The temperature of an ideal gas is increased from $140 \,K$ to $560 \,K$. If the r.m.s. speed of gas molecules is $v$ at $140 \,K$, then at $560 \,K$, the r.m.s. speed becomes:

The $r.m.s.$ speed of the molecules of a gas at a pressure $10^5 \ Pa$ and temperature $0^\circ C$ is $0.5 \ km \ sec^{-1}.$ If the pressure is kept constant but temperature is raised to $819^\circ C,$ the velocity will become ........ $km \ sec^{-1}.$

At what temperature will the root mean square speed $(\nu_{rms})$ of oxygen gas molecules be equal to the $\nu_{rms}$ of hydrogen gas molecules at $27 \, ^\circ C$? $(M_{O_2} = 32 \, g \, mol^{-1}, M_{H_2} = 2 \, g \, mol^{-1})$

If the $r.m.s.$ velocity values for hydrogen,nitrogen,and oxygen are $V_H, V_N$,and $V_O$ respectively at a given temperature,then:

If the $r.m.s.$ velocity of a gas at a given temperature (Kelvin scale) is $300 \ m/s$,what will be the $r.m.s.$ velocity of a gas having twice the molecular weight and half the temperature on the Kelvin scale?

The speeds of ten particles in $ms^{-1}$ are $0, 2, 3, 4, 4, 4, 5, 5, 6, 9$. The values of average speed,$rms$ speed,and most probable speed are respectively: