Depending on the details of the initial condition of the gas, it might relax to a vertical thermal profile almost anywhere between the DALR negative gradient and the infinity of zero to positive thermal gradient profiles that are all hydrostatically stable (bulk hydrostatic balance of buoyancy and gravity) and convectively stable (both static and dynamic viscosity that resist and damp out bulk motion perturbations so that they can not grow). (wattsupwiththat.com)
In order to maintain hydrostatic balance the necessary kinetic energy can not be radiated away to space hence that «additional» energy must be held at the surface over and above that which is required (by the surface and atmosphere combined) solely to radiate enough energy to space to match energy being received from space. (newclimatemodel.com)
Kinetic energy at the surface acting via conduction and convection supplies the upward pressure gradient force which offsets the downward force of gravity in order to constantly hold the mass of an atmosphere off the surface in hydrostatic balance. (newclimatemodel.com)