where p0 is the pressure at sea level and H is a constant approximately equal to
8 km. More specifically, H = RT/Mg, where M is the average molar mass of air and T
is the temperature. This formula represents the outcome of the competition between
the potential energy of the molecules in the gravitational field of the Earth and the
stirring effects of thermal motion; it is derived on the basis of the Boltzmann distribution
(Section F.5a). The barometric formula fits the observed pressure distribution
quite well even for regions well above the troposphere (Fig. 1.10). It implies that the
pressure of the air falls to half its sea-level value at h = H ln 2, or 6 km