Humid air and condensation
PDFThe first documented study of humid air seems to be the description made by Charles Leroy (1751), a medical doctor in Montpellier (France). He reported in 1751 to the Académie Royale des Sciences that water can be dissolved in air according to air temperature, the higher temperature corresponding to larger dissolution. In support of his claim he described several experiments. The most demounstrative was made with a bottle of air closed at daytime temperature. Once cooled at night, air was unable to hold all water dissolved at higher daytime temperature: The exceeding water lead to well visible condensed droplets inside the bottle.
Air is indeed never completely dry; it always holds in an invisible way some water vapour in different concentrations depending on its temperature. In addition to vapour, humid air can also contain water in visible condensed states: liquid (fog droplets), solid (frosty fog). In the latter cases where vapour and condensed phases coexist, humid air is said supersaturated.
Humid air can thus be considered of being formed of (1) dry air unlikely to condense in the conditions of temperature and pressure considered here, and (2) water vapour likely to condense in liquid or ice. Dry air is mainly composed of Nitrogen (≈ 78%) and Oxygen (≈ 21%). For regular conditions of temperature and pressure found at the earth surface, both gases are far from their critical point coordinates and both fluids can be accepted as ideal gases. Air will be thus considered as a single ideal gas. Water is also far from its critical point coordinates and can be also considered as an ideal gas.
1. Partial pressures: the Dalton Law
The partial pressure of a gas is the pressure that would have the gas if alone in a volume V. As both dry air and water are ideal gases, the total pressure is equal to the sum of the partial pressures: This is the Dalton law. With pa (resp pv) the partial pressure of air (resp., water), one gets pm = pa + pv. This additivity rule corresponds to neglect intermolecular forces among the gases molecules. Pressure being due to impacts of moving gas molecules, the total pressure is simply the addition of impacts of each type of molecules.
2. Equation of state
The equation of state for dry air and water vapour is the equation of ideal gas piV = niRT where the subscript i stands for air (i=a) or water vapor (i=v); ni = mi /nMi is the number of moles (i) of molar mass Mi and mass mi in a volume V, R = 8.314 J.mole-1.K-1 is the molar gas constant. The properties of humid air at given partial pressure of water vapour can be deduced from this simple equation of state.
3. Saturation; condensation
Let us consider the cooling process at constant pressure pm of a mass of humid air which contains a given mass of water. Mass conservation requires that the total mass and the water vapour mass remain constant during the process. This is therefore also the case for the number of moles of water vapour moles and the corresponding molar fraction nv / n = pv / pm (from the equation of state above). It results that the water vapour pressure remains constant during the cooling process. In the atmosphere, humid air cooling thus occurs at constant water vapour pressure.
Beysens, D. (2018). Dew water. Gistrup : Rivers Publisher]
Beysens
, D. (2018). Dew water. Gistrup : Rivers Publisher]
Saturated vapor pressure can then be reached in a given humid air in two ways. (i) Cooling a given mass of humid air: vapor pressure remains constant at pv but ps decreases until the equality pv = ps(Td) is fulfilled. (ii) Adding a water mass to a given humid air volume at constant temperature: The vapor pressure increases until it reaches at same temperature pv = ps. If more water at constant temperature is added, one obtains the coexistence of saturated vapor pressure and liquid. Humid air is then supersaturated.
From above, one can define the relative humidity RH as the ratio at given temperature of the vapour pressure and saturation vapour pressure, RH = pv(T)/ps(T). When cooling a given mass of humid air, RH increases to reach 100% at the saturation line. When adding water at constant temperature, RH also increase to 100% and reaches the saturation line. The relative humidity is a common index to determine how close to saturation is a given humid air. The larger RH, the smaller cooling or added mass is needed to obtain condensation.
Notes
Cover image. [Source : royalty free]
BEYSENS, D. (2018). Dew water. Gistrup : Rivers Publisher.
BEYSENS, D. (2022). The Physics of Dew, Breath Figures and Dropwise Condensation. Berlin: Springer Verlag.
MYLYMUK-MELNYTCHOUK, I., BEYSENS, D. (2016). Puits aériens : mythes et réalités ou Travaux russes & soviétiques sur la production d’eau à partir de l’air. Sarrebruck : Editions Universitaires Européennes.
BEYSENS, D., MILIMOUK-MELNYTCHOUK, I., MUSELLI, M. (2009). Condenseurs radiatifs de rosée. Techniques de l’Ingénieur, base documentaire « Génie énergétique », IN101- 04, 1-10.
MYLYMUK, I., BEYSENS, D. (2005). A la Poursuite des Fontaines Aériennes ou Les Incroyables Aventures de Français en Ukraine. Sofia-Antipolis: Book-eBook.
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