The temperature of an ideal gas is increased from $100 \ K$ to $400 \ K$. If '$x$' is the root mean square velocity of its molecules at $100 \ K$,what is the new root mean square velocity?

Derive the equation of $v_{rms}$ in terms of molar mass.

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 $K$)

Six molecules of an ideal gas have velocities $1, 3, 5, 5, 6$ and $5 \,m/s$ respectively. At any given temperature, if $\overline{V}$ and $V_{rms}$ represent average and rms speed of the molecules, then

The density of hydrogen gas at standard atmospheric pressure $(P = 1.01 \times 10^{5} \ Pa)$ is $0.09 \ kg/m^{3}$. Find the root mean square velocity $(v_{rms})$ and the average kinetic energy of $1 \ mole$ of the gas.

If the root mean square velocity of a hydrogen molecule at a given temperature and pressure is $2 \,km/s$, the root mean square velocity of oxygen at the same condition in $km/s$ is: