The temperature at which oxygen molecules have the same root mean square speed as helium atoms have at $300 \ K$ is (Atomic masses: $He = 4 \ u$,$O = 16 \ u$) (in $K$)

The ratio of the most probable speed,average speed,and $RMS$ speed is given by:

If the average velocity of $N_2$ molecule is $0.3 \, m/s$ at $27 \, ^\circ C$,then the velocity will be $0.6 \, m/s$ at ........... $K$.

If the most probable speed of $CO_2$ at $27^{\circ} C$ is $400 \ ms^{-1}$,the root mean square velocity of $CO_2$ at the same temperature in $ms^{-1}$ is approximately:

$RMS$ velocity of one mole of an ideal gas was measured at different temperatures. $A$ graph of $(u_{rms})^2$ (on y-axis) and $T(K)$ (on x-axis) gave a straight line passing through the origin and its slope is $249 \ m^2 \ s^{-2} \ K^{-1}$. What is the molar mass (in $kg \ mol^{-1}$) of the ideal gas? $(R=8.3 \ J \ mol^{-1} \ K^{-1})$

Initially,the root mean square $(rms)$ velocity of $N_2$ molecules at a certain temperature is $u$. If this temperature is doubled and all the nitrogen molecules dissociate into nitrogen atoms,then the new $rms$ velocity will be: