If the rms velocity of a perfect gas at $27^{\circ} C$ is $500 \,m \cdot s^{-1}$,the same at $927^{\circ} C$ will be

The temperature at which the rms speed of molecules in hydrogen gas will be double of its initial value at $27^{\circ} C$ is (in $^{\circ} C$)

The temperature at which the root mean square speed of a gas will be half of its value at $0\,^{\circ}C$ is ....... $^{\circ}C$.

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

At a given temperature,if $V_{rms}$ is the root mean square velocity of the molecules of a gas and $V_s$ is the velocity of sound in it,then these are related as $\left( \gamma = \frac{C_P}{C_v} \right)$:

Let $\overline{V}$,$V_{\text{rms}}$,and $V_{p}$ denote the mean speed,root mean square speed,and most probable speed of the molecules each of mass $m$ in an ideal monoatomic gas at absolute temperature $T$ Kelvin. Which statement$(s)$ is/are correct?