ENGINEERING THERMODYNAMICS

-II
Debre Markos University
Institute of Technology
School of Mechanical and Industrial Engineering

primed by:
Lijalem A.

2. Gas-steam mixtures and air conditioning

1
process
Objectives
 Differentiate between dry air and atmospheric air.
 Define and calculate the specific and relative humidity of
atmospheric air.
 Calculate the dew-point temperature of atmospheric air.
 Relate the adiabatic saturation temperature and wet-bulb
temperatures of atmospheric air.
 Use the psychrometric chart as a tool to determine the
properties of atmospheric air.
 Apply the principles of the conservation of mass and energy to
various air-conditioning processes.

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 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 vapor.
• Atmospheric air is a mixture of many gases plus water vapor and
a number of pollutants (Fig. below). The amount of water vapor
and pollutants vary from place to place.
• The concentration of water vapor 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 vapor. This
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mixture is known as moist air.
 4
Fig. Atmospheric air
 Introduction
• 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. The composition of dry air is
given table below.

• 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.

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 Introduction
• As mentioned before the air to be processed in air conditioning
systems is a mixture of dry air and water vapor.
• While the composition of dry air is constant, the amount of
water vapor present in the air may vary from zero to a
maximum depending upon the temperature and pressure of the
mixture (dry air + water vapor).
• 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 vapor
is taken as 18.015 and its gas constant is 461.52 J/kg.K.
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DRY AND ATMOSPHERIC AIR
Atmospheric air: Air in the atmosphere containing
some water vapor (or moisture).
Dry air: Air that contains no water vapor.
Water vapor in the air plays a major role in human
comfort. Therefore, it is an important consideration
in air-conditioning applications.

Water vapor in air behaves as if it existed alone The cp of air can be

and obeys the ideal-gas relation Pv = RT. Then the assumed to be constant
atmospheric air can be treated as an ideal-gas at 1.005 kJ/kg·°C in the
mixture: temperature range 10
to 50°C with an error
under 0.2%.
Pa Partial pressure of dry air
Pv Partial pressure of vapor (vapor pressure)
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 Dry and Atmospheric Air
 The assumption that the water vapor is an ideal gas is valid when the mixture
temperature is below 50oC.
 This means that the saturation pressure of the water vapor in the air-vapor mixture
is below 12.3 kPa.
 For these conditions, the enthalpy of the water vapor is approximated by
hv(T) = hg at mixture temperature T.
The following T-s diagram for water illustrates the ideal-gas behavior at low vapor
pressures.
 The saturated vapor value of the enthalpy
is a function of temperature and can be
expressed as

Note: Average Cp value in range of -10 to 50oC is 1.82 KJ/kg-K and The enthalpy of
vapor at 0oc is 2501.3KJ/kg. 8
 Dry and Atmospheric Air

• Note: For the dry air-water vapor mixture, the partial pressure
of the water vapor in the mixture is less that its saturation
pressure at the temperature.
Pv  Psat @Tmix

• Then the atmospheric air can be treated as an ideal-gas mixture

whose pressure is the sum of the partial pressure of dry air Pa
and that of water vapor Pv:
p = pa + pv

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 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 vapor pressure (psat) is the saturated partial pressure of
water vapor at the dry bulb temperature. This is readily available in
thermodynamic tables and charts.
• ASHRAE suggests the following regression equation for saturated
vapor pressure of water, which is valid for 0 to 100oC

• where psat = saturated vapor pressure of water in kilopascals

• T = temperature in K
• The regression coefficients c1 to c6 are given by:
• c1 = -5.80022006E+03, c2 = -5.516256E+00, c3 = -4.8640239E-02
• c4 = 4.1764768E-05, c5 = -1.4452093E-08, c6 = 6.5459673E+00
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 Specific and Relative Humidity of Air
 The amount of water vapor in the air can be specified in various
ways.
 Probably the most logical way is to specify directly the mass of
water vapor present in a unit mass of dry air.
This is called absolute or specific humidity (also called humidity
ratio) and is denoted by ω:

Mass of water vapor in air mv

 
Mass of dry air ma
PVM v / ( Ru T ) Pv M v
 v

PaVM a / ( Ru T ) Pa M a
P Pv
(kg water vapor/kg dry air)
 0.622 v  0.622
Pa P  Pv
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 Specific and Relative Humidity of Air
 Consider 1 kg of dry air. By definition, dry air contains no water
vapor, and thus its specific humidity is zero.
 Now let us add some water vapor to this dry air. The specific
humidity will increase. As more vapor or moisture is added, the
specific humidity will keep increasing until the air can hold no
more moisture.
 At this point, the air is said to be saturated with moisture,
and it is called saturated air.
 Any moisture introduced into saturated air will condense.
 The amount of water vapor in saturated air at a specified
temperature and pressure can be determined from above equation
by replacing Pv by Pg, the saturation pressure of water at that
temperature

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 Specific and Relative Humidity of Air
 The amount of moisture in the air has a definite effect on how
comfortable we feel in an environment.
 However, the comfort level depends more on the amount of moisture
the air holds (mv) relative to the maximum amount of moisture the
air can hold at the same temperature (mg).
The ratio of these two quantities is called the relative humidity (ϕ)
Mass of vapor in air mv
 
Mass of in saturated air mg
Pv

Pg where: pg = psat @T

Pv 1491
. kPa
Pg  Pv ,   1 or 100%,     0.47 13
Pg 3169
. kPa
 Using the definition of the specific humidity, the relative humidity may be expressed
as

P 0.622Pg
 and  
(0.622   ) Pg P  Pg

Volume of mixture per mass of dry air, v

V mm RmTm / Pm
v 
ma ma

After several steps, we can show (you should try this)

V RT
v  va  a m
ma Pa 14
 Specific and Relative Humidity of Air
So the volume of the mixture per unit mass of dry air is the specific volume of
the dry air calculated at the mixture temperature and the partial pressure of
the dry air.
mv
Mass of mixture: m  ma  mv  ma (1  )  ma (1   )
ma
Mass flow rate of dry air (m’a):

Based on the volume flow rate of mixture at a given state, the

mass flow rate of dry air is
V3
m /s kga
m a  3

v m / kga s
Enthalpy of mixture per mass dry air, h
Hm Ha  Hv ma ha  mv hv
h  
ma ma ma
 ha  hv 15
 Dew-Point Temperature
 Dry Bulb Temperature Tdb: the temperature measured by a thermometer
placed in a mixture of air and water-vapor.
Dew Point Temperature Tdp:
• Dew on the grass in morning !!! Water vapors on your car windscreen!!!
• is the temperature at which condensation begins when the air is cooled at
constant pressure.
• Tdp is the saturation temperature of water corresponding to the vapor
pressure:
Tdp = Tsat@Pv

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EXAMPLE 2.1:
A 5m X 5m X 3m room shown in Fig. below contains air at 25°C and 100kPa
at a relative humidity of 75 percent. Determine
(a) the partial pressure of dry air,
(b) the specific humidity,
(c) the enthalpy per unit mass of the dry air, and
(d ) the masses of the dry air and water vapor in the room.

Assignment: 1
Atmospheric air is at 25oC, 0.1MPa, 50 percent relative humidity. If the
mixture is cooled at constant pressure to 10oC, find ,
a) dew point temperature,
b) humidity ratio,
c) Enthalpy of the mixture per mass of dry air, and
d) the amount of water removed per mass of dry air.

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 The Adiabatic Saturation Process and Wet-Bulb Temperatures
 Air having a relative humidity less than 100 percent flows over water contained in
a well-insulated duct.
Since the air has ϕ < 100 percent, some of the water will evaporate and the
temperature of the air-vapor mixture will decrease.

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If the mixture leaving the duct is saturated and if the process is
adiabatic, the temperature of the mixture on leaving the device is
known as the adiabatic saturation temperature.
For this to be a steady-flow process, makeup water at the adiabatic
saturation temperature is added at the same rate at which water is
evaporated.
We assume that the total pressure is constant during the process.
Apply the conservation of energy to the steady-flow control volume
2 2
V V
Q net   m i (h   gz) i  Wnet   m e (h   gz) e
inlets 2 exits 2
Neglecting the kinetic and potential energies and noting that the heat transfer and work are
zero, we get
m a1ha1  m v1hv1  m l 2 hl 2  m a 2 ha 2  m v 2 hv 2
Conservation of mass for the steady-flow control volume is

 m   m
inlets
i
exits
e

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 For the dry air: m a1  m a 2  m a
For the water vapor:
m v1  m l 2  m v 2
The mass flow rate water that must be supplied to maintain steady-flow is,

 l2  m
m  v2  m v1
m a ( 2   1 )
Divide the conservation of energy equation by m a , then

ha1   1hv1  ( 2   1 )hl 2  ha 2   2 hv 2

What are the known's and unknowns in this equation?

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Solving for 1 ha 2  ha1   2 (hv 2  hl 2 )
1 
(hv1  hl 2 )
C pa (T2  T1 )   2 h fg 2

(hg1  h f 2 )

Pv1
Since 1 is also defined by  1  0.622
P1  Pv1

 1 P1
We can solve for Pv1. Pv1 
0.622   1

Pv1
Then, the relative humidity at state 1 is  1 
Pg1
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Wet-Bulb and Dry-Bulb Temperatures
Any temperature you measure with thermometer is dry bulb temperature.
The wet-bulb temperature is the temperature a parcel of air would have if
it were cooled to saturation by the evaporation of water into it, with the latent
heat being supplied by the parcel.
These temperatures are measured by using a device called a
psychrometer. The psychrometer is composed of two thermometers
mounted on a sling. One thermometer is fitted with a wet gauze and reads
the wet-bulb temperature. The other thermometer reads the dry-bulb, or
ordinary, temperature. As the psychrometer is slung through the air, water
vaporizes from the wet gauze, resulting in a lower temperature to be
registered by the thermometer.
 The wet-bulb temperature is approximately equal to the adiabatic
saturation temperature.

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Example 2.2
For the adiabatic saturation process shown below, determine the relative
humidity, humidity ratio (specific humidity), and enthalpy of the
atmospheric air per mass of dry air at state 1.

Assignment:2 Given the inlet and exit conditions to an air conditioner shown below. What
is the heat transfer to be removed per kg dry air flowing through the device? If the volume
flow rate of the inlet atmospheric air is 17 m3/min, determine the required rate of heat
transfer. Cooling fluid
In Out Insulated flow duct
Atmospheric
air
T1 = 30oC T2 = 20oC

P1 =100 kPa Condensate P2 = 98 kPa

ϕ 1 = 80% at 20oC ϕ2 = 95% 23
v 1= 17m3/min
 The Psychrometric Chart
The state of the atmospheric air at a specified pressure is completely specified by
two independent intensive properties.
Psychrometric charts present the moist air properties; they are used extensively in
air-conditioning applications.
For a given, fixed, total air-vapor pressure, the properties of the mixture are given
in graphical form on a psychrometric chart.

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Basic features of psychrometric chart are:
 The dry bulb temperatures are shown on the horizontal axis.
 The specific humidity ω is shown on the vertical axis.
 The curved line at the left end of the chart is the saturation line. All the saturated air
states are located on this curve. Thus, it also represents the curve of relative
humidity 100%. Other constant relative humidity curves have the same general
shape.
 Lines of constant wet-bulb temperature have a downhill appearance to the right.
 Lines of specific volume also have downhill appearance to the right with steeper
slopes.
 Lines of constant enthalpy lie very near to the constant wet-bulb temperature, thus
(in some charts) lines of constant wet-bulbs are used as constant-enthalpies.
 For saturated air, the dry-bulb, wet-bulb, and dew-point temperatures are identical.
 Thus the dew-point temperature of atmospheric air can be determined by drawing a
horizontal line to the saturated curve .
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Reprinted by permission of the Society of Heating and Air-Conditioning Engineers, Inc., Atlanta, Ga; used with permission.
Example 2.3
Consider air at 1 atm, 35°C and 40% relative humidity. Using
psychrometric chart, determine a) the specific humidity, b) the
enthalpy, c) the wet-bulb temperature, d) the dew-point
temperature and e) the specific volume of the air.

Assignment :3
The air in a room has a pressure of 1atm, a dry-bulb temperature
of 24°C, and a wet-bulb temperature of 17°C. Using the
psychrometric chart, determine (a) the specific humidity, (b)
the enthalpy (in kJ/kg dry air), (c) the relative humidity, (d )
the dew-point temperature, and (e) the specific volume of the
air (in m3/kg dry air).
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 Human Comfort and Air-Conditioning
 Depending on the type of activity, part of the rejected body heat is
dissipated through latent heat (sweating and breathing).
 The comfort of human body depends on three factors:
 Temperature: most important index of comfort, most people feel
comfortable when temperature is between 22 and 27°C.
 Relative humidity: it affects the amount of heat that body can
dissipate through evaporation. Relative humidity is a measure of
air’s ability to absorb moisture. Most people prefer relative
humidity of 40 to 60%.
 Air motion: it removes the warm, moist air that builds up around
body and replaces it with fresh air. Most people feel comfortable
at an airspeed of 15 m/min (0.25m/s).

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 Air-Conditioning processes
HVAC Processes:
Maintaining a living space or an industrial facility at the desired
temperature and humidity requires some processes called air
conditioning; including:
a) Simple heating: raising the air temperature.
b) Simple cooling: lowering the air temperature.
c) Humidifying: adding moisture.
d) Dehumidifying: removing moisture.
In many applications, a combination of these processes is needed to
bring the air to a desired condition.

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 Air-Conditioning processes

The air-conditioning processes:

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 Air-Conditioning processes
1) Simple Heating and Cooling (ω = Constant)
The amount of moisture in the air remains constant during this process
since no moisture is added or removed to or from the air.
Notice:
 the relative humidity of air decreases during a heating process and
increases in a cooling process.
 This is because the relative humidity is the ratio of the moisture
capacity of the air and it increases with increasing the air
temperature.

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 Air-Conditioning processes
The conservation of mass reduces to:
ma1 = ma2 = ma
ω1 = ω2
Neglecting any fan work, the conservation of energy yields:
Q’ = m’ (h2 – h1) or q = (h2 – h1)
Where: h1 and h2 are enthalpies per unit mass of dry air at the inlet and exit
of the heating/cooling section, respectively.

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 Air-Conditioning processes
2. Heating with Humidification
• To maintain comfortable relative humidity, simple heating is
typically accompanied with humidification, Fig. below. That is
accomplished by passing the air through a humidifying section.
• If steam is used in the humidifier, we will have additional heating;
thus T3 > T2.
• If water is sprayed in the humidifier section, part of the latent heat
of vaporization comes from the air which results in the cooling of
the air; thus T3 < T2.

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Fig.: Heating with humidification, using water spray or steam.

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 Air-Conditioning processes
3. Cooling with Dehumidification
 To remove some moisture from the air, it should be cooled below its dew-point
temperature.
 Passing through cooling coil, air temperature decreases and its relative humidity
increases at constant specific humidity until air temperature reaches its dew point
temperature.
 Any further cooling results in condensation of part of the moisture in the air.
 Note that air remains saturated during the entire condensation process.

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 Air-Conditioning processes
4. Evaporative Cooling
 Evaporative cooling is based on a simple principle: as water evaporates, the
latent heat of vaporization is absorbed from the water body and the surrounding
air.
 As a result, both water and air are cooled.
 The evaporative cooling is essentially identical to the adiabatic saturation
process. Thus the evaporative cooling process follows a line of constant wet-
bulb temperature on the psychrometric chart.

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 Air-Conditioning processes
5. Adiabatic Mixing of Air streams
 Mixing processes normally involve no work interactions.
 Then the mass and energy balances for the adiabatic mixing of two
airstreams reduce to:

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Fig: Adiabatic mixing of two streams
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Example 2.4
An air-conditioning system is to take in outdoor air at 10°C and 30
percent relative humidity at a steady rate of 45 m3/min and to
condition it to 25°C and 60 percent relative humidity. The outdoor
air is first heated to 22°C in the heating section and then humidified
by the injection of hot steam in the humidifying section. Assuming
the entire process takes place at a pressure of 100 kPa, determine
(a) the rate of heat supply in the heating section and (b) the mass
flow rate of the steam required in the humidifying section.
Example 2.5
Saturated air at 14°C at a rate of 50 m3/min is mixed adiabatically with
the outside air at 32°C and 60% relative humidity at a rate of 20
m3/min. Assuming that the mixing occurs at 1atm, determine: a) The
specific humidity, b) The relative humidity, c) The dry-bulb, and d)
The wet-bulb of the mixture.
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Assignment:4
For the air-conditioning system shown below in which atmospheric air is first
heated and then humidified with a steam spray, determine the required heat
transfer rate in the heating section and the required steam temperature in the
humidification section when the steam pressure is 1MPa.

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