Q: At what temperature will the rms speed of oxygen molecule will be sufficient for escaping from earth ? (v_{e} = 11.2 km/s, m = 2.76 × 10^{-26e kg and k = 1.38 × 10-23 J/K)}

Sol: If the temperature is T, according to kinetic theory of gases ,

Translational KE $\large = \frac{3}{2} k_B T $

The oxygen molecule will escape from earth if

$\large \frac{3}{2} k T > \frac{1}{2} m v_e^2 $

$\large T > \frac{m v_e^2}{3 k} $

$\large T > \frac{2.76 \times 10^{-26} \times (11.2 \times 10^3)^2}{3 \times 1.38 \times 10^{-23}} $

T > 8.36 × 10^{4} K