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 = Cz exp(-βmgz) dz and that the normalization constant Cz= mg/kT. This distribution is referred to as the law of atmospheres.
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 = Cz exp(-βmgz) dz and that the normalization constant Cz= mg/kT. This distribution is referred to as the law of atmospheres.
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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 = Cz exp(-βmgz) dz and that the normalization constant Cz= mg/kT. This distribution is referred to as the law of atmospheres.
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