If the rms velocity of a perfect gas at $27^{\circ} C$ is $500 \,m \cdot s^{-1}$,the same at $927^{\circ} C$ will be

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 $(\bar{K})$?

The $v_{rms}$ value for a hydrogen molecule at $300 \ K$ is $1930 \ m/s$. Then the $v_{rms}$ for an oxygen molecule at $900 \ K$ is . . . . . . $m/s$.

If a gas is compressed isothermally,then the r.m.s. velocity of its molecules

To what temperature should the hydrogen at $327^{\circ} C$ be cooled at constant pressure,so that the root mean square velocity of its molecules becomes half of its previous value (in $^{\circ} C$)?

The molecular masses of helium and oxygen are $4$ and $32$ respectively. The ratio of r.m.s speed of helium at $327^{\circ} C$ to r.m.s speed of oxygen at $27^{\circ} C$ will be