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.
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.
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 is the vapour pressure in mmHg and T is the temperature in kelvins. Constants are unattributed. | ||||||||||||||||
The Antoine equation | T is in degrees Celsius (°C) and the vapour pressure P is in mmHg. The (unattributed) constants are given as
| ||||||||||||||||
August-Roche-Magnus (or Magnus-Tetens or Magnus) equation | 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] See also discussion of Clausius-Clapeyron approximations used in meteorology and climatology. | ||||||||||||||||
Tetens equation | T is in °C and P is in kPa | ||||||||||||||||
The Buck equation. | T is in °C and P is in kPa. | ||||||||||||||||
The Goff-Gratch (1946) equation. [3] | (See article; too long) |
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.
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.
Vapor pressure or equilibrium vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases at a given temperature in a closed system. The equilibrium vapor pressure is an indication of a liquid's thermodynamic tendency to evaporate. It relates to the balance of particles escaping from the liquid in equilibrium with those in a coexisting vapor phase. A substance with a high vapor pressure at normal temperatures is often referred to as volatile. The pressure exhibited by vapor present above a liquid surface is known as vapor pressure. As the temperature of a liquid increases, the attractive interactions between liquid molecules become less significant in comparison to the entropy of those molecules in the gas phase, increasing the vapor pressure. Thus, liquids with strong intermolecular interactions are likely to have smaller vapor pressures, with the reverse true for weaker interactions.
Humidity is the concentration of water vapor present in the air. Water vapor, the gaseous state of water, is generally invisible to the human eye. Humidity indicates the likelihood for precipitation, dew, or fog to be present.
The dew point of a given body of air is the temperature to which it must be cooled to become saturated with water vapor. This temperature depends on the pressure and water content of the air. When the air is cooled below the dew point, its moisture capacity is reduced and airborne water vapor will condense to form liquid water known as dew. When this occurs through the air's contact with a colder surface, dew will form on that surface.
The heat index (HI) is an index that combines air temperature and relative humidity, in shaded areas, to posit a human-perceived equivalent temperature, as how hot it would feel if the humidity were some other value in the shade. For example, when the temperature is 32 °C (90 °F) with 70% relative humidity, the heat index is 41 °C (106 °F). The heat index is meant to describe experienced temperatures in the shade, but it does not take into account heating from direct sunlight, physical activity or cooling from wind.
A hygrometer is an instrument which measures the humidity of air or some other gas: that is, how much water vapor it contains. Humidity measurement instruments usually rely on measurements of some other quantities such as temperature, pressure, mass and mechanical or electrical changes in a substance as moisture is absorbed. By calibration and calculation, these measured quantities can lead to a measurement of humidity. Modern electronic devices use the temperature of condensation, or they sense changes in electrical capacitance or resistance to measure humidity differences. A crude hygrometer was invented by Leonardo da Vinci in 1480. Major leaps came forward during the 1600s; Francesco Folli invented a more practical version of the device, while Robert Hooke improved a number of meteorological devices including the hygrometer. A more modern version was created by Swiss polymath Johann Heinrich Lambert in 1755. Later, in the year 1783, Swiss physicist and Geologist Horace Bénédict de Saussure invented the first hygrometer using human hair to measure humidity.
Equivalent potential temperature, commonly referred to as theta-e, is a quantity that is conserved during changes to an air parcel's pressure, even if water vapor condenses during that pressure change. It is therefore more conserved than the ordinary potential temperature, which remains constant only for unsaturated vertical motions.
The density of air or atmospheric density, denoted ρ, is the mass per unit volume of Earth's atmosphere. Air density, like air pressure, decreases with increasing altitude. It also changes with variations in atmospheric pressure, temperature and humidity. At 101.325 kPa (abs) and 20 °C, air has a density of approximately 1.204 kg/m3 (0.0752 lb/cu ft), according to the International Standard Atmosphere (ISA). At 101.325 kPa (abs) and 15 °C (59 °F), air has a density of approximately 1.225 kg/m3 (0.0765 lb/cu ft), which is about 1⁄800 that of water, according to the International Standard Atmosphere (ISA). Pure liquid water is 1,000 kg/m3 (62 lb/cu ft).
Psychrometrics is the field of engineering concerned with the physical and thermodynamic properties of gas-vapor mixtures.
The Clausius–Clapeyron relation, in chemical thermodynamics specifies the temperature dependence of pressure, most importantly vapor pressure, at a discontinuous phase transition between two phases of matter of a single constituent. It's named after Rudolf Clausius and Benoît Paul Émile Clapeyron. However, this relation was in fact originally derived by Sadi Carnot in his Reflections on the Motive Power of Fire, which was published in 1824 but largely ignored until it was rediscovered by Clausius, Clapeyron, and Lord Kelvin decades later. Kelvin said of Carnot's argument that "nothing in the whole range of Natural Philosophy is more remarkable than the establishment of general laws by such a process of reasoning."
This page provides supplementary data to the article properties of water.
This page provides supplementary chemical data on methanol.
Boiling-point elevation is the phenomenon whereby the boiling point of a liquid will be higher when another compound is added, meaning that a solution has a higher boiling point than a pure solvent. This happens whenever a non-volatile solute, such as a salt, is added to a pure solvent, such as water. The boiling point can be measured accurately using an ebullioscope.
The Goff–Gratch equation is one amongst many experimental correlation proposed to estimate the saturation water vapor pressure at a given temperature.
The lifted condensation level or lifting condensation level (LCL) is formally defined as the height at which the relative humidity (RH) of an air parcel will reach 100% with respect to liquid water when it is cooled by dry adiabatic lifting. The RH of air increases when it is cooled, since the amount of water vapor in the air remains constant, while the saturation vapor pressure decreases almost exponentially with decreasing temperature. If the air parcel is lifting further beyond the LCL, water vapor in the air parcel will begin condensing, forming cloud droplets. The LCL is a good approximation of the height of the cloud base which will be observed on days when air is lifted mechanically from the surface to the cloud base.
Atmospheric thermodynamics is the study of heat-to-work transformations that take place in the Earth's atmosphere and manifest as weather or climate. Atmospheric thermodynamics use the laws of classical thermodynamics, to describe and explain such phenomena as the properties of moist air, the formation of clouds, atmospheric convection, boundary layer meteorology, and vertical instabilities in the atmosphere. Atmospheric thermodynamic diagrams are used as tools in the forecasting of storm development. Atmospheric thermodynamics forms a basis for cloud microphysics and convection parameterizations used in numerical weather models and is used in many climate considerations, including convective-equilibrium climate models.
The Arden Buck equations are a group of empirical correlations that relate the saturation vapor pressure to temperature for moist air. The curve fits have been optimized for more accuracy than the Goff–Gratch equation in the range −80 to 50 °C.
In atmospheric thermodynamics, the virtual temperature of a moist air parcel is the temperature at which a theoretical dry air parcel would have a total pressure and density equal to the moist parcel of air. The virtual temperature of unsaturated moist air is always greater than the absolute air temperature, however, as the existence of suspended cloud droplets reduces the virtual temperature.
The Antoine equation is a class of semi-empirical correlations describing the relation between vapor pressure and temperature for pure substances. The Antoine equation is derived from the Clausius–Clapeyron relation. The equation was presented in 1888 by the French engineer Louis Charles Antoine (1825–1897).
The Lee–Kesler method allows the estimation of the saturated vapor pressure at a given temperature for all components for which the critical pressure Pc, the critical temperature Tc, and the acentric factor ω are known.
The Tetens equation is an equation to calculate the saturation vapour pressure of water over liquid and ice. It is named after its creator, O. Tetens who was an early German meteorologist. He published his equation in 1930, and while the publication itself is rather obscure, the equation is widely known among meteorologists and climatologists because of its ease of use and relative accuracy at temperatures within the normal ranges of natural weather conditions.