Introduction

 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 analyze various
processes involving air is fundamental to air conditioning design.
 Psychrometry is the study of the properties of mixtures of air and
water vapour.
 Atmospheric air is a mixture of many gases (N2,O2,Ar,H2, etc) plus
water vapour and a number of pollutants (dust particles, fumes, etc.).
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.
 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.
 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.
 For calculation purposes, the molecular weight of water vapour
is taken as 18.015 and its gas constant is 461.52 J/kg-K.
 Estimation of Properties of Moist Air
 In order to perform air conditioning calculations, it is essential first
to estimate various properties of air. It is difficult to estimate the
exact property values of moist air as it is a mixture of several
permanent gases and water vapour. However, moist air upto 3 atm,
pressure is found to obey perfect gas law with accuracy sufficient
for engineering calculations.
 For higher accuracy Goff and Gratch tables can be used for
estimating moist air properties. These tables are obtained using
mixture models based on fundamental principles of statistical
mechanics that take into account the real gas behavior of dry air and
water vapour.
 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. According to this law, for a
homogeneous perfect gas mixture occupying a volume V and at
temperature T, each constituent gas behaves as though the other gases
are not present (i.e., there is no interaction between the gases). Each
gas obeys perfect gas equation. Hence, the partial pressures exerted
by each gas, p1,p2,p3 … and the total pressure pt are given by:

 Applying this equation to moist air.

where, p = pt = total barometric pressure, pa = partial pressure of dry
air, pv = partial pressure of water vapour
 Important 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. This is readily
available in thermodynamic tables and charts.
 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.

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 kg of dry air. Assuming both
water vapour and dry air to be perfect gases, the humidity ratio is
given by:

 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
oC. 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,
 Enthalpy: The enthalpy of moist air is the sum of the enthalpy of the
dry air and the enthalpy of the water vapour.
 The enthalpy of moist air is given by:
 Humid specific heat: From the equation for enthalpy of moist air, the
humid specific heat of moist air can be written as:

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 kg 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 kg of dry
air, i.e.,
 Wet Bulb Temperature (WBT)
A psychrometer is used for measuring humidity. A
psychrometer comprises of a dry bulb thermometer and a wet
bulb thermometer.
 The dry bulb thermometer is directly exposed to air and
measures the actual temperature of air.
 The bulb of the wet bulb thermometer is covered by a wick
thoroughly wetted by water. The temperature which is
measured by the wick covered bulb of such a thermometer
indicates the temperature of liquid-water in the wick and is
called the wet bulb temperature (t’).
 Psychrometric Chart
A Psychrometric chart graphically represents the
thermodynamic properties of moist air.
 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.

15
 Psychrometric Chart
 Psychrometric charts are readily available for standard
barometric pressure of 101.325 kPa at sea level and for
normal temperatures (0-50oC).
 ASHRAE has also developed psychrometric charts for
other temperatures and barometric pressures (for low
temperatures: -40 to 10oC, high temperatures 10 to
120oC and very high temperatures 100 to 120oC)

16
17
 Measurement of psychrometric properties
• Based on Gibbs’ phase rule, the thermodynamic state of moist air is
uniquely fixed if the barometric pressure and two other independent
properties are known.
• This means that at a given barometric pressure, the state of moist air
can be determined by measuring any two independent properties.
• One of them could be the dry-bulb temperature (DBT), as the
measurement of this temperature is fairly simple and accurate. The
accurate measurement of other independent parameters such as humidity
ratio is very difficult in practice.
• Since measurement of temperatures is easier, it would be convenient
if the other independent parameter is also a temperature. Of course,
this could be the dew-point temperature (DPT), but it is observed that
accurate measurement of dew-point temperature is difficult.
• In this context, a new independent temperature parameter called the
wet-bulb temperature (WBT) is defined. Compared to DPT, it is easier
to measure the wet-bulb temperature of moist air. Thus, knowing the dry-
bulb and wet-bulb temperatures from measurements, it is possible to find
the other properties of moist air.
• To understand the concept of wet-bulb temperature, it is essential to
understand the process of combined heat and mass transfer.
Combined heat and mass transfer: the straight line law
The straight line law states that “when air is transferring heat and mass
(water) to or from a wetted surface, the condition of air shown on a
psychrometric chart drives towards the saturation line at the temperature
of the wetted surface”.
For example, as shown in Fig.27.3, when warm air passes over a wetted
surface its temperature drops from 1 to 2. Also, since the vapor pressure of air
at 1 is greater than the saturated vapor pressure at tw, there will be moisture
transfer from air to water, i.e., the warm air in contact with cold wetted surface
cools and dehumidifies. According to the straight-line law, the final condition of
air (i.e., 2) lies on a straight line joining 1 with tw on the saturation line. This is
due to the value of unity of the Lewis number, that was discussed in an earlier chapter
on analogy between heat and mass transfer.
Adiabatic saturation and thermodynamic wet bulb temperature
• Adiabatic saturation temperature is defined as that temperature at which
water, by evaporating into air, can bring the air to saturation at the same
temperature adiabatically. An adiabatic saturator is a device using which one
can measure theoretically the adiabatic saturation temperature of air.
• As shown in Fig.27.4, an adiabatic saturator is a device in which air flows
through an infinitely long duct containing water.
• As the air comes in contact with water in the duct, there will
be heat and mass transfer between water and air. If the duct
is infinitely long, then at the exit, there would exist perfect
equilibrium between air and water at steady state.
• Air at the exit would be fully saturated and its temperature is
equal to that of water temperature. The device is adiabatic
as the walls of the chamber are thermally insulated.
• In order to continue the process, make-up water has to be
provided to compensate for the amount of water evaporated
into the air. The temperature of the make-up water is
controlled so that it is the same as that in the duct.
• After the adiabatic saturator has achieved a steady-state
condition, the temperature indicated by the thermometer
immersed in the water is the thermodynamic wet-bulb
temperature. The thermodynamic wet bulb temperature
will be less than the entering air DBT but greater than
the dew point temperature.
Certain combinations of air conditions will result in a given sump temperature, and this
can be defined by writing the energy balance equation for the adiabatic saturator.
Based on a unit mass flow rate of dry air, this is given by:

where hf is the enthalpy of saturated liquid at the sump or thermodynamic wet-bulb

temperature, h1 and h2 are the enthalpies of air at the inlet and exit of the adiabatic
saturator, and W1 and W2 are the humidity ratio of air at the inlet and exit of the
adiabatic saturator, respectively.
It is to be observed that the thermodynamic wet-bulb temperature is a thermodynamic
property, and is independent of the path taken by air. Assuming the humid specific heat
to be constant, from the enthalpy balance, the thermodynamic wet-bulb temperature
can be written as:

where hfg,2 is the latent heat of vaporization at the saturated condition 2. Thus
measuring the dry bulb (t1) and wet bulb temperature (t2) one can find the inlet
humidity ratio (W1) from the above expression as the outlet saturated humidity ratio
(W2) and latent heat of vaporizations are functions of t2 alone (at fixed barometric
pressure).
On the psychrometric chart as shown in Fig.27.4, point 1 lies below the line of
constant enthalpy that passes through the saturation point 2. t2 = f(t1,W1) is not a
unique function, in the sense that there can be several combinations of t1 and W1
which can result in the same sump temperature in the adiabatic saturator. A line
passing through all these points is a constant wet bulb temperature line. Thus all inlet
conditions that result in the same sump temperature, for example point 1’ have the
same wet bulb temperature. The line is a straight line according to the straight-line
law. The straight-line joining 1 and 2 represents the path of the air as it passes
through the adiabatic saturator.
Normally lines of constant wet bulb temperature are shown on the psychrometric
chart. The difference between actual enthalpy and the enthalpy obtained by following
constant wet-bulb temperature is equal to (w2-w1)hf.
 Wet-Bulb Thermometer
In practice, it is not convenient to measure the wet-bulb temperature using an
adiabatic saturator. Instead, a thermometer with a wetted wick is used to measure the
wet bulb temperature as shown in Fig.27.6. It can be observed that since the area of
the wet bulb is finite, the state of air at the exit of the wet bulb will not be saturated, in
stead it will be point 2 on the straight line joining 1 and i, provided the temperature of
water on the wet bulb is i. It has been shown by Carrier, that this is a valid
assumption for air-water mixtures. Hence for air-water mixtures, one can assume that
the temperature measured by the wet-bulb thermometer is equal to the
thermodynamic wet-bulb temperature4. For other gas-vapor mixtures, there can be
appreciable difference between the thermodynamic and actual wet-bulb
temperatures.
Calculation of Psychrometric Properties from
p, DBT and WBT
 To fix the thermodynamic state of moist air, we need to
know three independent properties. The properties that
are relatively easier to measure, are: the barometric
pressure, dry-bulb temperature and wet-bulb
temperature.
 For a given barometric pressure, knowing the dry bulb
and wet bulb temperatures, all other properties can be
easily calculated from the psychrometric equations. The
empirical relations for the vapor pressure of water in
moist air are given here.
27
➢ Once the vapor pressure is calculated, then all other
properties such as relative humidity, humidity ratio,
enthalpy, humid volume etc. can be calculated from the
psychrometric equations.
28
5. On a particular day the weather forecast states that the dry bulb temperature is
37oC, while the relative humidity is 50% and the barometric pressure is 101.325 kPa.
Find the humidity ratio, dew point temperature and enthalpy of moist air on this day.
7. Moist air at 1 atm. pressure has a dry bulb temperature of 32oC and a wet bulb
temperature of 26oC. Calculate a) the partial pressure of water vapour, b) humidity
ratio, c) relative humidity, d) dew point temperature, e) density of dry air in the
mixture, f) density of water vapour in the mixture and g) enthalpy of moist air using
perfect gas law model and psychrometric equations.

Note: Saturation pressure of water vapor at 26 C= 3.36 Pa

The saturation pressure of water temperature at 32oC = 4.7552 kPa

Tsat corresponding to 4.7552 kPa= 23.8

Ra=287.035 J/kgK
For water vapour, Ra= 461.52 J/kgK
 Psychrometric processes
• In the design and analysis of air conditioning plants,
the fundamental requirement is to identify the various
processes being performed on air.
• Once identified, the processes can be analyzed by
applying the laws of conservation of mass and energy.
• All these processes can be plotted easily on a
psychrometric chart.
• This is very useful for quick visualization and also for
identifying the changes taking place in important
properties such as temperature, humidity ratio,
enthalpy, etc.
• The important processes that air undergoes in a typical air
conditioning plant are
 Psychometric Processes
 Sensible heating
 Sensible cooling
 Humidifying
 Dehumidifying
 Heating and humidifying
 Cooling and dehumidifying
 Heating and dehumidifying
 Cooling and humidifying

35
 Sensible cooling
 During this process, the moisture content of air remains constant,
but its temperature decreases as it flows over a cooling coil.
 For moisture content to remain constant, the surface of the
cooling coil should be dry, and its surface temperature should be
greater than the dew point temperature of air.
 If the cooling coil is 100% effective, then the exit temperature of air
will be equal to the coil temperature. However, in practice, the exit
air temperature will be higher than the cooling coil temperature.
 Figure shows the sensible cooling process O-A on a psychrometric
chart. The heat transfer rate during this process is given by:

where, cpm is the humid specific heat (≈1.0216 kJ/kg dry air), and ma is the
mass flow rate of dry air (kg/s).
36
37
 Sensible Heating
 During this process, the moisture content of air remains
constant, and its temperature increases as it flows over a
heating coil. The heat transfer rate during this process is
given by:

38
39
 Cooling and Dehumidification
 When moist air is cooled below its dew-point by bringing
it in contact with a cold surface, some of the water vapor
in the air condenses and leaves the air stream as liquid,
as a result both the temperature and humidity ratio of air
decreases as shown.
 This is the process, air undergoes in a typical air
conditioning system. Although the actual process path
will vary depending upon the type of cold surface, the
surface temperature, and flow conditions, for simplicity
the process line is assumed to be a straight line.
40
41
42
➢ Thus we can see that the slope of the cooling and de-
humidification line is purely a function of the sensible
heat factor, SHF.

43
 In Fig., the temperature Ts is the effective surface temperature of the
cooling coil, and is known as apparatus dew-point (ADP)
temperature. In an ideal situation, when all the air comes in perfect
contact with the cooling coil surface, then the exit temperature of air
will be same as ADP of the coil. However, in actual case the exit
temperature of air will always be greater than the apparatus dew-
point temperature due to boundary layer development as air flows
over the cooling coil surface and also due to temperature variation
along the fins etc. Hence, we can define a by-pass factor (BPF) as:

 It can be easily seen that, higher the by-pass factor, larger will be the
difference between air outlet temperature and the cooling coil
temperature. When BPF is 1.0, all the air by-passes the coil and there
will not be any cooling or de-humidification.
 A contact factor(CF) can be defined which is given by:

45
 Cooling and Humidification
 As the name implies, during this process, the air temperature drops
and its humidity increases.
 As shown in the figure, this can be achieved by spraying cool water
in the air stream.
 The temperature of water should be lower than the dry-bulb
temperature of air but higher than its dew-point temperature to avoid
condensation (TDPT < Tw < TO).
 It can be seen that during this process there is sensible heat transfer
from air to water and latent heat transfer from water to air. Hence, the
total heat transfer depends upon the water temperature.
 Adiabatic saturation process is the special case of cooling and
humidification. 46
47
 Heating and Humidification
 During winter it is essential to heat and humidify the room air for
comfort. As shown in Fig., this is normally done by first sensibly
heating the air and then adding water vapour to the air stream
through steam nozzles as shown in the figure.
 Mass balance of water vapor for the control volume yields the rate
at which steam has to be added, i.e., mw:

 From energy balance:

where Qh is the heat supplied through the heating coil and hw is the
enthalpy of steam.
Since this process also involves simultaneous heat and mass
transfer, we can define a sensible heat factor for the process in a
way similar to that of a cooling and dehumidification process.
48
49
Heating and De-humidification
 This process can be achieved by using a hygroscopic
material, which absorbs or adsorbs the water vapor from
the moisture. This hygroscopic material can be a solid or
a liquid.
 In general, the absorption of water by the hygroscopic
material is an exothermic reaction, as a result heat is
released during this process, which is transferred to air
and the enthalpy of air increases.

50
51
 Mixing of Air Streams
 Mixing of air streams at different states is commonly
encountered in many processes, including in air
conditioning.
 Depending upon the state of the individual streams, the
mixing process can take place with or without
condensation of moisture.
 Without condensation

 With condensation

52
 Mixing without Condensation
 Figure shows an adiabatic mixing of two moist air
streams during which no condensation of moisture takes
place. As shown in the figure, when two air streams at
state points 1 and 2 mix, the resulting mixture condition 3
can be obtained from mass and energy balance.

53
 From the mass balance of dry air and water vapor

 From energy balance:

 From the above equations, it can be observed that the

final enthalpy and humidity ratio of mixture are weighted
averages of inlet enthalpies and humidity ratios.
 The point on the psychrometric chart representing the
mixture lies on a straight line connecting the two inlet
states.
 The ratio of distances on the line, i.e., (1-3)/(2-3) is equal
to the ratio of flow rates ma,2/ma,1.
54
 Mixing with Condensation
 As shown in Fig., when very cold and dry air mixes with warm
air at high relative humidity, the resulting mixture condition
may lie in the two-phase region, as a result there will be
condensation of water vapor and some amount of water will
leave the system as liquid water.
 Due to this, the humidity ratio of the resulting mixture (point 3)
will be less than that at point 4. Corresponding to this will be
an increase in temperature of air due to the release of latent
heat of condensation.
 This process rarely occurs in an air conditioning system, but
this is the phenomenon which results in the formation of fog or
frost (if the mixture temperature is below 0oC).
55
56
57
 Air Washers
 An air washer is a device for conditioning air. In an air
washer air comes in direct contact with a spray of water
and there will be an exchange of heat and mass (water
vapour) between air and water.
 The outlet condition of air depends upon the temperature
of water sprayed in the air washer. Hence, by controlling
the water temperature externally, it is possible to control
the outlet conditions of air, which then can be used for air
conditioning purposes.

58
59
 In the air washer, the
mean temperature of
water droplets in contact
with air decides the
direction of heat and
mass transfer.
 The heat transfer between
air and water droplets will
be in the direction of
decreasing temperature
gradient. Similarly, the
mass transfer will be in  OA- Cooling and dehumidification:
the direction of  OB- Adiabatic saturation
decreasing vapor  OC- Cooling and humidification
pressure gradient.  OD- Cooling and humidification
 OE- Heating and humidification
60
a) Cooling and dehumidification (tw < tDPT): Since the exit enthalpy of
air is less than its inlet value, from energy balance it can be shown that
there is a transfer of total energy from air to water. Hence to continue
the process, water has to be externally cooled. Here both latent and
sensible heat transfers are from air to water. This is shown by Process
O-A in Figure.
b) Adiabatic saturation (tw = tWBT): Here the sensible heat transfer from
air to water is exactly equal to latent heat transfer from water to air.
Hence, no external cooling or heating of water is required. That is this
is a case of pure water recirculation. This is shown by Process O-B in
Figure. This the process that takes place in a perfectly insulated
evaporative cooler.
c) Cooling and humidification (tDPT < tw < tWBT): Here the sensible heat
transfer is from air to water and latent heat transfer is from water to air,
but the total heat transfer is from air to water, hence, water has to be
cooled externally. This is shown by Process O-C in Fig.

61
 References
 NPTEL notes
 Refrigeration and Air-conditioning book by C.P. Arora.
 https://slideplayer.com/slide/4490936/