Question

At what temperatures does the RMS speed of O2 molecules equal the escape speed from the Earth and the Moon? (vesc,Earth = 11.2 km/s; vesc,Moon = 2.38 km/s;). Search for the range of temperature of the Moon (daily and night), then explain why the Moon cannot retain the air. 

Answer 1

1)

$$v=\sqrt{\frac{3RT}{M}}\\T=\frac{(11200)^2(0.0032)}{3(8.31)}=16101\ K$$

2)

$$v=\sqrt{\frac{3RT}{M}}\\T=\frac{(2380)^2(0.0032)}{3(8.31)}=727\ K$$