2. 1
Psychrometry
The specific objectives of this lecture are to:
1. Define psychrometry and the composition of moist air
2. Discuss the methods used for estimating properties of moist air
3. Present perfect gas law model for moist air
4. Define important psychrometric properties
5. Present graphical representation of psychrometric properties on a psychrometric chart
6. Discuss measurement of psychrometric properties
7. Discuss straight-line law as applied to air-water mixtures
8. Discuss the concept of adiabatic saturation and thermodynamic wet bulb temperature
9. Describe a wet-bulb thermometer
10. Discuss the procedure for calculating psychrometric properties from measured values of barometric
pressure, dry bulb and wet bulb temperatures
11. Describe a psychrometer and the precautions to be taken while using psychrometers (Section 27.5)
At the end of the lecture, the student should be able to:
1. Define psychrometry and atmospheric air
2. Use perfect gas law model and find the total pressure of air from partial pressures of dry air and
water vapour
3. Define and estimate psychrometric properties
4. Draw the schematic of a psychrometric chart
5. Discuss the straight-line law and its usefulness in psychrometry
6. Explain the concepts of adiabatic saturation and thermodynamic wet bulb temperature
7. Differentiate between thermodynamic WBT and WBT as measured by a wet bulb thermometer
8. Estimate various psychrometric properties given any three independent properties
9. Describe a psychrometer
3. 2
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 science of study of various properties of air, method of controlling its temperature and
moisture content or humidity and its effect on various materials and human beings. Studying Psychrometry
helps understanding different constituents of air and how they affect each other, which in turn unravels various
mysteries of the atmosphere and the nature. Some of the psychrometric properties of air that we are going to
study are: dry bulb temperature, wet bulb temperature, dew point temperature, relative humidity etc.
Composition of Air
Air comprises of mixture of various gases and water vapor or moisture. The air without any water vapor is
called as dry air, thus the ordinary air is the mixture of dry air and water vapor. As such the air always contains
some amount of water vapor so the pure dry air doesn’t really exists, however its concept is very important in
understanding the properties of the air and how various changes occur in the air conditioning process. The dry
air and water vapor mixture is merely physical one as there is no chemical reaction between the two.
The dry air is composed of various gases, chiefly nitrogen (78%), and oxygen (21%). The remaining 1% of the
gases includes carbon dioxide, and very small quantities of inert gases like hydrogen, helium, neon, and argon.
The water vapor is also small part of the air included among remaining 1% of the gases.
The amount of moisture in air by its mass keeps on varying from place to place and depending on the
atmospheric conditions at a particular place. The places located close to the sea areas contain more moisture
while the desert areas contain less moisture. Similarly, during the raining seasons the moisture content of the air
is high while during summers and winters its low. The air contains usually 1% to 3% of moisture by mass.
At the normal atmospheric temperature conditions oxygen gas exists in superheated conditions as gas since its
boiling point is -182.7 C (-297F). By nature oxygen is highly active agent causing rusting and corrosion of
metals. Nitrogen too exists in superheated condition as gas in the atmosphere since its boiling point is -195 C (-
319F) . However, nitrogen is an inert gas and does not cause any chemical reactions in the atmosphere. Since
the chief constituents of the air are oxygen and nitrogen and they both exist in superheated condition, the air also
exists in the superheated conditions as the gas.
It is important to note here that small changes in the temperature of the dry air during the air conditioning
process cause very small changes in its volume and density. It is also important to note that all the heat that is
added or removed from the air during air conditioning process is the sensible heat and no latent heat is involved
since the boiling point temperatures of oxygen and nitrogen are very low.
Another important point to note is that the water vapor exists in the superheated condition, but when it is cooled
or heated there is change in its phases, hence it absorbs or liberates sensible heat as well as the latent heat due to
changes in its phases. This is what makes the whole process of air conditioning highly complicated. Cooling of
water vapor results in its condensation, whiles its heating leads to superheating.
4. 3
Gas Mixture
One of the properties of gases is that they mix with each other. When they do so, they become a solution—a
homogeneous mixture. Some of the properties of gas mixtures are easy to determine if we know the composition
of the gases in the mix.
In gas mixtures, each component in the gas phase can be treated separately. Each component of the mixture
shares the same temperature and volume. (Remember that gases expand to fill the volume of their container;
gases in a mixture do that as well.) However, each gas has its own pressure. The partial pressure of a gas, Pi, is
the pressure that an individual gas in a mixture has. Partial pressures are expressed in KPa (Absolute); however,
we use the term pressure when talking about pure gases and the term partial pressure when we are talking
about the individual gas components in a mixture.
5. 4
Principles of Gas Mixture
1. Total mass of a mixture
imm
2. Mass fraction
m
m
x i
i
3. Total moles of a mixture
inn
4. Mole fraction
n
n
y i
i
5. Equation of state
Mass Basis
For the Mixture
Fort the Components
Mole Basis
For the Mixture
Fort the Components
6. Amagat’s Law
The total volume of a mixture of gases is equal to the sum of the volume occupied by each component
at the mixture pressure P and temperature T.
mRTPV
iiiii TRmVP
TRnPV
iiii TRnVP
6. 5
P = P1 = P2 = P3
T = T1 = T2 = T3
TR
PV
n;
TR
PV
n;
TR
PV
; n
TR
PV
n
nnnn
3
3
2
2
1
1
321
V
V
n
n
y
VV
VVVV
P
TR
TR
PV
TR
PV
TR
PV
TR
PV
TR
PV
TR
PV
TR
PV
TR
PV
ii
i
i
321
321
321
7. Dalton’s Law
The total pressure of a mixture of gases P is equal to the sum of the partial pressure that each gas would
exert at the mixture volume V and temperature T.
TR
VP
n;
TR
VP
n;
TR
VP
; n
TR
PV
n
nnnn
TTTT
VVVV
3
3
2
2
1
1
321
321
321
P
P
n
n
y
PP
PPPP
V
TR
TR
VP
TR
VP
TR
VP
TR
PV
TR
VP
TR
VP
TR
VP
TR
PV
ii
i
i
321
321
321
8. Molecular Weight Of A Mixture (M)
K-kg
KJ
R
3143.8
R
R
M
MyM ii
7. 6
9. Gas Constant (R)
K-kg
KJ
M
3143.8
M
R
R
RxR ii
10. Specific Heat Of A Mixture
At Constant Volume
viiv CxC
At Constant Pressure
RCC
CxC
vp
PiiP
11. Ratio Of Specific Heat
1k
R
C
1k
Rk
C
C
C
k
V
P
V
P
12. Gravimetric And Volumetric Analysis
Gravimetric analysis gives the mass fractions of the components in the mixture.
Volumetric analysis gives the volumetric or molal fractions of the components in the mixture.
CONVERSION
i
i
i
i
ii
ii
ii
i
M
x
M
x
yi
M
My
My
My
x
Where
m – mass in kg
n – number of moles, kgm
x – masss fraction
y – mole fraction
P – absolute pressure in KPa
V – volume in m3
R – Gas constant in KJ/kg-K
R - universal gas constant in KJ/kgm-K
T – absolute temperature in K
M – molecular weight in kg/kgm
Cp – specific heat at constant pressure in KJ/kg-C or KJ/kg-K
Cv – specific heat at constant volume KJ/kg-C or KJ/kg-K
Subscript
i – refers to the components
8. 7
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.
Composition of Dry Air
Constituents Molecular Weight Volumetric Fraction
Oxygen (O2) 32 0.2095
Nitrogen (N2) 28 0.7809
Argon (Ar) 39.944 0.0093
Carbon Dioxide (CO2) 44 0.0003
Based on the above composition the molecular weight of dry air is found to be 29.00 and the gas constant R is
0.287 KJ/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 vapor is taken as 18.0 and its gas constant is
0.462 KJ/kg - K.
FUNDAMENTAL PARAMETERS
Total Pressure(P): The total pressure of moist air is equal to the sum of the partial pressure of dry air and
water vapor.
KPaPPP va
9. 8
Vapor Pressure (Pv): The vapor pressure (Pv) is the partial of water vapor n the mixture (Moist air).
Cre,temperatubulbwet-tw
Cre,temperatubulbdry-td
C0For tw10x5.94A
C0For tw10x6.66A
Where
KPatt)A(PPP
4-
4-
wdwv
Saturation pressure at wet bulb temperature (Pw): Pw is the saturation pressure corresponding the wet bulb
temperature of the mixture, and can be determined from steam table.
Dry Bulb temperature (td): The dry-bulb temperature is the temperature of air measured by a thermometer
freely exposed to the air, but shielded from radiation and moisture. It is the temperature that is usually
thought of as air temperature, and it is the true thermodynamic temperature.
Wet Bulb temperature (tw): The wet-bulb temperatur is the temperature read by a thermometer covered in
water-soaked cloth (wet-bulb thermometer) over which air is passed.
Psychrometry Apparatus for measuring td and tw
Humidity Ratio (W): The humidity ratio W is the ratio of the mass of the water vapor mv to the mass of the
dry air ma in the mixture.
10. 9
v
a
v
a
v
av
va
a
a
v
v
a
a
a
v
v
v
a
v
PP
Pv622.0
W
P
P622.0
P462.0
P287.0
PR
PR
TR
VP
TR
VP
W
TR
VP
m
TR
VP
m
LawsAmagat'From
m
m
W
Relative Humidity (): The relative humidity is the ratio of the mole fraction of the water vapor yv in a
mixture to the mole fraction yd of the water vapor in a saturated mixture at the same temperature and
pressure:
100%x
P
P
P
P
P
P
y
y
d
v
d
v
d
v
Where:
Pd – saturation pressure corresponding the dry bulb temperature from steam table
Enthalpy (h): The enthalpy of a mixture of ideal gases is equal to the sum of the enthalpies of each
component:
kgda
KJ
)t(86.13.2501W)t(0045.1h
)t(86.13.2501h
)td(0045.1ha
Whhh
dd
dv
va
Specific Volume (): Specific volume is the ratio of the volume of dry air in the mixture.
kgda
m
PP
273t287.0 3
v
d
11. 10
Degree of Saturation (): 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,
d
v
s PP
PP
W
W
The Psychrometric Chart
A psychrometric chart is a graphical representation of the psychrometric processes of air. Psychrometric
processes include physical and thermodynamic properties such as dry bulb temperature, wet bulb temperature,
humidity, enthalpy, and air density. A psychrometric chart can be used in two different ways.
A psychrometric chart can be used in two different ways. The first is done by plotting multiple data points, that
represent the air conditions at a specific time, on the chart. Then, overlaying an area that identifies the ―comfort
zone.‖ The comfort zone is defined as the range within occupants are satisfied with the surrounding thermal
conditions. After plotting the air conditions and overlaying the comfort zone, it becomes possible to see how
passive design strategies can extend the comfort zone.
12. 11
C-kg
KJ
1.02Cp
nscalculationgconditioniairFor
C-kg
KJ
W86.10045.1C
sec
KJ
)tt(mCQs
p
12p
sec
kg
inairdryofrateflowmass-m
kg
KJ
2500hfg
Where
sec
KJ
h)WW(mQ fg12L
Ls
ss
QQ
Q
Q
Q
SHF
Sensible Heat and Latent Heat of Moist air
The sensible heat of moist air (Qs) is the thermal energy associated with the change of air temperature between
two state points without a change in phase. The sensible depends on its temperature T above the reference
temperature of 0C. Latent heat of moist air, often represented by (QL) is the thermal energy associated with the
change of phase of water vapor. Both of them are in KJ/kg.
Sensible Heat
Latent Heat
Sensible Heat Ratio or Sensible Heat Factor
The sensible heat ratio or sensible heat factor (SHR or SHF) of an air-conditioning process is defined as the ratio
of the change in absolute value of sensible heat to the change in absolute value of total heat, both in KJ/sec.
Example No. 1
The design indoor air temperature and relative humidity of an air conditioned space at sea level are 75°F
(23.9°C) and 50 percent. Find the humidity ratio, the enthalpy, and the density of the indoor moist air
Example No. 2
For a sample of air having 22ºC DBT, relative humidity 30 percent at barometric pressure of 760 mm of Hg,
Calculate:
a. Pv
b. W
c. H
d.
Example No. 3
Wet and dry bulb temperature measurements made outside on a cold day reveal that td = 5.0°C and tw = 4.0°C.
If P = 100 KPa, determine
a. Pv in KPa
b. W
c. H
d.
e. The RH, tw and Q if the mixture is heated at constant pressure to 25C
13. 12
21
d1d2p
12
WWW
1.86W1.0045Cp
)t-(tmCQs
)h-m(hQs
BalanceEnergyBy
Psychrometric Processes
The basic psychrometric processes involved in air conditioning to vary psychrometric properties of air
according to the requirement are as follows:
1. Sensible heating
2. Sensible cooling
3. Cooling and Dehumidifying
4. Heating and Humidifying
5. Humidifying
6. Adiabatic mixing of air streams
Sensible Heating
Sensible heating is the addition of heat tp moist air, without the addition of moisture. The process follows a
constant specific humidity line.
Let air at temperature td1 passes over a heating coil of temperature td3 , as shown in Figure. It may be noted that
the temperature of air leaving the heating coil (td2 ) will be less than td3 . The process of sensible heating, on the
psychrometric chart, is shown by a horizontal line 1-2 extending from left to right as shown in Figure. The point
3 represents the surface temperature of the heating coil. The heat absorbed by the air during sensible heating
may be obtained from the psychrometric chart by the enthalpy difference (h2 – h1) as shown in Figure. It may be
noted that the specific humidity during the sensible heating remains constant W1 = W2. The dry bulb
temperature increases from td1 to td2 and relative humidity reduces from 1 to 2.
Notes:
1. For sensible heating, steam or hot water is passed through the heating coil. The heating coil may be
electric resistance coil.
2. The sensible heating of moist air can be done to any desired temperature.
Sensible Cooling
A sensible cooling process removes heat from the moist air, resulting in a drop of its temperature; its humidity
ratio remains constant, as in the figure below. The sensible cooling process occurs when moist air flows through
a cooling coil containing chilled water at a temperature equal to or greater than the dew point of the entering
moist air. The temperature of moist air reduces from td1 to td2, with W1 = W2 which results an increased in
relative humidity.
15. 14
2dda
2as
LsH
w1212H
12w
2w1
ww12H
2wwH1
tt
5)hh(mQ
4QQQ
3h)WW(-)h-(hmQ
1equationto2Equation
2)WW(mm
mWmmW
balancemoistureBy
1hm-)h-m(hQ
mhhmQmh
balanceenergyBy
Ls
s
fg
d2fgfg
fga2L
a2L
1a
ap
1d2dps
QQ
Q
SHF
kg
KJ
2500h
table)steam(Fromat thh
8h)WW(mQ
7)hh(mQ
WW
W86.10045.1C
6ttmCQ
Heating and Humidifying Process
Heating and humidifying process is the addition of heat and moisture to moist air. This process is generally
required during the cold months of the year. It involves both sensible and latent heat transfer because water is
evaporated resulting an increase in humidity ratio. The sensible heat transfer is associated with an increase in
dry bulb temperature and the latent heat transfer is associated with an increase in specific humidity (or humidity
ratio).
Humidification
Humidification process is the addition of moisture to moist air without the addition of heat. Steam or water is
injected to moist air in order to increase its humidity ratio (or specific humidity). The direction of the process on
the psychrometric chart can therefore vary considerably, depending on the conditions of the injected water.
16. 15
lineretemperatubulbetconstant wthefollowsandat thghwc21
at thghwb21
at thghw2a1
lineretemperatubulbdryconstantthefollowsandat thghw21
chartricPsychrometon theocessesPronHumidicati
d1
d1
d1
d1
4
W
h
h
3
)WW(
)hh(
h
1equatonto2equation
2)WW(mm
mWmmW
balancemoistureBy
1
m
)hh(m
h
mhhmmh
balanceenergyBy
w
12
12
w
12w
2w1
w
12
w
2ww1
3hmhmhm
BalanceEnergy
2WmWmWm
BalanceMoisture
1mmm
BalanceMass
332211
332211
321
Adiabatic Mixing
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. two moist air streams, with m1 and m 2, are mixed together adiabatically and
a mixture m3 is formed in a mixing chamber as shown . Since the system is well insulated, the heat transfer
between the mixing chamber and ambient air is small and is usually neglected. The resulting condition of the
mixture point 3, lies on the segment connecting the two initial streams 1 and 2 and divides the segment
proportionally, and we can apply the principle of heat balance and conservation of mass.
17. 16
lS
S
S
QQ
Q
SHF
Q
Q
SHF
Sensible Heat Factor (SHF)
Sensible Heat factor is the ratio of the sensible heat to the total heat transfer for a process.
Apparatus Dew Point (ADP)
ADP
(Apparatus Dew
Point)
Cooling and
Dehumidifying
Process
19. 18
Comfort Zone
COMFORT ZONE
One of the major applications of the Psychrometric Chart is in air conditioning, and we find that most humans
feel comfortable when the temperature is between 22°C and 27°C, and the relative humidity RH between 40%
and 60%. This defines the "comfort zone" which is portrayed on the Psychrometric Chart as shown below. Thus
with the aid of the chart we either heat or cool, add moisture or dehumidify as required in order to bring the air
into the comfort zone.
Sample Problems
Example No. 1 (Sensible Heating)
Moist air enters a duct at 10C, 80% relative humidity, and a volumetric flow rate of 150 m3
/min. The mixture
is heated as it flows through the duct and exits at 30C. No moisture is added or removed, and the mixture pres-
sure remains approximately constant at 100 KPa. For steady-state operation, determine
a. the rate of heat transfer in kJ/min
b. the relative humidity at the exit
Changes in kinetic and potential energy can be ignored.
Example No. 2 (Cooling and dehumidifying)
Moist air at 30C and 50% relative humidity enters a dehumidifier operating at steady state with a volumetric
flow rate of 280 m3
/min. The moist air passes over a cooling coil and water vapor condenses. Condensate exits
the dehumidifier saturated at 10C. Saturated moist air exits in a separate stream at the same temperature. There
is no significant loss of energy by heat transfer to the surroundings and pressure remains constant at 101.325
KPa. Determine
a. The mass flow rate of the dry air, in kg/min
b. The rate at which water is condensed, in kg per kg of dry air flowing through the control volume
c. The required refrigerating capacity, in tons of refrigeration
Example No. 3 (Humidification)
Moist air with a temperature of 22C and a wet-bulb temperature of 9C enters a steam-spray humidifier. The
mass flow rate of the dry air is 90 kg/min. Saturated water vapor at 110C is injected into the mixture at a rate
20. 19
98.87h
C21athh
8873.0
76.48h
0041.0W
KPa6631.0P
RH10%andC38At
w
fw
1
1
1
v1
sec
kg
02.0)W-m(Wm
sec
kg
59.2
8873.0
3.2V
m
kgda
kgm
0111.0W
h)t(86.13.2501
)t(0045.1hWh
W
)t(0045.1hWhh)t(86.13.2501W
h)t(86.13.2501W)t(0045.1hWhW
W-W
h-)t(86.13.2501W)t(0045.1
h
)t(86.13.2501W)t(0045.1h
W-W
h-h
h
)W-m(Wm
mWmmW
balancemoistureBy
m
)h-m(h
h
mhhmmh
balanceenergyBy
12w
1
air
2
w2d
2dw11
2
2dw11w2d2
12d22dw1w2
12
12d22d
w
2d22d2
12
12
w
12w
2w1
w
12
w
2ww1
of 52 kg/h. There is no heat transfer with the surroundings, and the pressure is constant throughout at 100 KPa.
Determine at the exit
a. The humidity ratio
b. The temperature, in C
Example No. 4 (Humidification)
Air at 38C and 10% relative humidity enters an evaporative cooler with a volumetric flow rate of 2.4 m3
/sec.
Moist air exits the cooler at 21C. Water is added to the soaked pad of the cooler as a liquid at 21C and
evaporates fully into the moist air. There is no heat transfer with the surroundings and the pressure is constant
throughout at 101.325. Determine
a. The mass flow rate of the water to the soaked pad, kg/sec
b. The relative humidity of the moist air at the exit to the evaporative cooler.
21. 20
Example: Outside and Re-circulated air supplied with Re-heater
A commercial building to be air conditioned has a sensible heat load of 36 KW and a latent heat load of 10.2
KW. The building is to be maintained at 26C and 50% RH. Outside air is at 32C DB and 24C WB. Forty five
percent of the supply air is fresh air and the rest is re-circulated air. Conditioned air leaves the AC unit at 14C
and 100% RH then it is reheated to 19C and is supplied to building. Determine
a. The fan capacity in m3
/sec to the building
b. The tonnage capacity of the AC unit (Assume tw = 14C )
c. The heat required by the re-heater
Figure
