The Rankine-Kirchhoff approximations for moist thermodynamics

Abstract

The Rankine-Kirchhoff equation for the saturation vapor pressure has been derived independently many times, sometimes with the presumption of novelty. As a result, the equation is referred to in the literature by a bewildering number of different names and, often, by no name at all. In this work, the history of the Rankine-Kirchhoff equation is reviewed. The three approximations used to derive it (ideal gas, constant heat capacities, and zero-volume condensates) can be used to derive a whole system of accurate and analytic expressions of relevance to the atmosphere. Consequently, it is proposed that this set of approximations be elevated to a named entity, e.g., the Rankine-Kirchhoff approximations.