The molecular mass of a gas having $r.m.s.$ speed four times as that of another gas having molecular mass $32$ is

When the temperature of a gas is raised from $27^{\circ} C$ to $90^{\circ} C$,the increase in the rms velocity of the gas molecules is: (in $\%$)

At $T$ $K$ temperature,the average speed of $O_2$ will be $\left( \frac{7}{4} \right)$ of the $rms$ speed of $N_2$ at $47\,^oC$. Find the value of $T$.

At what temperature is the root mean square speed of an atom in an argon gas cylinder equal to the rms speed of a helium gas atom at $-20\,^{\circ} C$? (Atomic mass of $Ar = 39.9 \; u$,of $He = 4.0 \; u$)

If ${V_H}$,${V_N}$,and ${V_O}$ denote the root-mean-square velocities of molecules of hydrogen,nitrogen,and oxygen respectively at a given temperature,then:

The temperature at which the root mean square velocity of hydrogen molecules equals their escape velocity from the Earth is closest to: [Boltzmann constant $k_B = 1.38 \times 10^{-23} \, J/K$,Avogadro number $N_A = 6.02 \times 10^{23} \, mol^{-1}$,Molar mass of $H_2 = 2 \times 10^{-3} \, kg/mol$,Radius of Earth $R_e = 6.4 \times 10^6 \, m$,Gravitational acceleration $g = 10 \, m/s^2$]