Condensation: Passenger Not Driver in Atmospheric Thermodynamics

Abstract

The second law of thermodynamics states that processes yielding work or at least capable of yielding work are thermodynamically spontaneous, and that those costing work are thermodynamically nonspontaneous. Whether a process yields or costs heat is irrelevant. Condensation of water vapor yields work and hence is thermodynamically spontaneous only in a supersaturated atmosphere; in an unsaturated atmosphere it costs work and hence is thermodynamically nonspontaneous. Far more of Earth’s atmosphere is unsaturated than supersaturated; based on this alone evaporation is far more often work-yielding and hence thermodynamically spontaneous than condensation in Earth’s atmosphere—despite condensation always yielding heat and evaporation always costing heat. Furthermore, establishment of the unstable or at best metastable condition of supersaturation, and its maintenance in the face of condensation that would wipe it out, is always work-costing and hence thermodynamically nonspontaneous in Earth’s atmosphere or anywhere else. The work required to enable supersaturation is most usually provided at the expense of temperature differences that enable cooling to below the dew point. In the case of most interest to us, convective weather systems and storms, it is provided at the expense of vertical temperature gradients exceeding the moist adiabatic. Thus, ultimately, condensation is a work-costing and hence thermodynamically nonspontaneous process even in supersaturated regions of Earth’s or any other atmosphere. While heat engines in general can in principle extract all of the work represented by any temperature difference until it is totally neutralized to isothermality, convective weather systems and storms in particular cannot. They can extract only the work represented by partial neutralization of super-moist-adiabatic lapse rates to moist-adiabaticity. Super-moist-adiabatic lapse rates are required to enable convection of saturated air. Condensation cannot occur fast enough to maintain relative humidity in a cloud exactly at saturation, thereby trapping some water vapor in metastable supersaturation. Only then can the water vapor condense. Thus ultimately condensation is a thermodynamically nonspontaneous process forced by super-moist-adiabatic lapse rates. Yet water vapor plays vital roles in atmospheric thermodynamics and kinetics. Convective weather systems and storms in a dry atmosphere (e.g., dust devils) can extract only the work represented by partial neutralization of super-dry-adiabatic lapse rates to dry-adiabaticity. At typical atmospheric temperatures in the tropics, where convective weather systems and storms are most frequent and active, the moist-adiabatic lapse rate is much smaller (thus much closer to isothermality), and hence represents much more extractable work, than the dry—the thermodynamic advantage of water vapor. Moreover, the large heat of condensation (and to a lesser extent fusion) of water facilitates much faster heat transfer from Earth’s surface to the tropopause than is possible in a dry atmosphere, thereby facilitating much faster extraction of work, i.e., much greater power, than is possible in a dry atmosphere—the kinetic advantage of water vapor.