Thermodynamic Equilibrium of the Atmosphere

One of the issues of Thermodynamics is the question of what exactly thermodynamic equilibrium means. It is often interpreted as thermal equilibrium. The question is if this is correct. This is especially relevant for the case of the atmosphere, where gravitational energy also plays a role, which might allow for temperature gradients in equilibrium. In order to answer this question, this work goes back to Boltzmann’s original ideas. As will be shown here, thermodynamic equilibrium also means thermal equilibrium in this case. Moreover, it will also be shown why a lapse rate (a linear drop of temperature with altitude) is observed in a mechanically stable atmosphere. The implications for climate research are discussed.