For a given gas at $1\,atm$ pressure,the $rms$ speed of the molecules is $200\,m/s$ at $127\,^oC$. At $2\,atm$ pressure and at $227\,^oC$,the $rms$ speed of the molecules will be:

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 velocities of $4$ gas molecules are given by $1 \ km/s, 3 \ km/s, 5 \ km/s$ and $7 \ km/s$. Calculate the difference between the average velocity and the root mean square $(RMS)$ velocity. (in $km/s$)

If a container is filled with a mixture of $H_2$ and $O_2$ gases at the same temperature,then:

Consider a sample of oxygen behaving like an ideal gas. At $300 \, K$,the ratio of root mean square (rms) velocity to the average velocity of gas molecules would be: (Molecular weight of oxygen is $32 \, g/mol$,$R = 8.3 \, J \, K^{-1} \, mol^{-1}$)

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