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The vapour pressure of water is the pressure at which water vapour is in thermodynamic equilibrium with its condensed state. At higher pressures water would condense. The water vapour pressure is the partial pressure of water vapour in any gas mixture in equilibrium with solid or liquid water. As for other substances, water vapour pressure is a function of temperature and can be determined with the Clausius–Clapeyron relation.

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Approximation formulas[edit]

There are many published approximations for calculating saturated vapour pressure over water and over ice. Some of these are (in approximate order of increasing accuracy):

• ${\displaystyle P=\exp \left(20.386-\frac{5132}{T}\right),(Eq.1)}$

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where P is the vapour pressure in mmHg and T is the temperature in kelvins.

• The Antoine equation

${\displaystyle {\log }_{10}P=A-\frac{B}{C+T},}$

where the temperature T is in degrees Celsius (°C) and the vapour pressure P is in mmHg. The constants are given as

• The August-Roche-Magnus (or Magnus-Tetens or Magnus) equation, as described in Alduchov and Eskridge (1996).^[2] Equation 25 in ^[2] provides the coefficients used here. See also discussion of Clausius-Clapeyron approximations used in meteorology and climatology.

${\displaystyle P=0.61094\exp \left(\frac{17.625T}{T+243.04}\right),}$

where temperature T is in °C and vapour pressure P is in kilopascals (kPa)

• The Tetens equation

${\displaystyle P=0.61078\exp \left(\frac{17.27T}{T+237.3}\right),}$

where temperature T is in °C and P is in kPa

• The Buck equation.

${\displaystyle P=0.61121\exp \left(\left(18.678-\frac{T}{234.5}\right)\left(\frac{T}{257.14+T}\right)\right),}$

where T is in °C and P is in kPa.

• The Goff-Gratch (1946) equation.^[3]

Accuracy of different formulations[edit]

Here is a comparison of the accuracies of these different explicit formulations, showing saturation vapour pressures for liquid water in kPa, calculated at six temperatures with their percentage error from the table values of Lide (2005):

A more detailed discussion of accuracy and considerations of the inaccuracy in temperature measurements is presented in Alduchov and Eskridge (1996). The analysis here shows the simple unattributed formula and the Antoine equation are reasonably accurate at 100 °C, but quite poor for lower temperatures above freezing. Tetens is much more accurate over the range from 0 to 50 °C and very competitive at 75 °C, but Antoine's is superior at 75 °C and above. The unattributed formula must have zero error at around 26 °C, but is of very poor accuracy outside a very narrow range. Tetens' equations are generally much more accurate and arguably simpler for use at everyday temperatures (e.g., in meteorology). As expected, Buck's equation for T > 0 °C is significantly more accurate than Tetens, and its superiority increases markedly above 50 °C, though it is more complicated to use. The Buck equation is even superior to the more complex Goff-Gratch equation over the range needed for practical meteorology.

Numerical approximations[edit]

For serious computation, Lowe (1977)^[4] developed two pairs of equations for temperatures above and below freezing, with different levels of accuracy. They are all very accurate (compared to Clausius-Clapeyron and the Goff-Gratch) but use nested polynomials for very efficient computation. However, there are more recent reviews of possibly superior formulations, notably Wexler (1976, 1977),^[5][6] reported by Flatau et al. (1992).^[7]

Graphical pressure dependency on temperature[edit]

See also[edit]

References[edit]

1. ^Lide, David R., ed. (2004). CRC Handbook of Chemistry and Physics, (85th ed.). CRC Press. pp. 6–8. ISBN978-0-8493-0485-9.
2. ^ ^abAlduchov, O.A.; Eskridge, R.E. (1996). 'Improved Magnus form approximation of saturation vapor pressure'. Journal of Applied Meteorology. 35 (4): 601–9. Bibcode:1996JApMe.35.601A. doi:10.1175/1520-0450(1996)035<0601:IMFAOS>2.0.CO;2.
3. ^Goff, J.A., and Gratch, S. 1946. Low-pressure properties of water from −160 to 212 °F. In Transactions of the American Society of Heating and Ventilating Engineers, pp 95–122, presented at the 52nd annual meeting of the American Society of Heating and Ventilating Engineers, New York, 1946.
4. ^Lowe, P.R. (1977). 'An approximating polynomial for the computation of saturation vapor pressure'. Journal of Applied Meteorology. 16 (1): 100–4. Bibcode:1977JApMe.16.100L. doi:10.1175/1520-0450(1977)016<0100:AAPFTC>2.0.CO;2.
5. ^Wexler, A. (1976). 'Vapor pressure formulation for water in range 0 to 100°C. A revision'. Journal of Research of the National Bureau of Standards Section A. 80A (5–6): 775–785. doi:10.6028/jres.080a.071.
6. ^Wexler, A. (1977). 'Vapor pressure formulation for ice'. Journal of Research of the National Bureau of Standards Section A. 81A (1): 5–20. doi:10.6028/jres.081a.003.
7. ^Flatau, P.J.; Walko, R.L.; Cotton, W.R. (1992). 'Polynomial fits to saturation vapor pressure'. Journal of Applied Meteorology. 31 (12): 1507–13. Bibcode:1992JApMe.31.1507F. doi:10.1175/1520-0450(1992)031<1507:PFTSVP>2.0.CO;2.

Further reading[edit]

• 'Thermophysical properties of seawater'. Matlab, EES and Excel VBA library routines. MIT. 20 February 2017.
• Garnett, Pat; Anderton, John D; Garnett, Pamela J (1997). Chemistry Laboratory Manual For Senior Secondary School. Longman. ISBN978-0-582-86764-2.
• Murphy, D.M.; Koop, T. (2005). 'Review of the vapour pressures of ice and supercooled water for atmospheric applications'. Quarterly Journal of the Royal Meteorological Society. 131 (608): 1539–65. Bibcode:2005QJRMS.131.1539M. doi:10.1256/qj.04.94.
• Speight, James G. (2004). Lange's Handbook of Chemistry (16th ed.). McGraw-Hil. ISBN978-0071432207.

External links[edit]

• Vömel, Holger (2016). 'Saturation vapor pressure formulations'. Boulder CO: Earth Observing Laboratory, National Center for Atmospheric Research. Archived from the original on June 23, 2017.
• 'Vapor Pressure Calculator'. National Weather Service, National Oceanic and Atmospheric Administration.