The root mean square velocity of molecules of a gas is

At a given temperature,the $r.m.s.$ velocity of molecules of a gas is

The given diagram shows isotherms for a fixed mass of an ideal gas at temperatures $T_1$ and $T_2$. What is the value of the ratio $\frac{\text{r.m.s. speed of the molecules at temperature } T_2}{\text{r.m.s. speed of the molecules at temperature } T_1}$?

At what temperature is the root mean square (rms) speed of Neon gas atoms equal to the rms speed of Helium gas atoms at $-33^{\circ} C$ (in $K$)? (Atomic mass of $Ne = 20.2 \ u$ and that of $He = 4.0 \ u$)

$A$ container is divided into two equal parts $L$ and $R$. If the root mean square (rms) speed of the molecules in part $L$ is equal to the average speed of the molecules in part $R$,find the ratio of the mass of a molecule in part $L$ to the mass of a molecule in part $R$.

Nitrogen gas is at $300^{\circ} C$ temperature. The temperature (in $K$) at which the $rms$ speed of a $H_{2}$ molecule would be equal to the $rms$ speed of a nitrogen molecule is........ (Molar mass of $N_{2}$ gas = $28 \ g/mol$,Molar mass of $H_{2}$ gas = $2 \ g/mol$)