## Lesson 26. Psychrometric chart and its application

Module 7. Psychrometry

Lesson 26
PSYCHROMETRIC CHART AND ITS APPLICATION

26.1 Introduction

It is necessary to study the various psychrometric relations in order to understand the psychrometric chart.

26.2 Dalton's Law of Partial Pressure

According to Daltons Law of partial pressure the total pressure of a mixture of gases is equal to the sum of the partial pressures exerted by each gas when it occupies the mixture volume at the mixture temperature.

Fig. 26.1 Diagram Explaining the principle of Dalton's Law

Gas A, B and C are filled in three different containers at temperature T and the partial pressures exerted by these gases are Pa, Pb and Pc respectively as shown in the Fig. 26.1. The total pressure (Pt) of the mixture of the gases will be equal to the sum of Pa, Pb and Pc.
Mathematically,

Pt = Pa + Pb + Pc

If this law is applied to the moist air which contains dry air and water vapour, then
Pt = Pa + Pv
Where, Pt = Total pressure of moist air
Pa = Partial pressure of dry air

Pv = Partial pressure of water vapour of the air
Specific Humidity (ω)
As per the definition of specific humidity,
ω = Mass of water vapor in mixture / Mass of dry air in mixture = mv/ma
The mass of mixture is (ma + mv). The definition is given in terms of mass of dry air instead of total mass of mixture because the mass of mixture for a given volume of air changes with humidity.

26.3 Degree of Saturation(µ)

Where, Pvs is the partial pressure of water vapour when the air is fully saturated at the same temperature of the air. This can be calculated from steam table corresponding to the dry-bulb temperature of the air.

26.4 Relative Humidity(ø)

As per the definition of relative humidity,

Relative humidity plays very important role in comfort air conditioning and deciding the performance of many unit operations such as drying, evaporative cooling etc.

26.5 Enthalpy of Moist Air

The enthalpy of moist air is the sum of the enthalpy of one dry air and the enthalpy of water vapour associated with one kg dry air.

The value of CPW and CPV used in deriving the equation are 4.186 kJ/kg K and 1.88 kJ/kg K respectively. The value of CPa is taken as 1.005 kJ/kg K.

26.6 Psychrometric Chart

Psychrometric chart shows the inter-relation of all the important properties of air. Using the chart, it is easy to obtained psychrometric properties of air and it helps to decide the various processes to be followed to achieve required quality of air. It saves lot of time and labour required for calculation of different properties of air and such values can be directly read from the chart.

Standard psychrometric charts are bounded by the dry-bulb temperature line (abscissa) and the vapour pressure or humidity ratio (ordinate). The left hand side of the psychrometric chart is bounded by the saturation line. Fig.26.4 shows the schematic of a psychrometric chart.
Psychrometric charts are readily available for standard barometric pressure of 101.325 kPa at sea level and for normal temperatures (0-50 oC). ASHRAE has also developed psychrometric charts for other temperatures and barometric pressures.
The constructional procedure is of psychrometric chart is based on the calculations for relative humidity, enthalpy, specific humidity etc. under different conditions using various psychrometric relations.
The actual psychrometric chart is depicted in Fig. 26.2. It is necessary to know to parameters to locate the quality of air on psychrometric chart. After locating the point of quality, many other properties can be easily obtained from the chart. In majority of situations, dbt and wbt of the air are measured to find the location of the point on the psychrometric chart. If dbt and % Relative Humidity (RH) are known, then also it is possible to locate the point on the chart to read other properties of air.

Fig. 26.2 Schematic psychrometric chart

Fig. 26.3 Psychrometric chart

26.7 How to Use the Psychrometric Chart?

Suppose, when the quality of air is measured by using dry bulb thermometer and wet bulb thermometer, the values obtained are: dbt = 30 oC and wbt = 20 oC
This point is located on psychrometric chart as indicated below and the values of specific humidity, relative humidity, enthalpy and dew point temperature are as under.
Specific humidity = 10.75 g/kg dry air
Relative humidity = 40 %
Enthalpy = 57.5 kJ/kg dry air
Dew point temperature = 15 oC
Partial pressure of water vapour of the air = 12.75 mm of Hg
The above values obtained from psychrometric chart can be also calculated by using various pychrometric relations. By knowing any two of the parameters the quality of the air can be located and all other parameters found out from the Psychrometric chart in the similar manner.