The temperature of an ideal gas is reduced from $927^\circ C$ to $27^\circ C$. The $r.m.s.$ velocity of the molecules becomes

What is $v_{rms}$? Write the equation of $v_{rms}$ in terms of: $(1)$ density,$(2)$ mass of a molecule,$(3)$ molar mass.

The temperature of a gas is $-73^{\circ}C$. To what temperature should the gas be heated so that the $rms$ speed of the molecules is doubled (in $^{\circ}C$)?

At a pressure of $24 \times 10^5 \, \text{dyne/cm}^2$,the volume of $O_2$ is $10 \, \text{litre}$ and its mass is $20 \, \text{gm}$. The $r.m.s.$ velocity will be ....... $m/s$.

Let $\overline{V}$, $V_{\text{rms}}$, and $V_{p}$ denote the mean speed, root mean square speed, and most probable speed of the molecules each of mass $m$ in an ideal monoatomic gas at absolute temperature $T$ Kelvin. Which statement$(s)$ is/are correct?

If $V_{rms}$ of $O_2$ molecule is equal to $V_{rms}$ of $H_2$ molecule at $20 K$,the temperature of $O_2$ is: