Consider a gas of molecules of mass m in thermal equilibrium at temperature T.
(i) What is the ratio of n(h)/n(0) of the density n(h) of molecules at height h to the density n(0) of molecules at height 0 ? Hint: use Maxwell-Boltzmann statistics and consider the gravitational potential energy of each molecule U(h) = mgh.
(ii) Using the ideal gas law PV = NkBT show that P(h)/P(0) = n(h)/n(0).
(iii) Assuming that the Earth's atmosphere is 100% nitrogen (N2) [Note: it's actually 79% N2 and 20% O2] calculate the ratio R of the air-pressure at a height of 30, 000 feet above the Earth's surface (typical cruising altitude of an airliner) to that at the Earth's surface.