The temperature at which oxygen molecules will have the same r.m.s. speed as helium molecules at $57^{\circ} C$ is (molecular masses of oxygen and helium are $32$ and $4$ respectively.) (in $K$)

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

The temperature at which the $r.m.s.$ speed of hydrogen molecules is equal to the escape velocity on the Earth's surface will be ...... $K$.

When the temperature of a gas is raised from $27^o C$ to $90^o C$,the percentage increase in the $r.m.s.$ velocity of the molecules will be ..... $\%$

$A$ 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 room temperature,the $r.m.s.$ speed of the molecules of a certain diatomic gas is found to be $1920\, m/s$. The gas is