Temperature lapse rates at restricted thermodynamic equilibrium. Part II: Saturated air and further discussions

•Thermodynamic study of adiabatic temperature lapse rates by numerical simulation.•New hypothesis, adiabatic lapse rates represent restricted thermodynamic equilibrium.•It is supported by a criterion from Gibbs' theory on thermodynamic equilibrium.•Turbulent heat transfer may give rapid relaxation towards such restricted equilibrium.•This hypothesis agrees with Kelvin's old idea of “convective equilibrium of heat”.

In the first part of this work equilibrium temperature profiles in fluid columns with ideal gas or ideal liquid were obtained by numerically minimizing the column energy at constant entropy, equivalent to maximizing column entropy at constant energy. A minimum in internal plus potential energy for an isothermal temperature profile was obtained in line with Gibbs' classical equilibrium criterion. However, a minimum in internal energy alone for adiabatic temperature profiles was also obtained. This led to a hypothesis that the adiabatic lapse rate corresponds to a restricted equilibrium state, a type of state in fact discussed already by Gibbs. In this paper similar numerical results for a fluid column with saturated air suggest that also the saturated adiabatic lapse rate corresponds to a restricted equilibrium state. The proposed hypothesis is further discussed and amended based on the previous and the present numerical results and a theoretical analysis based on Gibbs' equilibrium theory.