Lapse rate

Remarks

The dry adiabatic lapse rate is $\Gamma_d = g/c_p$, where $g$ is the gravitational acceleration and $c_p$ the specific heat of dry air at constant pressure. It follows from the energy balance $c_p \, dT = dp/\rho$ of a rising parcel without heat exchange together with hydrostatic balance $dp = -\rho g \, dz$, which give $dT/dz = -g/c_p$. With $g = 9.81$ m/s² and $c_p = 1004$ J/(kg K), $\Gamma_d \approx 9.8$ K/km. Example: in the International Standard Atmosphere, $T(z) = 288.15 - 0.0065 z$ in kelvin, with $z$ in metres, up to 11 km, so $\Gamma = 6.5$ K/km. Non-example: the rate $-\partial T/\partial t$ at which the air at a fixed place cools at night is not a lapse rate. It is a derivative in time, not in height. In a temperature inversion the temperature increases with height, so $\Gamma < 0$ there. For dry air, a layer with $\Gamma < \Gamma_d$ is statically stable and a layer with $\Gamma > \Gamma_d$ is unstable.