When the temperature of a gas is raised from $27^{\circ} C$ to $90^{\circ} C$,the increase in the rms velocity of the gas molecules is: (in $\%$)

The $rms$ velocity of molecules of a given mass of gas at $27^{\circ}C$ and $1.0 \times 10^5 \, Nm^{-2}$ pressure is $200 \, m \, s^{-1}$. What will be the $rms$ velocity if the temperature and pressure are $127^{\circ}C$ and $0.5 \times 10^5 \, Nm^{-2}$ respectively?

If the $rms$ speeds of helium and oxygen are equal,then the ratio of the temperatures of helium and oxygen is

The speeds of the seven molecules are $1, 3, 5, 7, 2, 4$ and $6 \text{ km/s}$ respectively. The ratio of their r.m.s. velocity and average velocity will be

The $r.m.s.$ speed of gas molecules at $800 \ K$ will be

For a gas at room temperature of $27^{\circ}C$,the value of $\nu_{rms}$ is $1930 \, m/s$. The gas is.......... $(R = 8.3 \, J/mol \cdot K)$.