If the temperature of gas molecules is raised from $127^{\circ} C$ to $527^{\circ} C$,the ratio of the r.m.s. speed of the molecules is respectively:

Let the r.m.s. velocity of a molecule of a given mass of gas be $C_{1}$ at temperature $27^{\circ} C$. When the temperature is increased to $327^{\circ} C$,the r.m.s. velocity is $C_{2}$. Then the ratio $\frac{C_{2}}{C_{1}}$ is

Three vessels $A$,$B$,and $C$ contain gases at the same temperature. Vessel $A$ contains $O_2$ gas,vessel $B$ contains $N_2$ gas,and vessel $C$ contains a mixture of $O_2$ and $N_2$ gases. If the average velocity of $O_2$ in vessel $A$ is $V_1$ and the average velocity of $N_2$ in vessel $B$ is $V_2$,what is the average velocity of $O_2$ in vessel $C$?

The $rms$ speed of helium gas at $27\,^{\circ}C$ and $1\,atm$ pressure is $900\,ms^{-1}$. Then the $rms$ speed of helium molecules at temperature $27\,^{\circ}C$ and $2\,atm$ pressure is ...... $m/s$.

For a given gas,the velocities of $5$ molecules are $2, 3, 4, 5,$ and $6$. What is the $rms$ velocity?

$A$ gas is at a temperature of $0^{\circ}C$. To what temperature in $^{\circ}C$ must the gas be heated so that the $rms$ speed of its molecules becomes double?