Question

1. Boltzmann factor for an isothermal atmosphere (15 points) Our derivation of Debye shielding hinged on the assumption that the electron density in a potential ф(x) is given by the Boltzmann factor ne(x) - noexp[ep(x)/kBT]. The following problem is intended to provide an intuitive motivation for the Boltzmann factor. Consider a gas atmosphere in a uniform gravitational field g. If the gas is at a temperature T, show that the gas density n will decrease with altitude h as where no is the gas density at zero altitude and m is the mass of a gas particle

Answer 1