Formulations of moist thermodynamics for atmospheric modelling

TL;DR

This paper develops analytical formulas for moist-air thermodynamic quantities like enthalpy and entropy, grounded in the Third Law, enabling consistent atmospheric modeling across different saturation states.

Contribution

It introduces a general moist-air entropy potential temperature and specific enthalpy definitions based on the Third Law, improving thermodynamic consistency in atmospheric models.

Findings

Defined and computed a moist-air entropy potential temperature.

Derived analytical formulas for moist-air specific enthalpy and entropy.

Established a thermodynamic framework applicable to saturated and unsaturated conditions.

Abstract

Internal energy, enthalpy and entropy are the key quantities to study thermodynamic properties of the moist atmosphere, because they correspond to the First (internal energy and enthalpy) and Second (entropy) Laws of thermodynamics. The aim of this chapter is to search for analytical formulas for the specific values of enthalpy and entropy and for the moist-air mixture composing the atmosphere. The Third Law of thermodynamics leads to the definition of absolute reference values for thermal enthalpies and entropies of all atmospheric species. It is shown in this Chapter 22 that it is possible to define and compute a general moist-air entropy potential temperature, which is really an equivalent of the moist-air specific entropy in all circumstances (saturated, or not saturated). Similarly, it is shown that it is possible to define and compute the moist-air specific enthalpy, which is different from the thermal part of what is called Moist-Static-Energy in atmospheric studies.