At what temperature is the $rms$ speed of air molecules doubled compared to its value at $NTP$?

The curve between absolute temperature $T$ and ${v^2}_{rms}$ is

If the rms speed of the molecules of a diatomic gas at a temperature of $322 \ K$ is $2000 \ m \ s^{-1}$,then the gas 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 $^{\circ} C$)?

If the root mean square (rms) speed of nitrogen molecules at room temperature is $100 \ m \ s^{-1}$, then the rms speed of Helium molecules at the same temperature is

To what temperature should the hydrogen at $327^{\circ} C$ be cooled at constant pressure,so that the root mean square velocity of its molecules becomes half of its previous value (in $^{\circ} C$)?