The temperature of an ideal gas increases from $120 \ K$ to $480 \ K$. If the root mean square velocity of the gas molecules at $120 \ K$ is $v$,then at $480 \ K$ it will be .......

The root mean square speeds at $STP$ for the gases $H_2, N_2, O_2$ and $HBr$ are in the order

Explain the Maxwell-Boltzmann distribution law with a graph.

Write the relationship between $u_{rms}$,$u_{mp}$,and $u_{av}$.

The $RMS$ velocity of dihydrogen $(H_2)$ is $\sqrt{7}$ times more than that of dinitrogen $(N_2)$. If $T_{H_2}$ and $T_{N_2}$ are the temperatures of dihydrogen and dinitrogen respectively, then the correct relationship between them is:

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.