Vapour pressure of water

Vapor 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 vapor 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 vapor pressure is the pressure at which water vapor is in thermodynamic equilibrium with its condensed state. At pressures higher than vapor pressure, water would condense, while at lower pressures it would evaporate or sublimate. The saturation vapor 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 vapor pressure equals the ambient pressure. Water supercooled below its normal freezing point has a higher vapor pressure than that of ice at the same temperature and is, thus, unstable.

Calculations of the (saturation) vapor pressure of water are commonly used in meteorology. The temperature-vapor 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 altitudes. An understanding of vapor pressure is also relevant in explaining high altitude breathing and cavitation.

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In this experiment we will see what happens to a beaker of water when we lower the surrounding air pressure. We will use this vacuum pump, a liquid nitrogen cold trap, two pressure gauges, one hundred liters of room temperature water, and a bell jar. First, we fill the cold trap with liquid nitrogen. This will prevent any water from entering the pump. Now let's turn on the pump, and gradually open the valve to the bell jar. When the pressure reaches about twenty millimeters of mercury, the water begins to bubble. The water boils because its vapor pressure exceeds the pressure in the bell jar. As the water boils it loses heat, and it's temperature decreases. The pressure must drop to keep it boiling. Eventually, we see the water inside the bell jar freeze, even as it's boiling. When we return the bell jar to atmospheric pressure, we see the water remains frozen.

Approximation formulas

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

Name

Formula

Description

"Eq. 1" (August equation)

P=\exp \left(20.386-{\frac {5132}{T}}\right)

P

is the vapour pressure in mmHg and

T

is the temperature in kelvins. Constants are unattributed.

The Antoine equation

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

T

is in degrees Celsius (°C) and the vapour pressure

P

is in mmHg. The (unattributed) constants are given as

$A$	$B$	$C$	$T min$ , °C	$T max$ , °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

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

Temperature

T

is in °C and vapour pressure

P

is in kilopascals (kPa). The coefficients given here correspond to equation 21 in Alduchov and Eskridge (1996).^[2]

Tetens equation

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

T

is in °C and

P

is in kPa

The Buck equation.

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

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 vapor 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 narrow range. Tetens' equations are generally much more accurate and arguably more straightforward for use at everyday temperatures (e.g., in meteorology). As expected,^{[clarification needed]} 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]

In 2018 a new physics-inspired approximation formula was devised and tested by Huang ^[9] who also reviews other recent attempts.

Graphical pressure dependency on temperature

References

^ Lide, David R., ed. (2004). CRC Handbook of Chemistry and Physics (85th ed.). CRC Press. pp. 6–8. ISBN 978-0-8493-0485-9.
^ 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.
^ 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.
^ 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.
^ 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.
^ 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. PMC 5295832.
^ 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.
^ Clemenzi, Robert. "Water Vapor - Formulas". mc-computing.com.
^ Huang, Jianhua (2018). "A Simple Accurate Formula for Calculating Saturation Vapor Pressure of Water and Ice". Journal of Applied Meteorology and Climatology. 57 (6): 1265–72.

External links

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.

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