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Tension of Aqueous Vapour(1)

The determination of the amount of water contained in the atmosphere as vapour is a problem of great importance, especially to meteorology. There are several ways in which we may attempt to make the determination, and the result of the experiment may also be variously expressed.
The quantity of water which can be contained in air at a given temperature is limited by the condition that the pressure(1) of the vapour (considered independently of the pressure of the atmosphere containing it) cannot exceed a certain amount, which is definite for a definite temperature, and which for temperatures usually occurring, viz. between -10C. and +30C, lies between 2 mm. of mercury and 31.5 mm. Dalton concluded, from experiments of his own, that this maximum pressure, which water vapour could exert when in the atmosphere, was the same as that which the vapour could exert if the air were removed, and indeed that the dry air and the vapour pressed the sides of the vessel containing them with a pressure entirely independent one of the other, the sum of the two being the resultant pressure of the damp air (see the previous experiment, 41).

This law of Dalton's has been shown by Regnault to be true, within small limits of error, at different temperatures for saturated air, that is, for air which contains as much vapour as possible; and it is now a generally accepted principle, not only for the vapour of water and air, but for all gases and vapours which do not act chemically upon one another, and accordingly one of the most usual methods of expressing the state of the air with respect to the moisture it contains is to quote the pressure exerted by the moisture at the time of the observation. Let this be denoted by e; then by saying that the pressure of aqueous vapour in the atmosphere is e, we mean that if we enclose a quantity of the air without altering its pressure, we shall reduce its pressure by e, if we remove from it, by any means, the whole of its water without altering its volume. The quantity we have denoted by e is often called the tension of aqueous vapour in the air. Relative Humidity. - From what has gone before, it will be understood that when the temperature of the air is known we can find by means of a table of pressures of water vapour in vacuo the maximum pressure which water vapour can exert in the atmosphere. This may be called the saturation tension for that temperature. Let the temperature be t and the saturation tension et then if the actual tension at the time be e, the so-called fraction of saturation will be e/et and the percentage of saturation will be 100*e/et. This is known as the relative humidity.

Dew Point

If we suppose a mass of moist air to be enclosed in a perfectly flexible envelope, which prevents its mixing with the surrounding air but exerts no additional pressure upon it, and suppose this enclosed air to be gradually diminished in temperature, a little consideration will show that if both the dry air and vapour are subject to the same laws of contraction from diminution of temperature under constant pressure,(2) the dry air and vapour will contract the same fraction of their volume, but the pressure of each will be always the same as it was originally, the sum of the two being always equal to the atmospheric pressure on the outside of the envelope.

If, then, the tension of aqueous vapour in the original air was e, we shall by continual cooling arrive at a temperature - let us call it τ - at which e is the saturation tension; and if we cool the air below that we must get some of the moisture deposited as a cloud or as dew. This temperature is therefore known as the dew point.

If we then determine the dew point to be τ, we can find e, the tension of aqueous vapour in the air at the time, by looking out in the table of tensions eτ the saturation tension at τ, and we have by the foregoing reasoning

e = eτ.

(1) The words 'tension' and 'pressure' are here used, in accordance with custom, as synonymous.
(2) The condition here stated has been proved by the experiments of Regnault, Herwig, and others, to be very nearly fulfilled in the case of water vapour.

Last Update: 2011-03-27