The temperature at which $RMS$ velocity of $SO_2$ molecules is half that of $He$ molecules at $300 \ K$ is ............... $K$.

If a gas contains only three molecules that move with velocities of $100, 200, 500 \ ms^{-1}$. What is the rms velocity of that gas in $ms^{-1}$?

At a temperature of $27\,^{\circ}C$,$0.5 \, mol$ of $O_2$ gas is filled in a $50 \, L$ container at a pressure of $2 \, atm$. If half of the $O_2$ molecules are removed from the container,the $rms$ speed of the $O_2$ molecules will........

The following graph is obtained for a gas at different temperatures $T_1$,$T_2$,$T_3$. What is the correct order of temperature? ($x$-axis $=$ velocity; $y$-axis $=$ number of molecules)

Molecular velocities of two gases at the same temperature $(T)$ are $u_{1}$ and $u_{2}$. Their masses are $m_{1}$ and $m_{2}$ respectively. Which of the following expressions is correct at temperature $T$?

The average speed of $CH_4$ molecules at $300 \ K$ is equal to the average speed of $O_2$ molecules at ............ $K$.