Scale height

Remarks

Equivalently, $H = k_B T/(m g)$, with $k_B$ the Boltzmann constant and $m$ the mean mass of a molecule. If the layer is in hydrostatic balance $dp/dz = -\rho g$ and obeys the ideal gas law $p = \rho R T/M$, then $dp/dz = -p/H$. So for constant $T$ the pressure is $p(z) = p(0) \, e^{-z/H}$, an exponential function, and it falls by the factor $e$ over each height $H$. Example: for dry air, $M = 0.02896$ kg/mol, with $T = 288$ K, $g = 9.81$ m/s² and $R = 8.314$ J/(mol K), one gets $H \approx 8.4$ km. Non-example: in a layer whose temperature changes with height, $H$ is a function of height, and the pressure is not a single exponential in $z$.