For an ideal gas with constant pressure,the root mean square velocity $v_{rms}$ is proportional to . . . . . . .

The $rms$ speed of a molecule of a diatomic gas is $v$. When the temperature is doubled,the molecule dissociates into two atoms. The new $rms$ speed of the atom is:

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

$N$ $(N < 100)$ molecules of a gas have velocities $1, 2, 3, ..., N \text{ km/s}$ respectively. Then:

The temperature at which oxygen molecules will have the same r.m.s. speed as helium molecules at $57^{\circ} C$ is (molecular masses of oxygen and helium are $32$ and $4$ respectively.) (in $K$)

The $rms$ speed of gas molecules in a container is $400 \, ms^{-1}$. If half of the gas is removed at a constant temperature,the new $rms$ speed will be .... $ms^{-1}$.