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

$A$ mixture of $2$ moles of helium gas (atomic mass $= 4 \ amu$) and $1$ mole of argon gas (atomic mass $= 40 \ amu$) is kept at $300 \ K$ in a container. The ratio of the rms speeds $\left(\frac{v_{\text{rms}} \text{ (helium)}}{v_{\text{rms}} \text{ (argon)}}\right)$ is:

Equal volumes of two gases,having their densities in the ratio of $1: 16$,exert equal pressures on the walls of two containers. The ratio of their rms speeds $(c_1: c_2)$ is

The temperature at which the $r.m.s.$ speed of hydrogen molecules is equal to the escape velocity on the Earth's surface will be ...... $K$.

At which temperature will the velocity of $O_2$ molecules be equal to the velocity of $N_2$ molecules at $0 ^\circ C$?

The curve between absolute temperature $T$ and ${v^2}_{rms}$ is