The r.m.s. velocity of gas molecules kept at temperature $27^{\circ} C$ in a vessel is $61 \ m/s$. The molecular weight of the gas is nearly:
$[R = 8.31 \ J \ mol^{-1} \ K^{-1}]$

Let $\overline{V}$, $V_{\text{rms}}$, and $V_{p}$ denote the mean speed, root mean square speed, and most probable speed of the molecules each of mass $m$ in an ideal monoatomic gas at absolute temperature $T$ Kelvin. Which statement$(s)$ is/are correct?

Five molecules of a gas have speeds $1, 2, 4, 8$ and $16 \, m/s$ at some instant. The root mean square velocity of the gas molecules is ..... $m/s$.

$A$ sample of gas is at $0^{\circ}C$. To what temperature must it be raised in order to double the $r.m.s.$ speed of the molecules? (in $^{\circ}C$)

In thermal equilibrium,the average velocity of gas molecules is

The $rms$ speed of air molecules in a vessel is $90 \times 10^2 \ m/s$. If half of the gas leaks out at constant temperature,the $rms$ speed of the remaining air molecules will be