At $300\,K$,the rms speed of oxygen molecules is $\sqrt{\frac{\alpha+5}{\alpha}}$ times its average speed in the gas. Then,the value of $\alpha$ will be (use $\pi=\frac{22}{7}$):

$A$ sample contains a mixture of helium and oxygen gas. The ratio of the root mean square speed of helium to oxygen in the sample is:

At what temperature will the molecules of nitrogen have the same $r.m.s.$ velocity as the molecules of oxygen at $127^{\circ}C$ (in $^{\circ}C$)?

The temperature at which the root mean square velocity of hydrogen molecules equals their escape velocity from the Earth is closest to: [Boltzmann constant $k_B = 1.38 \times 10^{-23} \, J/K$,Avogadro number $N_A = 6.02 \times 10^{23} \, mol^{-1}$,Molar mass of $H_2 = 2 \times 10^{-3} \, kg/mol$,Radius of Earth $R_e = 6.4 \times 10^6 \, m$,Gravitational acceleration $g = 10 \, m/s^2$]

The molecules of a given mass of a gas have a $r.m.s.$ velocity of $200 \, m/s$ at $27^{\circ}C$ and $1.0 \times 10^5 \, N/m^2$ pressure. When the temperature is $127^{\circ}C$ and pressure is $0.5 \times 10^5 \, N/m^2$,the $r.m.s.$ velocity in $m/s$ will be

What is the ${v_{rms}}$ of gas molecules in equilibrium?