By what factor will the $r.m.s.$ velocity change if the temperature is raised from $27^\circ C$ to $327^\circ C$?

The temperature of a gas is $-68^{\circ} C$. To what temperature should it be heated,so that the r.m.s. velocity of the molecules be doubled (in $^{\circ} C$)?

The following graph shows two isotherms for a fixed mass of an ideal gas. The ratio of $r.m.s.$ speed of the molecules at temperatures $T_2$ and $T_1$ is

At what temperature $K$ will the $r.m.s.$ speed of hydrogen gas be equal to the $r.m.s.$ speed of oxygen molecules at $47^{\circ}C$?

The speeds of gas molecules are $2, 3, 4, 5, 6 \ km/s$. The $rms$ speed is ............. $km/s$.

Let $\bar{v}$,${v_{rms}}$ and ${v_p}$ respectively denote the mean speed,root mean square speed,and most probable speed of the molecules in an ideal monoatomic gas at absolute temperature $T$. The mass of a molecule is $m$. Then