If $U$ be the internal energy of a diatomic gas of molar mass $M$, then r.m.s velocity of the gas mo

Question

If $U$ be the internal energy of a diatomic gas of molar mass $M$, then r.m.s velocity of the gas molecules is

Professor PC Thomas Classes · Answer

Kinetic energy per mole of gas is $\frac{1}{2} M v_{r m s}^2=\frac{3}{2} R T$ Internal energy of a diatomic gas $U=\frac{5}{2} R T$ \ $ \begin{aligned}  	herefore \quad \frac{1}{2} M v_{r m s}^2=\frac{3}{5} U \  	ext { or } \quad v_{r m s}=\sqrt{\frac{6}{5} \frac{U}{M}} \end{aligned} $