic molecules when the two vessels are connected by a thin nonconducting tube. Boltzmann's constant, \(\mathrm{k}_{\mathrm{G}}=1.38 \times 10^{-23} \mathrm{~J} / \mathrm{K}\)