Abstract
The statistical thermodynamics of a classical ideal gas column of height H in a uniform gravitational field g has been treated by the canonical ensemble at temperature T. A key parameter is X≡mgH/kT where m is the mass of a particle. The internal energy U rises with X from 1.5 NkT at X=0 where N is the number of particles. If extrapolated beyond the region of applicability U reaches 2.5 NkT at X=∞. On the other hand, the entropy drops to zero (as X is increased) at a critical value XC of X, at which the model has already failed. The value of XC rises, extending the range of validity of the model, (a) as the gas becomes more dilute, (b) as the temperature is increased, and (c) as the particle mass is increased. The ideal quantum gas, treated by the grand canonical ensemble, leads to results consistent with those obtained from the canonical ensemble.
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