The $RMS$ velocity of $CO$ gas molecules at $27^{\circ} C$ is approximately $1000 \ m / s$. For molecules at $600 \ K$,the $RMS$ velocity is approximately (in $m / s$)

Case $-1:$ An ideal gas of molecular weight $M$ at temperature $T$.
Case $-2:$ Another ideal gas of molecular weight $2M$ at temperature $T/2$.
Identify the correct statement in the context of the above two cases.

What change occurs in the velocity distribution graph when the temperature is increased?

For a gaseous state,if the most probable speed is denoted by $C^*$,average speed by $\overline{C}$,and root mean square speed by $C$,then for a large number of molecules,the ratio of these speeds is:

The $rms$ speed of $N_2$ molecules in a gas is $v$. If the temperature is doubled and the nitrogen molecules dissociate into nitrogen atoms,the $rms$ speed becomes

The average speed $(U_{avg})$ of $O_2$ at $\pi \times 10 \ bar$ pressure in an $8 \ L$ container containing $2 \ moles$ is: