From AMS Glossary
The lapse rate of temperature in such an atmosphere is known as the autoconvective lapse rate and is equal to g/R (or approximately 3.4°C/100 m), where g is the acceleration of gravity and R is the gas constant for air. A homogeneous atmosphere has a finite total thickness that is given by RdTv/g, where Rd is the gas constant for dry air and Tv is the virtual temperature (K) at the surface. For a surface temperature of 273 K, the vertical extent of the homogeneous atmosphere is approximately 8000 m. At the top of such an atmosphere both the pressure and absolute temperature vanish.
Same as adiabatic atmosphere.