Vapour pressure of water

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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 Clausius–Clapeyron relation.

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

Approximation formulas

The saturated vapour pressure of water may be approximated by the following relations (in order of increasing accuracy):

• ${\displaystyle P{\text{ (mmHg)}}=\exp \left(20.386-{\frac {5132}{T}}\right),}$
where P is the vapour pressure in mmHg and T is the temperature in kelvins.
${\displaystyle \log _{10}P=A-{\frac {B}{C+T}},}$
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
${\displaystyle P=0.61078\exp \left({\frac {17.27T}{T+237.3}}\right),}$

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

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

where T is in °C and P is in kPa.

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.

Numerical approximations

For serious computation, Lowe (1977)[2] 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),[3][4] reported by Flatau et al. (1992).[5]

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. ^ David R. Lide, ed. (2005). CRC Handbook of Chemistry and Physics. Boca Raton, Florida: CRC Press. p. 6-8.
2. ^ 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
3. ^ Wexler, A. 1976. Vapor pressure formulation for water in range 0 to 100°C. A revision. J. Res. Natl. Bur. Stand. 80A: 775-285.
4. ^ Wexler, A. 1977. Vapor pressure formulation for ice. J. Res. Natl. Bur. Stand. 81A: 5-20.
5. ^ Flatau, P.J., Walko, R.L., and Cotton, W.R. 1992. Polynomial fits to saturation vapor pressure. J. Applied Meteorology 31: 1507-1513.