The $rms$ speed of hydrogen molecules at room temperature $(300 \ K)$ will be:

Equal volumes of two gases are kept in different containers having densities in the ratio $1:16$. They exert equal pressures on the walls of their respective containers. Then the ratio of their r.m.s. velocities is

For a gas at a temperature $T$,the root-mean-square velocity ${v_{rms}}$,the most probable speed ${v_{mp}}$,and the average speed ${v_{av}}$ obey the relationship:

An $HCl$ molecule has rotational,translational,and vibrational motions. If the $rms$ velocity of $HCl$ molecules in its gaseous phase is $\bar{v}$,$m$ is its mass,and $k_B$ is the Boltzmann constant,then its temperature will be:

At temperature $T$,$N$ molecules of gas $A$ each having mass $m$ and at the same temperature $2N$ molecules of gas $B$ each having mass $2m$ are filled in a container. The mean square velocity of molecules of gas $B$ is $v^2$ and the mean square of the $x$-component of velocity of molecules of gas $A$ is $w^2$. The ratio of $w^2/v^2$ is:

The temperature of an ideal gas is increased from $200 \ K$ to $800 \ K$. If the r.m.s. speed of the gas at $200 \ K$ is $v_0$,then the r.m.s. speed of the gas at $800 \ K$ will be: