Measurement of Humidity Hygrometers Psychrometers

Many methods have been devised to measure humidity of the air. The instruments are generally called hygrometers or psychrometers. The most commonly used humidity-measuring instrument is that of wet and dry bulb thermometers, which consists of two similar mercury thermometers, one of which (dry-bulb) records the actual air temperature, while the other (wet-bulb) records the temperature of the air after it has been cooled by evaporation of water at the bulb which is kept wet by water supplied to it from a small reservoir by a muslin cloth wrapped round the bulb. The difference between the temperatures measured by the two thermometers is an index to the degree of wetness of the air in the atmosphere. Qualitatively, a small value of the depression of temperature at the wet bulb indicates that the air is already very moist, while a large value indicates extreme dryness of the air. The thermodynamics of this hygrometer is discussed below. The treatment given here is that due to Normand (1921).

Let x be the mixing-ratio of a sample of air at temperature T and pressure p, which flows over the wet-bulb thermometer and delivers a quantity of heat to the wet-bulb thermometer so as to evaporate some water and drop its temperature to T' before leaving the wet-bulb with a mixing-ratio of x' saturated at the wet-bulb temperature T' at the same total pressure p. The difference (x'-x) is then the quantity of water that was evaporated at the wet-bulb and that brought down its temperature to T'. The heat exchange at the wet-bulb is then given by

where cp, cp' are the specific heat at constant pressure of dry air and water vapour respectively and L' the latent heat of vaporization of water at the wet-bulb temperature T'. Since (cp' x/cp) is C 1, (4.4.1) may be written as cp(T - T')=L'(x'- x) Or, T +(L'x/cp) = T' + (L'x'/cp) (4.4.2)

We now consider a temperature T'' of totally dry air(x = 0) which has a wet-bulb temperature T', so that

The temperature T'' is known as the equivalent temperature. It is the temperature which a sample of moist air would assume if it were expanded saturated-adiabatically to have all its latent heat converted into sensible heat and then compressed dry-adiabatically to its original pressure.

If, in (4.3.1), we use the partial water vapour pressure e instead of the humidity-mixing-ratio x, and use the relationships, x =e e/(p-e), and xf =e e'/ (p-e'), where e' is the saturation vapour pressure of water at temperature T', we get

[{ e (e'- e)pL'}/{(p - e)(p - e')}] = [(T - T){cp + e cp'e/(p - e)}] (4.4.4)

For small values of e compared to p, e cp'/cp has a value close to unity. The Eq. (4.4.4) may thus be simplified to e'- e = Ap(T - T) (4.4.5)

Since the value of e/p is only a very small fraction of unity, it may be neglected and the expression (4.4.5) may be used to measure the existing vapour pressure e of the air at temperature T, since e' which is the saturation vapour pressure at temperature T' can be found from standard meteorological tables. The relative humidity of the air may then be determined from the percentage ratio, e x 100/es, where es is the saturation vapour pressure of water at temperature T, which can be found from the Tables.

Normand showed that the dry adiabat line through the dry-bulb temperature T, the saturated adiabat line through the wet-bulb temperature T' and the saturated-mixing-ratio line through the dew-point Td of a sample of air all meet at a point P which came to be called the Normand point. The level of P is also called the lifting condensation level (LCL), as shown in Fig. 4.1.

In Fig. 4.1, the wet-bulb temperature T' lies in between the dry-bulb temperature T and the dew-point temperature Td.This is due to the fact that saturation at the wet-bulb is attained partly by evaporative cooling of air and partly by addition of water vapour into it.

If the dry adiabat through the equivalent temperature T'' is extended to a standard pressure, say 1000 mb, the temperature reached at this pressure is called the equivalent potential temperature which is denoted by 9e. Likewise, if the saturated adiabat

Fig. 4.1 The Normand diagram showing the Lifting Condensation Level (LCL)

through the wet-bulb temperature T' is extended to a standard pressure 1000 mb, the temperature then attained is called the wet-bulb potential temperature, which is denoted by 0w. The equivalent potential temperature 0e and the wet-bulb potential temperature 0w are both conserved during dry and moist adiabatic processes. Hence they are useful parameters in the identification of airmasses.

Psychrometers are instruments that make use of the principle of the dry and wet-bulb hygrometer as discussed above to measure humidity. Different types of psy-chrometers are in use. A portable variety called a sling psychrometer is very handy and in wide use. Other psychrometers include the Assmann psychrometer and the aspiration psychrometer.

The physical and chemical properties of many substances are affected by humidity of the air. For example, the physical dimension of a human hair changes with absorption of water vapour and this fact is made use of in making a class of hygrometers, such as a hair hygrometer, a torsion hygrometer or a goldbeater's skin hygrometer. A change in the physical and electrical properties of some substances due to absorption of water vapour forms the basis of another class of hygrometers, called absorption hygrometers, electrical hygrometers and carbon-film hygrometers. Besides these, we have the diffusion hygrometer the working of which depends upon the diffusion of water vapour through a porous membrane and the spectral hygrometer which depends upon measurements of the absorption spectra of water vapour.

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