Assume that we encompass a gas in thermal equilibrium at temperature T. Each and every molecule of gas consists of a mass m.
i) Determine the ratio of the number of molecules at the surface of earth to the number at height h with a potential mgh?
ii) Determine the ratio of the density of the gas at height h to the density at the surface?
iii) Would you anticipate this simple model to provide a sufficient explanation of the earth's atmosphere? Explain how does it fail?