From AMS Glossary
(Also called exponential atmosphere.) An idealized atmosphere in hydrostatic equilibrium in which the temperature is constant with height and in which, therefore, the pressure decreases exponentially upward.
In such an atmosphere the thickness between any two heights is given by
where Rd is the gas constant for dry air, Tv the virtual temperature (°K), g the acceleration of gravity, and PA and PB the pressures at the heights zA and zB, respectively. In the isothermal atmosphere there is no finite height at which the pressure vanishes.