$A$ perfect gas of volume $10 \ L$ is compressed isothermally to a volume of $1 \ L$. The $rms$ speed of the molecules will

The root mean square speed of the molecules of a gas is

At what temperature will the $rms$ speed of oxygen molecules become just sufficient for escaping from the Earth's atmosphere $?$ (Given: Mass of oxygen molecule $(m) = 2.76 \times 10^{-26} \, kg$,Boltzmann's constant $k_B = 1.38 \times 10^{-23} \, JK^{-1}$)

When the temperature of an ideal gas is increased from $27^{\circ} C$ to $127^{\circ} C$,calculate the percentage increase in its $v_{\text{rms}}$. (in $\%$)

The root mean square velocity of a gas molecule of mass $m$ at a given temperature is proportional to

$A$ container is divided into two equal halves by a diathermic partition. Two different ideal gases are filled in the left $(L)$ and right $(R)$ parts. The $rms$ speed of the molecules in the $L$ part is equal to the average speed of the molecules in the $R$ part. Find the ratio of the mass of a molecule in the $L$ part to the mass of a molecule in the $R$ part.