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Version 1 ME, IIT Kharagpur 1

Lesson 27

Psychrometry

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The specific objectives of this lecture are to:
1. Define psychrometry and the composition of moist air (*Section 27.1*)
2. Discuss the methods used for estimating properties of moist air (*Section 27.2*)
3. Present perfect gas law model for moist air (*Section 27.2.1*)
4. Define important psychrometric properties (*Section 27.2.2*)
5. Present graphical representation of psychrometric properties on a psychrometric
chart (*Section 27.2.3*)
6. Discuss measurement of psychrometric properties (*Section 27.3*)
7. Discuss straight-line law as applied to air-water mixtures (*Section 27.3.1*)
8. Discuss the concept of adiabatic saturation and thermodynamic wet bulb
temperature (*Section 27.3.2*)
9. Describe a wet-bulb thermometer (*Section 27.3.3*)
10. Discuss the procedure for calculating psychrometric properties from measured
values of barometric pressure, dry bulb and wet bulb temperatures (*Section 27.4*)
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
27.1. 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 plus water vapour and a number
of pollutants (Fig.27.1). 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*.

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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. It is given in Table 27.1.

**Constituent Molecular weight Mol fraction
**Oxygen 32.000 0.2095
Nitrogen 28.016 0.7809
Argon 39.944 0.0093
Carbon dioxide 44.010 0.0003

*Table 27.1**: Composition of standard air
*

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**.

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**Water vapour Mixture of permanent
gases (N2,O2,Ar,H2,…)
**

**Dust particles,
fumes etc
**

**Atmospheric air
**

**After filtration
**

**Water vapour
**

**Mixture of permanent
gases (N2,O2,Ar,H2,…)
**

**Moist air for
conditioning
**

*Fig.27.1**: Atmospheric air
*

27.2. Methods for estimating properties of moist air:

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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 behaviour of dry air and water vapour. However, these tables are valid for a barometric pressure of 1 atm. only. Even though the calculation procedure is quite complex, using the mixture models it is possible to estimate moist air properties at

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other pressures also. However, since in most cases the pressures involved are low,
one can apply the perfect gas model to estimate psychrometric properties.
**
27.2.1. 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:

**......pppp
**

**......
V
**

**TRnp;
V
**

**TRnp;
V
**

**TRnp
**

**321t
**

**u3
3
**

**u2
2
**

**u1
1
**

+++=

=== (27.1)

where n1,n2,n3,… are the number of moles of gases 1,2,3,… Applying this equation to moist air.

**vat pppp **+== (27.2)

where p = pt = total barometric pressure
pa = partial pressure of dry air
pv = partial pressure of water vapour
**27.2.2. 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. ASHRAE suggests the following regression equation for saturated vapour
pressure of water, which is valid for 0 to 100oC.

**)Tln(cTcTcTcc
T
c)pln( 6
**

**3
5
**

**2
432
**

**1
sat **+++++= (27.3)

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
*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:

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**sat
**

**v
p
p
**

**etemperatursameatvapourwaterpureofpressuresaturation
vapourwaterofpressurepartial
**

==φ

(27.4)

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 air1. Assuming both water vapour and dry air to be perfect gases2, the humidity ratio is given by:

**avt
**

**vv
**

**aa
**

**vv
R/)pp(
**

**R/p
TR/Vp
TR/Vp
**

**airdryofkg
vapourwaterofkgW
**

− === (27.5)

Substituting the values of gas constants of water vapour and air Rv and Ra in

the above equation; the humidity ratio is given by:

**vt
**

**v
pp
**

**p622.0W
**−

= (27.6)

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:

**235
ln)235DBT(4030
)235DBT(4030DPT **−
φ+−

+ = (27.7)

where Φ is the relative humidity (in fraction). DBT & DPT are in oC. 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 or using Eqn.(27.3).

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 for engineering calculations (less than 0.7 percent as shown by Threlkeld). However, more accurate results can be obtained by using the data developed by Goff and Gratch in 1945.

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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.,

**P,tsW
W
**

=μ (27.8)

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 0oC, and for water vapour the enthalpy of saturated water is taken as zero at 0oC. The enthalpy of moist air is given by:

**)tch(WtcWhhh pwfgpga **++=+= (27.9)
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, oC
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 0oC, kJ/kg
The unit of h is kJ/kg of dry air. Substituting the approximate values of cp and hg, we
obtain:

**)t88.12501(Wt005.1h **++= (27.10)
Humid specific heat: From the equation for enthalpy of moist air, the humid specific
heat of moist air can be written as:

**pwppm c.Wcc **+= (27.11)
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.,

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3 Though the water vapor in moist air is likely to be superheated, no appreciable error results if we assume it to be saturated. This is because of the fact that the constant temperature lines in the superheated region on a Mollier chart (h vs s) are almost horizontal.

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**airdrykg/m
pp
TR
**

**p
TRv 3
**

**vt
**

**a
**

**a
**

**a
**−

== (27.12)

**
27.2.3. 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. Figure 27.2 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 (0-50oC). 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)

**Lines of
constant RH
**

**DBT, oC
**

**W
(kgw/kgda)
**

**Saturation curve
(RH = 100%)
**

*Fig.27.2**: Schematic of a psychrometric chart for a given barometric pressure
*

**Lines of
constant
sp.volume
**

**Lines of
constant
enthalpy
**

27.3. 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

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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.
**27.3.1. 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.

*Fig.27.3**: Principle of straight-line law for air-water mixtures
*

**27.3.2. 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

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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:

**f1221 h)WW(hh **−−= (27.13)
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:

**)ww(
c
h
**

**tt 12
pm
**

**2,fg
12 **−−= (27.14)

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 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.

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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*.

**Perfect insulation
**

**Water at t2
**

**Moist air
t1,W1,p
**

**Moist air
t2,W2,p
**

**Make-up water
**

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**(W2-W1) per kgda
**

*Fig.27.4**: The process of adiabatic saturation of air
*

*Fig.27.5**: Adiabatic saturation process 1-2 on psychrometric chart
*

**t1t2
**

**W2
**

**W1
**

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**27.3.3. Wet-Bulb Thermometer:
**
In practice, it is not convenient to measure the wet-bulb temperature using an
adiabatic saturator. In stead, 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.

*Fig.27.6**: Schematic of a wet-bulb thermometer and the process
on psychrometric chart
*

**Wet wick
**

**DBT
**

**W
**

4 By performing energy balance across the wet-bulb, it can be shown that, the temperature measured by the wet-bulb thermometer is:

**tcoefficientransfermasstheiskwhere);ww(h)h/k(tt wifgcw12 **−−=
for air-water mixtures, the ratio (hc/kwcpm) = Lewis number is ≈1, hence, the wick
temperature is approximately equal to the thermodynamic wet-bulb temperature.

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It should be noted that, unlike thermodynamic WBT, the WBT of wet bulb thermometer is not a thermodynamic property as it depends upon the rates of heat and mass transfer between the wick and air.

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27.4. Calculation of psychrometric properties from p, DBT and
WBT:
As mentioned before, 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 following are the empirical relations for the vapor pressure of water in
moist air:
**i) Modified Apjohn equation***:*

**2700
)tt(p8.1pp
**

**,
,
vv
**

− −= (27.15)

**ii) Modified Ferrel equation:
**

⎥⎦ ⎤

⎢⎣ ⎡ +−−=

**1571
t8.11)tt(p00066.0pp ,,vv ** (27.16)

**iii) Carrier equation:
**

**)32t8.1(3.12800
)tt)(pp(8.1
**

**pp
,,
**

**v,
vv **+−

−− −= (27.17)

where t = dry bulb temperature, oC t’ = wet bulb temperature, oC p = barometric pressure pv = vapor pressure pv’ = saturation vapor pressure at wet-bulb temperature The units of all the pressures in the above equations should be consistent. 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 presented earlier. 27.5. Psychrometer: Any instrument capable of measuring the psychrometric state of air is called a psychrometer. As mentioned before, in order to measure the psychrometric state of air, it is required to measure three independent parameters. Generally two of these are the barometric pressure and air dry-bulb temperature as they can be measured easily and with good accuracy. Two types of psychrometers are commonly used. Each comprises of two thermometers with the bulb of one covered by a moist wick. The two sensing bulbs are separated and shaded from each other so that the radiation heat transfer between them becomes negligible. Radiation shields may have to be used over the bulbs if the surrounding temperatures are considerably different from the air temperature.

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The *sling psychrometer* is widely used for measurements involving room air
or other applications where the air velocity inside the room is small. The sling
psychrometer consists of two thermometers mounted side by side and fitted in a
frame with a handle for whirling the device through air. The required air circulation (≈
3 to 5 m/s) over the sensing bulbs is obtained by whirling the psychrometer (≈ 300
RPM). Readings are taken when both the thermometers show steady-state readings.
In the *aspirated psychrometer*, the thermometers remain stationary, and a
small fan, blower or syringe moves the air across the thermometer bulbs.
The function of the wick on the wet-bulb thermometer is to provide a thin film
of water on the sensing bulb. To prevent errors, there should be a continuous film of
water on the wick. The wicks made of cotton or cloth should be replaced frequently,
and only distilled water should be used for wetting it. The wick should extend beyond
the bulb by 1 or 2 cms to minimize the heat conduction effects along the stem.
Other types of psychrometric instruments:

1. Dunmore Electric Hygrometer 2. DPT meter 3. Hygrometer (Using horse’s or human hair)

Questions and answers:
**1.** Which of the following statements are TRUE?
a) The maximum amount of moisture air can hold depends upon its temperature and
barometric pressure
b) Perfect gas model can be applied to air-water mixtures when the total pressure is
high
c) The minimum number of independent properties to be specified for fixing the state
of moist air is two
d) The minimum number of independent properties to be specified for fixing the state
of moist air is three
**Ans.: a) and d)
**
2. Which of the following statements are TRUE?
a) Straight-line law is applicable to any fluid-air mixtures
b) Straight-line law is applicable to any water-air mixtures only
c) Straight-line holds good as long as the Prandtl number is close to unity
d) Straight-line holds good as long as the Lewis number is close to unity
**Ans.: b) and d)
3. **Which of the following statements are TRUE?
a) When the dry bulb temperature is equal to dew point temperature, the relative
humidity of air-water mixture is 1.0

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b) All specific psychrometric properties of moist air are based on unit mass of water
vapour
c) All specific psychrometric properties of moist air are based on unit mass of dry air
d) All specific psychrometric properties of moist air are based on unit mass of moist
air
**Ans.: a) and d)
****4.** Which of the following statements are TRUE?
a) Thermodynamic WBT is a property of moist air, while WBT as measured by wet
bulb thermometer is not a property
b) Both the thermodynamic WBT and WBT as measured by wet bulb thermometer
are properties of moist air
c) Under no circumstances, dry bulb and wet bulb temperatures are equal
d) Wet bulb temperature is always lower than dry bulb temperature, but higher than
dew point temperature
**Ans.: a)
****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.
**Ans.:
**
At 37oC the saturation pressure (ps) of water vapour is obtained from steam tables as
**6.2795 kPa.
**
Since the relative humidity is 50%, the vapour pressure of water in air (pv) is:

**pv = 0.5 x ps = 0.5 x 6.2795** = **3.13975 kPa**
the humidity ratio W is given by:

**W = 0.622 x pv/(pt**−**pv) = 0.622 x 3.13975/(101.325**−**3.13975) = 0.01989 kgw/kgda
**

**(Ans.)
**The enthalpy of air (h) is given by the equation:
**h = 1.005t+W(2501+1.88t) = 1.005 x 37+0.01989(2501+1.88 x 37) = 88.31 kJ/kgda
**

**(Ans.)
****6.** Will the moisture in the above air condense when it comes in contact with a cold
surface whose surface temperature is 24oC?
**Ans.:** Moisture in condense when it is cooled below its dew point temperature.
The dew point temperature of the air at 37oC and 50 % relative humidity is equal to
the saturation temperature of water at a vapour pressure of 3.13975 kPa.

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From steam tables, the saturation temperature of water at 3.13975 Kpa is 24.8oC,
hence moisture in air will condense when it comes in contact with the cold surface
whose temperature is lower than the dew point temperature. **(Ans.)
****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.
**Ans.:
**
a) Using modified Apjohn equation and the values of DBT, WBT and barometric
pressure, the vapour pressure is found to be:

**pv = 2.956 kPa (Ans.)
**
b) The humidity ratio W is given by:

**W = 0.622 x 2.956/(101.325-2.956) = 0.0187 kgw/kgda (Ans.)
**
c) Relative humidity RH is given by:
RH = (pv/ps) x 100 = (pv/saturation pressure at 32oC) x 100
From steam tables, the saturation pressure of water at 32oC is **4.7552 kPa**, hence,

**RH = (2.956/4.7552) x 100 = 62.16% (Ans.)
**
d) Dew point temperature is the saturation temperature of steam at 2.956 kPa.
Hence using steam tables we find that:

**DPT = Tsat(2.956 kPa) = 23.8oC (Ans.)
**
e) Density of dry air and water vapour
Applying perfect gas law to dry air:
**Density of dry air **ρ**a =(pa/RaT)=(pt**−**pv)/RaT = (101.325**−**2.956)/(287.035 x 305)x103
**

**= 1.1236 kg/m3 of dry air (Ans.)
**
f) Similarly the density of water vapour in air is obtained using perfect gas law as:
**Density of water vapour **ρ**v = (pv/RvT) = 2.956 x 103/(461.52 x 305) = 0.021 kg/m3
**

**(Ans.)
**g) Enthalpy of moist air is found from the equation:

**h = 1.005 x t+W(2501+1.88 x t) = 1.005 x 32 + 0.0187(2501+1.88 X 32)
h= 80.05 kJ/kg of dry air (Ans.)
**

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