Determining the potential temperature for real gases: Application to Venus's lower atmosphere

The potential temperature is an important meteorological parameter quantifying the response of an atmosphere to dynamic perturbations. It is defined as the temperature that a gas parcel would have if it were transported adiabatically from the local pressure to a reference pressure. It is obtained by invoking the First Law of thermodynamics for enthalpy in adiabatic conditions. For ideal gases, the infinitesimal fractional changes of pressure and temperature are coupled simply through the constant isobaric specific heat, making the integration from the reference to the local point trivial. For real gases, however, the coupling between pressure and temperature fluctuations is no longer constant, depending instead on the local pressure, density, and temperature. Therefore, the potential temperature can be obtained either by approximation or numerically. We present the framework for incorporating the Peng-Robinson real-gas equation of state in setting up the adiabatic pressure-temperature differential equation. Then, we discuss its solutions in terms of the compressibility factor and their implications to the stability and buoyancy frequency of the Venusian atmosphere using ambient data acquired during the descent of the Vega-2 probe.