At what temperature $(K)$ will the $r.m.s.$ velocity of hydrogen gas be equal to the escape velocity from the Earth?

The rms speed of a gas molecule is $V$ at pressure $P$. If the pressure is increased by two times,then the rms speed of the gas molecule at the same temperature will be

At a temperature of $27^{\circ}C$ and a pressure of $1 \, atm$,the ratio of the root mean square velocities $(\nu_{rms})_{H_2} / (\nu_{rms})_{O_2}$ for hydrogen and oxygen molecules is:

The temperature of an ideal gas is reduced from $927^\circ C$ to $27^\circ C$. The $r.m.s.$ velocity of the molecules becomes

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:

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: