Question

The normalized speed distribution for molecules in an ideal gas is given by: m akt 3/2 e-ma/21 (1) a): Calculate the average velocity of O2 (mass of 32 g/mol) in our atmosphere (assume room temperature, start from first principles) b): Calculate the average speed of O2 in our atmosphere (assume room temperature, start from first principles) c): Calculate the rms speed of O2 in our atmosphere (assume room temperature, start from first princi- ples). Compare this to the result of the equipartition theorem. d): Escape velocity near the Earth is ~ 11 km/s; Escape velocity of the Moon is ~ 2.4 km/s. Briefly discuss the implications for why the Moon has no atmosphere.

Answer 1

velociter ve The sun fraction of gas moreules having and ved is given by 312 muz f(v) dv= 450 ( m m y Jar. I tika @ Now the average veloul of the gas molecules = 0 Because If you consider the velocity of the indivisual molecules, all are randomly orianted in all possible direction making average velocily = 0. the 6 Now Avenze speed a 8 KBT mл Let the room temp= 300 kelvin. mass of or moleute = 5.3181020 i Aug & speed - 1881.38 *123 x 300 5,31x1026 x IT exced - 18x1-38*183 x 300 445.57 m/s Now (7 = 100 F f ( dr = a (mes) 3 12-meston dav <D 3kg &ms speed = В КАТ v m 3x1-38 X To 23 x300 5.31X To 26 x T = 272.86 m/s V @ The escape velocily at moon is about 2-4 km/s. As the escape velocily is very low compared to the earth most of the gas molecules wrien has much more speed thah 2.4km/s and all the gas moleales have & escaped to the space.