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

If $V_{rms}$ for $O_2$ molecules is $V$ at temperature $T \ K$. Then $V_{rms}$ for oxygen atoms at temperature $2T$ will be

The r.m.s. speed of a group of $7$ gas molecules having speeds $(6, 4, 2, 0, -2, -4, -6) \, m/s$ is ...... $m/s$.

The root mean square speed of smoke particles of mass $5 \times 10^{-17} \, kg$ in their Brownian motion in air at $NTP$ is approximately $....... \, mm \, s^{-1}$. [Given $k = 1.38 \times 10^{-23} \, J \, K^{-1}$ and $T = 293 \, K$]

The root mean square velocity of molecules of a gas is

The root mean square speed of hydrogen molecules of an ideal hydrogen gas kept in a gas chamber at $0^{\circ}C$ is $3180 \ m/s$. The pressure on the hydrogen gas is ..... $atm$ (Density of hydrogen gas is $8.99 \times 10^{-2} \ kg/m^3$,$1 \ atm = 1.01 \times 10^5 \ N/m^2$).