Explain why:
$(a)$ there is no atmosphere on the Moon.
$(b)$ there is a fall in temperature with altitude.

(N/A) The gravitational force on the Moon is very weak,resulting in a low escape speed of approximately $2.3 \ km/s$. The root-mean-square speed of gas molecules at the Moon's surface temperature,given by $v_{rms} = \sqrt{\frac{3 k_{B} T}{m}}$,exceeds this escape speed. Consequently,gas molecules escape the Moon's gravitational pull,preventing the formation of an atmosphere.
$(b)$ As air molecules move upward in the atmosphere,they work against the gravitational field,which increases their potential energy. According to the law of conservation of energy,this increase in potential energy leads to a corresponding decrease in their kinetic energy. Since the temperature of a gas is directly proportional to the average kinetic energy of its molecules $(E_k = \frac{3}{2} k_{B} T)$,the temperature decreases with increasing altitude.