Local balance equations for atmospheric exergies and anergies

Abstract

The basic differential system of equations for mass specific thermodynamic potentials is extended to a system that describes the thermodynamics of finite differences. This system is characterized by mass specificexergies andanergies of the original thermodynamic potentials which are split up into exergies and anergies. Equations for the differentials of exergies and anergies replace the wellknown differential relationships of thermodynamics and are the basis of a more general energetics of the atmosphere, an energetics with an “entropy flavor” (Dutton, 1992). Here, a special state of reference is not prescribed. It turns out that mass specific exergy of internal energy combined with specific kinetic energy, and mass specific anergy of internal energy combined with potential energy leads to local balance equations for these energies. They represent the balance equation of total energy split up into two separate equations. The physical meaning of the two equations is clearly understood. In particular, irreversible processes and entropy production play a dominant role in all energy equations so derived. Finally, integration over the entire atmosphere leads to generalized global energy equations. The production (destruction) of kinetic energy depends on the rate of change with time of exergy of internal energy, and vice versa on the rate of change with time of anergy via a rate of change of potential energy. J. A. Dutton's (1973) relationship between global entropy difference and the sum of global kinetic energy and static entropic energy is recovered and static entropic energy is identified with global exergy of internal energy. In case of ideal gases, local exergy of enthalpy can be split up into a temperature potential and a pressure potential. For both potentials local balance equations are derived.