Escape velocity from Earth's atmosphere is \(10.8 \mathrm{~km} / \mathrm{s}\).

a. Based on that number, to what temperature would \(\mathrm{He}, \mathrm{O}_{2}, \mathrm{CO}_{2}\) need to be heated so that their mean velocity would allow them to escape into interplanetary space?

b. Given the Maxwell-Boltzmann velocity distribution of equation (3.1), an escape velocity from the moon of \(2.4 \mathrm{~km} / \mathrm{s}\), and a mean moon surface temperature of \(127^{\circ} \mathrm{C}\), what fraction of \(\mathrm{O}_{2}\) would have enough speed to escape the moon's gravity? Why might the moon have no atmosphere?

Transcribed Image Text:

P (v) = m 2kT 3/2 m(v+v+v) Maxwell- Boltzmann exp (3.1) 2k T velocity distribution