Suppose we have a gas in thermal equilibrium at temperature T. Each molecule of gas has a mass m.
a) What is the ratio of the number of molecules at the earth's surface to teh number at height h with a potential mgh?
b) What is the ratio of the density of the gas at height h to the density at the surface?
c) Would you expect this simple model to give an adequate description of the earth's atmosphere? How does it fail?