The temperature of the gas is raised from $27\,^oC$ to $927\,^oC$. The root mean square velocity is:

By how many folds will the temperature of a gas increase when the root mean square velocity of the gas molecules in a container of fixed volume is increased from $5 \times 10^4 \ cm/s$ to $10 \times 10^4 \ cm/s$?

At what temperature will the $rms$ speed of $N_2$ gas at $1 \, atm$ pressure be equal to the $rms$ speed of $CO_2$ at $STP$?

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 $400 \ K$,the root mean square $(rms)$ speed of a gas $X$ (molecular weight $= 40$) is equal to the most probable speed of gas $Y$ at $60 \ K$. The molecular weight of the gas $Y$ is:

What is the approximate most probable velocity of oxygen,if the kinetic energy of one mole of oxygen is $3741.3 \ J$?