Entropy and Potential Temperature

Abstract

The theoretical investigations presented in this paper show that the various definitions of potential temperatures, such as the potential temperature of dry air and of moist air, the equivalent potential temperature, the liquid water potential temperature, the ice-liquid water potential temperature and the wet equivalent potential temperature can be unified by one single definition. This general potential temperature is named the entropy temperature as it is a measure of entropy. The entropy state function for a system of cloudy air and the entropy budget are presented and discussed. For each of the potential temperatures the respective thermodynamic equation for which the potential temperature is an integral of the form, ? = constant, is reviewed on the basis of the entropy concept. As one result, it is found that the ice-liquid water potential temperature ?il is only an integral of the corresponding thermodynamic equation if saturation or chemical equilibrium between water vapor and liquid water or ice is assumed. A prognostic equation for the entropy temperature is derived using the entropy budget equation. This equation describes irreversible effects and holds also for an open system. From this equation exact prognostic equations for each of the potential temperatures can, at least in principle, be derived.