Psychrometry is the study of the properties of mixtures of air and water vapour.

Atmospheric air makes up the environment in almost every type of air conditioning system. Hence a thorough understanding of the properties of atmospheric air and the ability to analyse various processes involving air is fundamental to air conditioning design.

Atmospheric air is a mixture of many gases plus water vapour and a number of pollutants. The amount of water vapour and pollutants vary from place to place. The concentration of water vapour and pollutants decrease with altitude, and above an altitude of about 10 km, atmospheric air consists of only dry air. The pollutants have to be filtered out before processing the air. Hence, what we process is essentially a mixture of various gases that constitute air and water vapour. This mixture is known as moist air.

The moist air can be thought of as a mixture of dry air and moisture. For all practical purposes, the composition of dry air can be considered as constant. In 1949, a standard composition of dry air was fixed by the International Joint Committee on Psychrometric data.

Based on the above composition the molecular weight of dry air is found to be 28.966 and the gas constant R is 287.035 J/kg.K.

As mentioned before the air to be processed in air conditioning systems is a mixture of dry air and water vapour. While the composition of dry air is constant, the amount of water vapour present in the air may vary from zero to a maximum depending upon the temperature and pressure of the mixture (dry air + water vapour).

At a given temperature and pressure the dry air can only hold a certain maximum amount of moisture. When the moisture content is maximum, then the air is known as saturated air, which is established by a neutral equilibrium between the moist air and the liquid or solid phases of water.

For calculation purposes, the molecular weight of water vapour is taken as 18.015 and its gas constant is 461.52 J/kg.K.

Basic gas laws for moist air:

According to the Gibbs-Dalton law for a mixture of perfect gases, the total pressure exerted by the mixture is equal to the sum of partial pressures of the constituent gases.

p = pt = pa + pv

where p = pt = total barometric pressure pa = partial pressure of dry air pv = partial pressure of water vapour

PSYCHROMETRIC PROPERTIES

Dry bulb temperature (DBT) is the temperature of the moist air as measured by a standard thermometer or other temperature measuring instruments.

Saturated vapour pressure (Psat) is the saturated partial pressure of water vapour at the dry bulb temperature.

Relative humidity (Φ) is defined as the ratio of the mole fraction of water vapour in moist air to mole fraction of water vapour in saturated air at the same temperature and pressure. Using perfect gas equation we can show that:

Φ = partial pressure of water vapour / saturation pressure of pure water vapour at same temperature

= Pv / Psat

Relative humidity is normally expressed as a percentage. When Φ is 100 percent, the air is saturated.

Humidity ratio (W): The humidity ratio (or specific humidity) W is the mass of water associated with each kilogram of dry air. Assuming both water vapour and dry air to be perfect gases, the humidity ratio is given by:

W = kg of water vapour / kg of dry air

Substituting the values of gas constants of water vapour and air Rv and Ra in the above equation; the humidity ratio is given by:

For a given barometric pressure pt, given the DBT, we can find the saturated vapour pressure Psat from the thermodynamic property tables on steam. Then using the above equation, we can find the humidity ratio at saturated conditions, Wsat.

It is to be noted that, W is a function of both total barometric pressure and vapor pressure of water.

Dew-point temperature: If unsaturated moist air is cooled at constant pressure, then the temperature at which the moisture in the air begins to condense is known as dew-point temperature (DPT) of air. An approximate equation for dew-point temperature is given by:

where Φ is the relative humidity (in fraction). DBT & DPT are in °C. Of course, since from its definition, the dew point temperature is the saturation temperature corresponding to the vapour pressure of water vapour, it can be obtained from steam tables.

Degree of saturation μ: The degree of saturation is the ratio of the humidity ratio W to the humidity ratio of a saturated mixture Ws at the same temperature and pressure, i.e.,

Enthalpy: The enthalpy of moist air is the sum of the enthalpy of the dry air and the enthalpy of the water vapour. Enthalpy values are always based on some reference value. For moist air, the enthalpy of dry air is given a zero value at 0°C, and for water vapour the enthalpy of saturated water is taken as zero at 0°C. The enthalpy of moist air is given by:

h = Ha + W.Hg =Cp.t +W(Hfg + Cpw.t)

where Cp = specific heat of dry air at constant pressure, kJ/kg.K

Cpw = specific heat of water vapor, kJ/kg.K

t = Dry-bulb temperature of air-vapor mixture, °C

W = Humidity ratio, kg of water vapor/kg of dry air

Ha = enthalpy of dry air at temperature t, kJ/kg

Hg = enthalpy of water vapor3 at temperature t, kJ/kg

Hfg = latent heat of vaporization at 0°C, kJ/kg

The unit of H is kJ/kg of dry air. Substituting the approximate values of Cp and Hg, we obtain:

H =1.005 t +W (2501 + 1.88t)

Humid specific heat: From the equation for enthalpy of moist air, the humid specific heat of moist air can be written as:

Cpm = Cp + W.Cpw

where cpm = humid specific heat, kJ/kg.K

cp = specific heat of dry air, kJ/kg.K

cpw = specific heat of water vapor, kJ/kg

W = humidity ratio, kg of water vapor/kg of dry air

Since the second term in the above equation (w.cpw) is very small compared to the first term, for all practical purposes, the humid specific heat of moist air, Cpm can be taken as 1.0216 kJ/kg dry air.K

Specific volume: The specific volume is defined as the number of cubic meters of moist air per kilogram of dry air. From perfect gas equation since the volumes occupied by the individual substances are the same, the specific volume is also equal to the number of cubic meters of dry air per kilogram of dry air, i.e.,

NOTES:

1. Properties such as humidity ratio, enthalpy and specific volume are based on 1 kg of dry air. This is useful as the total mass of moist air in a process varies by the addition/removal of water vapour, but the mass of dry air remains constant.
2. Dry air is assumed to be a perfect gas as its temperature is high relative to its saturation temperature, and water vapour is assumed to be a perfect gas because its pressure is low relative to its saturation pressure. These assumptions result in accuracies, that are, sufficient only for engineering calculations.