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Vapour pressure of water

## Summary

Vapour pressure of water (0–100 °C)[1]
T, °C T, °F P, kPa P, torr P, atm
0 32 0.6113 4.5851 0.0060
5 41 0.8726 6.5450 0.0086
10 50 1.2281 9.2115 0.0121
15 59 1.7056 12.7931 0.0168
20 68 2.3388 17.5424 0.0231
25 77 3.1690 23.7695 0.0313
30 86 4.2455 31.8439 0.0419
35 95 5.6267 42.2037 0.0555
40 104 7.3814 55.3651 0.0728
45 113 9.5898 71.9294 0.0946
50 122 12.3440 92.5876 0.1218
55 131 15.7520 118.1497 0.1555
60 140 19.9320 149.5023 0.1967
65 149 25.0220 187.6804 0.2469
70 158 31.1760 233.8392 0.3077
75 167 38.5630 289.2463 0.3806
80 176 47.3730 355.3267 0.4675
85 185 57.8150 433.6482 0.5706
90 194 70.1170 525.9208 0.6920
95 203 84.5290 634.0196 0.8342
100 212 101.3200 759.9625 1.0000

The vapour pressure of water is the pressure exerted by molecules of water vapor in gaseous form (whether pure or in a mixture with other gases such as air). The saturation vapour pressure is the pressure at which water vapour is in thermodynamic equilibrium with its condensed state. At pressures higher than vapour pressure, water would condense, whilst at lower pressures it would evaporate or sublimate. The saturation vapour pressure of water increases with increasing temperature and can be determined with the Clausius–Clapeyron relation. The boiling point of water is the temperature at which the saturated vapour pressure equals the ambient pressure.

Calculations of the (saturation) vapour pressure of water is commonly used in meteorology. The temperature-vapour pressure relation inversely describes the relation between the boiling point of water and the pressure. This is relevant to both pressure cooking and cooking at high altitude. An understanding of vapour pressure is also relevant in explaining high altitude breathing and cavitation.

## Approximation formulas

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):

Name Formula Description
"Eq. 1" (August equation) ${\displaystyle P=\exp \left(20.386-{\frac {5132}{T}}\right)}$, where P is the vapour pressure in mmHg and T is the temperature in kelvins. Constants are unattributed.
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 (unattributed) 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
August-Roche-Magnus (or Magnus-Tetens or Magnus) equation ${\displaystyle P=0.61094\exp \left({\frac {17.625T}{T+243.04}}\right)}$, where temperature T is in °C and vapour pressure P is in kilopascals (kPa)

As described in Alduchov and Eskridge (1996).[2] Equation 21 in [2] provides the coefficients used here. See also discussion of Clausius-Clapeyron approximations used in meteorology and climatology.

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] (See article; too long)

### Accuracy of different formulations

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):

T (°C) P (Lide Table) P (Eq 1) P (Antoine) P (Magnus) P (Tetens) P (Buck) P (Goff-Gratch)
0 0.6113 0.6593 (+7.85%) 0.6056 (-0.93%) 0.6109 (-0.06%) 0.6108 (-0.09%) 0.6112 (-0.01%) 0.6089 (-0.40%)
20 2.3388 2.3755 (+1.57%) 2.3296 (-0.39%) 2.3334 (-0.23%) 2.3382 (+0.05%) 2.3383 (-0.02%) 2.3355 (-0.14%)
35 5.6267 5.5696 (-1.01%) 5.6090 (-0.31%) 5.6176 (-0.16%) 5.6225 (+0.04%) 5.6268 (+0.00%) 5.6221 (-0.08%)
50 12.344 12.065 (-2.26%) 12.306 (-0.31%) 12.361 (+0.13%) 12.336 (+0.08%) 12.349 (+0.04%) 12.338 (-0.05%)
75 38.563 37.738 (-2.14%) 38.463 (-0.26%) 39.000 (+1.13%) 38.646 (+0.40%) 38.595 (+0.08%) 38.555 (-0.02%)
100 101.32 101.31 (-0.01%) 101.34 (+0.02%) 104.077 (+2.72%) 102.21 (+1.10%) 101.31 (-0.01%) 101.32 (0.00%)

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

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]

Examples of modern use of these formulae can additionally be found in NASA's GISS Model-E and Seinfeld and Pandis (2006). The former is an extremely simple Antoine equation, while the latter is a polynomial.[8]

## Graphical pressure dependency on temperature

Vapour pressure diagrams of water; data taken from Dortmund Data Bank. Graphics shows triple point, critical point and boiling point of water.

## References

1. ^ Lide, David R., ed. (2004). CRC Handbook of Chemistry and Physics, (85th ed.). CRC Press. pp. 6–8. ISBN 978-0-8493-0485-9.
2. ^ a b Alduchov, 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. PMC 5312760. PMID 32196299.
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.
8. ^ Clemenzi, Robert. "Water Vapor - Formulas". mc-computing.com.