Isothermal equilibrium

From Glossary of Meteorology

isothermal equilibrium

(Also called conductive equilibrium.) The state of a hypothetical atmosphere, at rest and uninfluenced by radiative heating or cooling, in which the conduction of heat from one part to another has, after a sufficient length of time, produced a uniform temperature throughout its entire mass.

If such an atmosphere consisted of more than one gas, the pressure of each gas would be distributed exponentially according to Dalton's law, so that
where pno is the surface pressure and the nth constituent gas, mn its mean molecular mass, g the acceleration of gravity, h the geometric height, k Boltzmann's constant (1.3804 × 10-23 J K-1), and T the absolute temperature. At a sufficiently great height the lighter gases will predominate. The time necessary for the establishment of isothermal equilibrium in a mixed atmosphere by diffusion of one gas through another has been estimated to decrease rapidly with height from about one year near 100 km to a matter of seconds near 200 km.
See diffusive equilibrium, isothermal atmosphere.

Lettau, H. 1951. Compendium of Meteorology. 320–333.