Serway & Jewett — The Kinetic Theory of Gases: Problem 25.

Assume the Earth’s atmosphere has a uniform temperature of \(20.0^\circ\text{C}\) and uniform composition, with an effective molar mass of \(28.9\text{ g/mol}\). (a) Show that the number density of molecules depends on height \(y\) above sea level according to \(n_V(y) = n_0 e^{-m_0 g y / k_B T}\) where \(n_0\) is the number density at sea level (where \(y = 0\)). This result is called the law of atmospheres. (b) Commercial jetliners typically cruise at an altitude of \(11.0\text{ km}\). Find the ratio of the atmospheric density there to the density at sea level.