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

D. Koutsoyiannis, Clausius-Clapeyron equation and saturation vapour pressure: simple theory reconciled with practice, European Journal of Physics, 33 (2), 295–305, doi:10.1088/0143-0807/33/2/295, 2012.



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. Removing this assumption 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.

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A much funnier proof can be found in (section 3.6)

Our works referenced by this work:

1. D. Koutsoyiannis, Hurst-Kolmogorov dynamics as a result of extremal entropy production, Physica A: Statistical Mechanics and its Applications, 390 (8), 1424–1432, doi:10.1016/j.physa.2010.12.035, 2011.
2. D. Koutsoyiannis, Lecture Notes on Hydrometeorology: A probability-based introduction to atmospheric thermodynamics, 45 pages, doi:10.13140/RG.2.2.22700.87686, Department of Water Resources and Environmental Engineering – National Technical University of Athens, Athens, 2011.

Our works that reference this work:

1. D. Koutsoyiannis, Reply to the Comment by T. López-Arias on “Clausius-Clapeyron equation and saturation vapour pressure: simple theory reconciled with practice”, European Journal of Physics, 33, L13–L14, 2012.
2. D. Koutsoyiannis, Entropy: from thermodynamics to hydrology, Entropy, 16 (3), 1287–1314, doi:10.3390/e16031287, 2014.
3. D. Koutsoyiannis, and S.M. Papalexiou, Extreme rainfall: Global perspective, Handbook of Applied Hydrology, Second Edition, edited by V.P. Singh, 74.1–74.16, McGraw-Hill, New York, 2017.
4. D. Koutsoyiannis, Revisiting the global hydrological cycle: is it intensifying?, Hydrology and Earth System Sciences, 24, 3899–3932, doi:10.5194/hess-24-3899-2020, 2020.
5. D. Koutsoyiannis, Rethinking climate, climate change, and their relationship with water, Water, 13 (6), 849, doi:10.3390/w13060849, 2021.
6. P. Dimitriadis, D. Koutsoyiannis, T. Iliopoulou, and P. Papanicolaou, A global-scale investigation of stochastic similarities in marginal distribution and dependence structure of key hydrological-cycle processes, Hydrology, 8 (2), 59, doi:10.3390/hydrology8020059, 2021.
7. D. Koutsoyiannis, Stochastics of Hydroclimatic Extremes - A Cool Look at Risk, Edition 3, ISBN: 978-618-85370-0-2, 391 pages, doi:10.57713/kallipos-1, Kallipos Open Academic Editions, Athens, 2023.

Works that cite this document: View on Google Scholar, ResearchGate or ResearchGate (additional)

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1. Sarkar, M., Theoretical comparison of cooling loads of an air handling unit in blow-through and draw-through configurations, Energy and Buildings, 10.1016/j.enbuild.2013.04.025, 2013.
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6. Sarkar, M., A new theoretical formulation of dew point temperatures applicable for comfort air-cooling systems, Energy and Buildings, 86, 243-256, 10.1016/j.enbuild.2014.10.029, 2015.
7. Girona, T., F. Costa, B. Taisne, B. Aggangan and S. Ildefonso, Fractal degassing from Erebus and Mayon volcanoes revealed by a new method to monitor H2O emission cycles, Journal of Geophysical Research B: Solid Earth, 120 (5), 2988-3002, 2015.
8. Kakade, R.S., Least-enthalpy based control of cabin air recirculation, SAE Technical Papers, 2015-01-0372, 10.4271/2015-01-0372, 2015.
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Tagged under: Course bibliography: Hydrometeorology, Determinism vs. stochasticity, Entropy, Papers initially rejected