Still a third, though not independent relation may be read from equation (1), thus: when the volume of a gas is kept constant, the pressure is proportional to the absolute temperature. In particular, if the temperature is changed one degree, the pressure varies accordingly by 1/T part of itself. For example, if an air tank or gas tank, in a room at 500° F., changes one degree in temperature, its pressure will change 1/500 part.
With minute detail these three conclusions from the general equation (1) have been set forth and illustrated, because of their practical importance. Other valuable results may be obtained by similar reasoning. Thus equation (2) may be read; the volume of a unit mass of any substance is the reciprocal of its density. Hence, if in the three foregoing conclusions, the reciprocal of the density is everywhere written for the volume, three new relations will be obtained which are of frequent practical use. Two of them may be expressed in the following important law; the density of a gas varies directly as its pressure and inversely as its temperature. Useful applications of this law in aëronautics suggest themselves at once.
By means of the various foregoing equations, the value of either one of the four quantities P, V, T, ρ, representing respectively the pressure, volume, absolute temperature, and the density, may be obtained in terms of any two of the others. If then any two of the quantities is observed, the others can be at once computed. If, for example, the pressure and temperature of dry air be observed at any point, its density can be computed from the formulæ, also its volume per kilogram weight, and thence its volume for any other weight. It is important therefore to be able to measure satisfactorily at least two of the four quantities. In usual studies of the atmosphere the pressure and temperature are observed directly. The method and instruments employed for that purpose are too well known to require description here.
In some speculations the pressure and temperature of the atmosphere are assumed, and certain interesting conclusions drawn. For instance, if the temperature is assumed constant throughout a dry atmosphere, the fluid will obey Boyle’s law, and it can be easily shown that the height of such a medium is the same whether it comprise much gas or little.[58] Again assuming the temperature and pressure constant, the height of the normal homogeneous atmosphere can be computed by dividing the pressure per square unit by its weight per cubic unit. In this way the height of the normal homogeneous atmosphere has been found to be about five miles. But these are hypothetical cases, of purely theoretic interest. In practice the temperature may, on the average, be assumed to decrease 6° C. for each kilometer of ascent, and the pressures may then be computed for various elevations by use of Boyle’s law, as done for Table I.
This leads us to a study of the gaseous properties of moist air. By moist air is meant a mixture of dry air and aqueous vapor in the form of an invisible elastic gas. The definition does not comprise air containing visible steam, or mist, or cloud, but clear moist air such as one ordinarily breathes. The study of this mixture may be preceded by a brief account of the gaseous properties of the vapor alone.
If water in sufficiently small quantity be introduced in a vacuum bottle at any ordinary temperature, it will promptly evaporate, forming an invisible gas known as aqueous vapor, filling the bottle and exerting a uniform pressure on its walls, except for the minute difference at top and bottom due to gravity. The vapor weighs 0.622 as much as dry air having the same volume, temperature and pressure, or quite accurately ⅝ as much. It obeys all the laws given above for ordinary gases and dry air. But it has one singularity; at ordinary atmospheric temperatures, it cannot be indefinitely compressed without condensing to a liquid. In this respect it differs from the chief components of the atmosphere, which at ordinary temperatures can endure indefinite pressure without liquefaction. The ammonia and carbon dioxide in the air can, it is true, be condensed by pressure at their usual temperatures, but not by such pressures as occur in the free atmosphere, thus still leaving aqueous vapor the one singular constituent.
Reverting to the behavior of the water in the assumed vacuum bottle at fixed temperature, it may be observed that the pressure of the invisible vapor is directly proportional to the amount of liquid evaporated. In other words, for any fixed temperature the vapor pressure is directly proportional to its density. When this density reaches a certain definite amount, dependent solely upon the temperature, no further evaporation will occur, unless some of the vapor condenses. The pressure of saturation for that temperature has been reached, and any attempt to increase the pressure, by diminishing the volume of the vapor, will cause liquefaction at constant temperature.
If, however, the space is not saturated, the mass of vapor present may be expressed as a percentage of the amount required for saturation at that temperature. This percentage is called the relative humidity. Thus if the relative humidity is seventy per cent, the actual mass of water vapor present at the observed temperature is seventy per cent of the maximum that can exist in the given space, at the given temperature. In other words, the relative humidity is the ratio of the actual to the possible humidity at a given temperature.
In like manner, for any given vapor pressure there is a definite saturation temperature, known as the dew-point. If with constant pressure the vapor is given various temperatures higher than the dew-point, it will remain gaseous and invisible; but if it falls in temperature to the dew-point, liquefaction occurs, and drops of water appear on the inner wall of the vessel. Further cooling will entail still further liquefaction and reduction of pressure; for the lower the temperature the less the possible mass and pressure of saturation. But for all temperatures, down to freezing and considerably below, some vapor exists, and obeys the same laws as at higher temperatures. When, however, saturation occurs below freezing, the vapor may be precipitated as snow instead of water. This is a familiar phenomenon in the free atmosphere.
The actual mass of water vapor present in a cubic unit of space is sometimes called the absolute humidity. A formula giving the absolute humidity f, in kilograms per cubic meter, for any observed temperature t, and vapor pressure e, may be written as follows: