# HUMIDITY

Humidity is the term used to denote the vapor content of a gas and usually refers to the air-water system. In all work on the related subjects of Air Conditioning and water cooling, it is customary to base definitions on unit mass of dry air (or other gas). Thus, the humidity of air is the mass of water vapor associated with unit mass of dry air. It is a dimensionless quantity (kg/kg or lb/lb) and, therefore, has the same numerical value whatever system of coherent units is employed.

On the assumption that the ideal gas law is applicable, the humidity of a gas may be expressed in terms of its total pressure (p) and absolute temperature (T), the molecular weights of the components and the partial pressure (pv) of the vapor.

In unit volume of humid gas, the mass mv of vapor of molecular weight Mv is given by:

or

Similarly, the mass mG of dry gas of molecular weight MG is:

Thus the humidity, H = mv/mG = pv/(p − pv) · Mv/MG.

For the air water system, therefore H = pv/(p − pv) · 18/29 approximately.

For a gas, saturated with vapor, the corresponding saturation humidity Ho is:

where pvo is the saturated vapor pressure at the temperature T.

The percentage humidity, h,

i.e.,

The percentage humidity should not be confused with the percentage relative humidity (R), which is the ratio of the partial pressure of the vapor to its saturation value at the same temperature (× 100), i.e.:

Thus

The percentage humidity and the percentage relative humidity are approximately equal only when:

1. pvo (and pv) are small compared with p;

2. pv is close to pvo, i.e., the gas is nearly saturated.

Unlike the percentage relative humidity, the humidity and the percentage humidity are a function of the total pressure p.

For convenience, humidity may be shown as a function of temperature on a Humidity Chart (or Psychrometric Chart), for various values of the percentage relative humidity (see Air Conditioning). The region above the saturation curve (100% relative humidity) represents supersaturation conditions in which excess water is normally present as a mist composed of liquid droplets. The usual humidity chart applies to the air-water system at atmospheric pressure; charts can be constructed for any gas-liquid system at any pressure.

Other quantities, which are frequently shown on a humidity chart are:

• Humid volume, which is the volume occupied by unit mass of air, together with its associated water vapor.

• Saturated volume, which is the humid volume of air when saturated with water.

• Humid heat, which is the specific heat capacity of unit mass of air and associated water, vapor (= ca + H cw) (J/kgK) where ca is the specific heat capacity of air, and cw is the specific heat capacity of water vapor.

#### REFERENCES

Coulson, J. M. and Richardson, J. F. (1996) Chemical Engineering, Vol. 1, 5th edn., Pergamon Press, Oxford.

Penman, H. L. (1955) Humidity, Institute of Physics, London.

Treybal, R. E. (1980) Mass Transfer Operations, 3rd edn., McGraw Hill Book Co.