To obtain the Maxwell speed distribution, we assumed a uniform temperature, a kinetic-only energy of E = ½m(v2x + v2y + v2z) and we assumed that we wished to find the average of an arbitrary function of v. Along the way, we obtained a probability per unit speed, P(v). (a) Assuming a uniform temperature and an energy of E = ½m(v2x + v2y + v2z) + mgy and assuming we wish to find the average of an arbitrary function of y, obtain a probability per unit height, P(y). (b) Assuming a temperature of 300 K, how much less is the density of the atmosphere's N2 at an altitude of 800 m (about 3000 ft) than at sea level? (c) What of the O2 in the atmosphere?
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