International Journal of Thermophysics

, Volume 36, Issue 1, pp 44–68 | Cite as

Virial Approximation of the TEOS-10 Equation for the Fugacity of Water in Humid Air

  • Rainer FeistelEmail author
  • Jeremy W. Lovell-Smith
  • Olaf Hellmuth


Fugacity is considered the proper real-gas substitute for the partial pressure commonly used to describe ideal-gas mixtures. However, in several fields such as geophysics, meteorology, or air conditioning, partial pressure is still preferred over fugacity when non-equilibrium conditions of humid air are quantified. One reason may be that for ambient air, the deviations from ideal-gas behavior are small, another that explicit correlation equations for the fugacity of water vapor in humid air are scarce in the literature. This situation has improved with the publication of the new oceanographic standard TEOS-10, the International Thermodynamic Equation of Seawater 2010, which provides highly accurate values for the chemical potential and the fugacity of water vapor in humid air over wide ranges of pressure and temperature. This paper describes the way fugacity is obtained from the fundamental equations of TEOS-10, and it derives computationally more convenient virial approximations for the fugacity, consistent with TEOS-10. Analytically extracted from the TEOS-10 equation of state of humid air, equations for the 2nd and 3rd virial coefficients are reported and compared with correlations available from the literature. The virial fugacity equation is valid in the temperature range between \({-}80\,^{\circ }\hbox {C}\) and +200 \(^{\circ }\hbox {C}\) at pressures up to 5 MPa, and between \({-}130\,^{\circ }\hbox {C}\) and +1000 \(^{\circ }\hbox {C}\) at low pressures such as those encountered in the terrestrial atmosphere at higher altitudes.


Equation of state Fugacity Humid air Moist air Partial pressure Real gas Thermodynamics Uncertainty Virial Coefficients Water vapor 



The authors are grateful to Donald Gatley, Allan Harvey, Sebastian Herrmann, Jan Hruby, and Hans-Joachim Kretzschmar for various hints regarding virial equations for humid air. They also thank the two anonymous reviewers for their critical comments and helpful suggestions. This work contributes to the tasks of the IAPWS/SCOR/IAPSO Joint Committee on Seawater (JCS).


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Rainer Feistel
    • 1
    Email author
  • Jeremy W. Lovell-Smith
    • 2
  • Olaf Hellmuth
    • 3
  1. 1.Leibniz Institute for Baltic Sea Research (IOW)WarnemündeGermany
  2. 2.Measurement Standards Laboratory (MSL)Lower HuttNew Zealand
  3. 3.Leibniz Institute for Tropospheric Research (TROPOS)LeipzigGermany

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