Explain why
(a) there is no atmosphere on moon
(b) there is fall in temperature with altitude

Explanation

The moon has small gravitiational force (pull) and hence , the escape velocity is small . The value of escape velocity for the moon is 4.6 `km//s`
The air molecules have large range of speeds . Even though the rms speed of the air molecules is smaller than the escape velocity on the moon a signrificant number of molecules have speed greater than escape veloity and they escape.
Now rest of the molecules arrange the speed distribution for the equilibrium temperature . Again a significant number of molecules escape as their speed exceed escape speed. Hence, over a long time the moon has lost most of its atmosphere.
`At 300 K, V_("rms")= sqrt((3KT)/(m)) = sqrt((3xx1.38 xx10^(-23) xx 300)/(7.3 xx 10^(-26)) )=1.7 km//s`
`V_(es) " for moon " =4.6 km//s " "[V_(es) ="escape velocity"]`
(b). As the molecules move higher , their potential energy increase and hence kinetic energy decreases and hence, temperature reduces.
At greater height more volume is availble and gas expands and hence, some cooling takes place.
Note. We should not relate temperature directly with potential energy .it is directly related with kinetic energy of hte molecules.