Four molecules of a gas have speeds $1, 2, 3$ and $4 \ km/s$. The value of root mean square speed of the gas molecules is

For a mixture of three different gases with molecular masses $m_1 > m_2 > m_3$ at the same temperature,what is the relationship between their root mean square speeds $(v_{rms})$ and average kinetic energies $(\bar{K})$?

In two vessels of the same volume,atomic hydrogen and helium at pressures of $1\, atm$ and $2\, atm$ are filled,respectively. If the temperature of both samples is the same,then the average speed of hydrogen atoms $\langle C_H \rangle$ will be related to that of helium $\langle C_{He} \rangle$ as:

The root mean square speed of molecules of nitrogen gas at $27^{\circ} C$ is approximately $.......m/s$. (Given: mass of a nitrogen molecule $= 4.6 \times 10^{-26} \, kg$ and Boltzmann constant $k_{B} = 1.4 \times 10^{-23} \, J K^{-1}$)

The temperature of a gas is $-50^{\circ}C$. To what temperature should the gas be heated so that the $rms$ speed is increased by $3$ times?

If the $rms$ speed of hydrogen gas is equal to the $rms$ speed of oxygen gas at $47^{\circ}C$,find the temperature of the hydrogen gas in $K$.