At what temperature will the molecules of nitrogen have the same $r.m.s.$ velocity as the molecules of oxygen at $127^{\circ}C$ (in $^{\circ}C$)?

$A$ flask contains argon and chlorine in the ratio of $2:1$ by mass. The temperature of the mixture is $27^{\circ}\text{C}$. The ratio of root mean square speed of the molecules of the two gases $\left(\frac{v_{\text{rms}}^{\text{Ar}}}{v_{\text{rms}}^{\text{Cl}}}\right)$ is : (Atomic mass of argon $= 40.0 \text{u}$ and molecular mass of chlorine $= 70.0 \text{u}$)

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 $27\,^oC$,the $rms$ velocity of $H_2$ gas is $100\, m/s$. Find the $rms$ velocity of $O_2$ gas at $327\,^oC$.

In a sample of chlorine gas at $300 \ K$,the average kinetic energy per molecule is $6.21 \times 10^{-21} \ J$ and the root mean square speed $\nu_{rms}$ is $325 \ m/s$. What will be the values of these quantities at $600 \ K$?

At what temperature (in $K$) is the $rms$ velocity of a hydrogen molecule equal to that of an oxygen molecule at $47^o \ C$?