The temperature of an ideal gas is increased from $27^{\circ} C$ to $927^{\circ} C$. The r.m.s. speed of its molecules becomes

At a given temperature,the root mean square velocities of oxygen and hydrogen molecules are in the ratio:

If the temperature of a gas is increased from $27^{\circ} C$ to $159^{\circ} C$, the increase in the rms speed of the gas molecules is (in $\%$)

At a temperature of $300 \ K$,the kinetic energy of $O_2$ is $6.21 \times 10^{-21} \ J$ and its $rms$ speed is $484 \ m/s$. What will be the kinetic energy and $rms$ speed at $600 \ K$?

Three closed vessels $A, B$ and $C$ are at the same temperature $T$ and contain gases. Vessel $A$ contains only $O_2$,vessel $B$ contains only $N_2$,and vessel $C$ contains a mixture of equal quantities of $O_2$ and $N_2$. If the rms speed of $O_2$ molecules in vessel $A$ is $v_1$ and that of $N_2$ molecules in vessel $B$ is $v_2$,then the rms speed of $O_2$ molecules in vessel $C$ is:

$A$ gas is allowed to expand isothermally. The root mean square velocity of the molecules