Publication | Open Access
Entropy and Potential Temperature
68
Citations
0
References
1987
Year
EngineeringExperimental ThermodynamicsTemperature PredictionEarth ScienceRefrigerationThermodynamic ModellingFluid PropertiesMolecular ThermodynamicsPotential TemperatureThermodynamicsEquilibrium Thermodynamic PropertyThermodynamic EquilibriumMeteorologyPhysicsHeat TransferLiquid WaterEntropyEntropy ProductionEquilibrium ThermodynamicsEntropy Temperature
The paper introduces the entropy temperature, a unified potential temperature that measures entropy, and presents its state function and entropy budget for cloudy air. The authors review the thermodynamic equations for each potential temperature as integrals, then derive a prognostic equation for the entropy temperature from the entropy budget that accounts for irreversible effects and applies to open systems. The study shows that all conventional potential temperatures can be unified under the entropy temperature, that the ice‑liquid water potential temperature is an integral only under saturation or equilibrium, and that exact prognostic equations for each potential temperature can be derived in principle.
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, θ = constant, is reviewed on the basis of the entropy concept. As one result, it is found that the ice-liquid water potential temperature θil 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.