If the temperature of a gas is increased from $127^{\circ} C$ to $527^{\circ} C$, then the rms speed of the gas molecules

$A$ 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.

At what temperature will the root mean square $(rms)$ speed of oxygen molecules be sufficient to escape from the Earth's atmosphere? (Mass of an oxygen molecule $m = 2.76 \times 10^{-26} \, kg$,Boltzmann constant $k_B = 1.38 \times 10^{-23} \, JK^{-1}$,Escape velocity of Earth $v_e = 11.2 \, km/s$)

The $rms$ speed of gas molecules in a container is $400 \, ms^{-1}$. If half of the gas is removed at a constant temperature,the new $rms$ speed will be .... $ms^{-1}$.

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 ..... $m/s$.

At $27\,^oC$,the $rms$ velocity of $H_2$ gas is $100\, m/s$. Find the $rms$ velocity of $O_2$ gas at $327\,^oC$.