Use the law of atmospheres (Problem 43) to compare the air densities at sea level, Chicago (altitude 176 m), Denver (altitude 1610 m), and the summit of Mt. Rainier (altitude 4390 m), assuming the same temperature 273 K in each case.
Assume that air is an ideal gas under a uniform gravitational field, so that the potential energy of a molecule of mass m at altitude z is mgz. Show that the distribution of molecules varies with altitude as given by the distribution function f(z) dz = Czexp(-βmgz) dz and that the normalization constant Cz = mg/kT. This distribution is referred to as the law of atmospheres.
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