Clausius–Clapeyron equation and saturation vapour pressure: simple theory reconciled with practice

Abstract

While the Clausius-Clapeyron equation is very important as it determines the saturation vapour pressure, in practice it is replaced by empirical, typically Magnus type, equations which are more accurate. It is shown that the reduced accuracy reflects an inconsistent assumption that the latent heat of vaporization is constant. Not only is this assumption unnecessary and excessive, but it is also contradictory to entropy maximization. There is an additional erroneous assumption for the derivation of the Clausius-Clapeyron equation, related to the equality of chemical potentials of the two phases, which does not affect the final result but puts into question the logical coherence of the equation's derivation. Removing these assumptions and using a pure entropy maximization framework we obtain a simple closed solution, which is both theoretically consistent and accurate. Our discussion and derivation are relevant to students and specialists in statistical thermophysics and in geophysical sciences, and our results are ready for practical application in physics as well as in such disciplines as hydrology, meteorology and climatology.

Technical note: A noniterative approach to modelling moist thermodynamics

“…As mentioned earlier, improved accuracy may also be achieved with the use of even higher degrees of polynomials for parameter fits. However, such precision is unlikely to be necessary, as some of the thermodynamic relationships used in the truth iterative computations contain substantially larger errors than those introduced by the above optimization procedure (Davies-Jones, 2009;Koutsoyiannis, 2012). Moreover, conventional pseudoadiabatic diagrams, such as those used by US Air Force, Environment Canada and Air Transport Association of America, differ from each other by nearly 1 • C at the 20 kPa pressure level (Bakhshaii and Stull, 2013).…”

Entropy: From Thermodynamics to Hydrology

“…The latter is the standard solution of the Clausius-Clapeyron equation appearing in books, which however is an inconsistent approximate description of the phenomenon [34]. Figure 3 (upper) compares the proposed Equation (40) with the standard Equation (41); they seem indistinguishable.…”

“…However, the lower panel of the figure, which compares relative differences from measurements, clearly indicates the superiority of Equation (40) derived here. A slightly more accurate version, based on experimental values of specific heats, instead of using integral degrees of freedom, can be found in [34] (the slight differences are in the numerical values of the constants, i.e., (β B /2 -β A /2 -1) = 5.06 and ξ/θ 0 = 24.921). (40), as well as by Equation (41), with accurate measurement data of different origins, as indicated in the legend (for details on data see [34]).…”

A new theoretical formulation of dew point temperatures applicable for comfort air-cooling systems

“…Here, a modified form of the Clausius-Clapeyron equation for vapor pressures is applied for deriving a simple equation for DPT. From literature study, it can be seen that the modified Clausius-Clapeyron equation gives acceptable vapor pressures with minor deviations in results corresponding to temperatures within the scope of comfort air cooling applications [40,41].…”