If the ratio of vapour density for hydrogen and oxygen is $\frac{1}{16}$,then under constant pressure,the ratio of their rms velocities will be

The $rms$ speed of $n$ molecules in a gas having speeds $\upsilon_1, \upsilon_2, \upsilon_3, \dots, \upsilon_n$ is equal to:

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 ..... $\%$

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:

The root mean square speed of the molecules of a diatomic gas is $v$. When the temperature is doubled,the molecules dissociate into two atoms. The new root mean square speed of the atom is

The temperature of a gas is $-80^{\circ} C$. To what temperature should the gas be heated so that the r.m.s. speed is increased by $2$ times (in $^{\circ} C$)?