Vapour pressure of water
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 Clausius–Clapeyron relation.
|T, °C||T, °F||P, kPa||P, torr||P, atm|
The saturated vapour pressure of water may be approximated by the following relations (in order of increasing accuracy):
- Using the Antoine equation
- where the temperature T is in degrees Celsius and the vapour pressure P is in torr. The constants are given as
A B C Tmin, °C Tmax, °C 8.07131 1730.63 233.426 1 99 8.14019 1810.94 244.485 100 374
- Using the Tetens equation
- Using the Buck equation.
where T is in °C and P is in kPa.
Accuracy of different formulations
Here is a comparison of the accuracies of these different explicit formulations, showing vapour pressures in kPa, calculated at six temperatures with their % error from the table values of Lide (2005):
T (°C) P (Table) P (Eq 1) P (Antoine) P (Tetens) P (Buck) 0 0.6113 0.6593 (+7.85%) 0.6056 (-0.93%) 0.6108 (-0.09%) 0.6112 (-0.01%) 20 2.3388 2.3755 (+1.57%) 2.3296 (-0.39%) 2.3399 (+0.05%) 2.3383 (-0.02%) 35 5.6267 5.5696 (-1.01%) 5.6090 (-0.31%) 5.6289 (+0.04%) 5.6268 (+0.00%) 50 12.344 12.065 (-2.26%) 12.306 (-0.31%) 12.354 (+0.08%) 12.349 (+0.04%) 75 38.563 37.738 (-2.14%) 38.463 (-0.26%) 38.718 (+0.40%) 38.595 (+0.08%) 100 101.32 101.31 (-0.01%) 101.34 (+0.02%) 102.43 (+1.10%) 101.31 (-0.01%)
So 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 reportedly even superior to the Goff-Gratch equation.
For serious computation, Lowe (1977) 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), reported by Flatau et al. (1992).
Graphical pressure dependency on temperature
- Dew point
- Gas laws
- Molar mass
- Goff-Gratch equation
- Antoine equation
- Tetens equation
- Arden Buck equation
- Lee–Kesler method
- David R. Lide, ed. (2005). CRC Handbook of Chemistry and Physics. Boca Raton, Florida: CRC Press. p. 6-8.
- Lowe, P.R. 1977. An approximating polynomial for the computation of saturation vapor pressure. J. Applied Meteorology 16: 100-104. http://dx.doi.org/10.1175/1520-0450(1977)016<0100:AAPFTC>2.0.CO;2
- Wexler, A. 1976. Vapor pressure formulation for water in range 0 to 100°C. A revision. J. Res. Natl. Bur. Stand. 80A: 775-285.
- Wexler, A. 1977. Vapor pressure formulation for ice. J. Res. Natl. Bur. Stand. 81A: 5-20.
- Flatau, P.J., Walko, R.L., and Cotton, W.R. 1992. Polynomial fits to saturation vapor pressure. J. Applied Meteorology 31: 1507-1513.
- http://web.mit.edu/seawater/ MIT page of seawater properties, with Matlab, EES and Excel VBA library routines
- Garnett, Pat; Anderton, John D; Garnett, Pamela J (1997). Chemistry Laboratory Manual For Senior Secondary School. Longman. ISBN 0-582-86764-9.
- Murphy, D. M. and 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): 1539–1565. doi:10.1256/qj.04.94
- James G. Speight : Lange's Handbook of Chemistry ISBN 0071432205