Humidity - More Funny Composition Units

Full lecture slides are here.

The air-water system is a unique on (we all live in it for a start...) and there are correspondingly a range of rather unusual measures used for it.

Despite their appearance, all these are just ways of expressing the amount of water in air, i.e. the composition of the air (w.r.t. water) or the concentration of water in air.

Although there is a lot of water around (in the sea etc.) the local composition of the atmosphere is in general not in thermodynamic equilibrium with water at ambient temperature. This does sometimes happen though, e.g. when it is raining, and it is also sometimes arranged that air used in a chemical process is in equilibrium with water. The air is then said to be saturated with water.

Humidity

The basic measure of the amount of water in air is called humidity or absolute humidity. This is defined as the weight ratio of water to air:

Humidity (kg/kg), H = (mass of water) / (mass of dry air)

Since the actual amount of water in air ir normally quite small this is very nearly the same as the mass fraction of water in air. The mol fraction of water in air can thus be estimated by multiplying the humidity by the ratio of the molecular weights, i.e. by (29/18).

Saturation and Relative Humidity

If air at pressure P and temperature T reaches thermodynamic equilibrium with water it is said to be saturated, and the usual equilibrium relationships will apply.

The vapour pressure of water at T can be determined and the mol fraction of water in the saturated air, yo determined:

P yo = P*(T)

From yo we can estimate Ho the saturation humidity by multiplying by the appropriate ratio of molecular weights.

At saturation the humidity of the air is Ho. Its precentage humidity is said to be 100%. Precentage humidity is defined as:

Percentage humidity = H / Ho x 100%

If the air contains less than the thermodynamic maximum then its percentage humidity is less than 100%.

The relative humidity of air which is less than saturated is also expressed as a percentage, but this is not the same (confusingly!) the above percentage humidity, as relative humidity is defined in mol fraction terms:

Relative humidity (%) =
100 x (mol fraction of water in air) / (mol fraction of water in saturated air)

Both percentage humidity and relative humidity obviously depend on temperature as well as the amount of water in the air. Fully saturated air is 100% humidity by both measures, but otherwise these differ somewhat. It can be shown that the realtionship between them is:

percent humidity = relative humidity x (1-yo) / (1 - y)

Since the mol fractions are relatively small the measures are quite similar, and approach each other at towards 100%.

Dew Point Temperature

This is another way of expressing the amount of water in air. If the gas is saturated then it is by definition at its dew point, i.e. it is in equilibrium with water which can be thought of as just starting to condense out of the gas.

Thus at temperature T the dew point of saturated air, i.e. at 100% humidity or relative humidity is just T.

However, if the gas is less than saturated it would have to be cooled until condensation started. The temperature to which it would be cooled is called the dew point temperature Td and can be seen to depend only on the water concentration.

At 1 atm:
y = P*(Td)

The dew point temperature is sometines called the saturation temperature.

Wet Bulb Temperature

A wet bulb thermometer is a thermometer whose bulb in surrounded by a porous wick which dips into a resovoir of water. The bulb is thus kept moist and water continually evaporates from its surface. It is thus not unreasonable to consider that the water and air are at thermodynamic equilibrium, and that the temperature read by the thermometer is the saturation temperature. (these are often combined in a single device called a wet-and-dry-bulb thermometer.)

In fact, the situation is somewhat more complex, since the equilibrium is a dynamic rather than the static one which thermodynamics assumes. Water is evaporating from the wick, a process which requires energy to supply latent heat. Except at 100% relative humidity (when no water will evaporate because the air is saturated) the temperature will fall and so heat will be transferred from the suroundings to exactly balance this energy.

The temperature indicated by such a device is called the wet bulb temperature. The physical properties of the air-water system relevant to heat and mass transfer are such that this dynamic equilibrium produces, to within a fraction of a degree, the same temperature as the static equilibrium saturation temperature, and so these can be considered for all practical purposes to be the same. (This is not in general true for other liquid gas/systems, e.g. for an evaporating hydrocarbon in CO2.)

The terms dew point, saturation and wet bulb temperatures can thus be considered all to refer to the same thing, and to be merely an indirect way of expressing the concentration of water in air!

Vapour Pressure of Water

The very simple vapour pressure equation previously given does not work well for water. The following equations can be used

log10 P* (mm Hg) = A - B/(T+C)

Here T is in oC, and the constants A, B and C are:
ToC A B C
0-60 8.10765 1750.286 235
60-150 7.96681 1668.21 228
(Data from `Lange's Handbook of Chemistry', Handbook Publishers, 1956, quoted in Felder and Rousseau, `Elementary Principles of chemical Processes', 3rd Edition.)

A calculator for these equations is here.

Humidity Chart

The humidity chart, sometimes called a psychometric chart, is a combined temperature-composition and enthalpy-composition diagram for the air-water system. It differs from `conventional' Txy or Hx diagrams in its choice of axes and units, in that the liquid phase will contain only water (not liquid air!) and in the addition, in most cases of a number of additional esoteric quantities.

An example chart is here.