Thermodynamics ME 2105 Credit: 4 - KUET · 2021. 1. 24. · Psychrometry The psychrometry is that...

ThermodynamicsME 2105Credit: 4.0

Md. Shariful IslamLecturer

Department of Mechanical EngineeringKhulna University of Engineering & Technology

Presented By

Psychrometry

Psychrometry

The psychrometry is that branch of engineering science,which deals with the study of moist air i. e. dry air mixedwith water vapour.

It also includes the study of behaviour of dry air andwater vapour mixture under various sets of conditions.

Though the earth's atmosphere is a mixture of gasesincluding nitrogen (N2), oxygen (O2), argon (Ar)

and carbon dioxide (CO2), yet for the purpose ofpsychrometry, it is considered to be a mixture of dry airand water vapour only.

3/5/2020 Md. Shariful Islam, Lecturer, Department of Mechanical Engineering, KUET 2

Hygroscopic Substance

A hygroscopic substance is the substance that readilyattracts water from its surroundings, either by absorptionor by adsorption.

Most hygroscopic materials are salts, but many othermaterials display the property

Examples: Honey, glycerin, ethanol, methanol,concentrated H2SO4, concentrated NaOH


Properties of Atmospheric Air

Dry Air: Dry air is a mechanical mixture of the gases:oxygen, nitrogen, carbon dioxide, hydrogen, argon, neon,krypton, helium, ozone, and xenon. However, oxygenand nitrogen make up the major part of the combination.Dry air is considered to consist of 21% oxygen and79%nitrogen by volume, and 23% oxygen and 77%nitrogen by mass.

Moist Air: It is a mixture of dry air and water vapour.The amount of water vapour, present in the air, dependsupon the absolute pressure and temperature of themixture.

Saturated Air: It is a mixture of dry air and watervapour, when the air has diffused the maximum amountof water vapour into it.



Completely dry air does not exist in nature. Water vapour invarying amounts is diffused through it. If pa and pw are thepartial pressures of dry air and water vapour respectively, thenby Dalton’s law of partial pressures

pa + pw= p

where p is the atmospheric pressure,

So, mole-fraction of dry air, xa

=pa

�= pa ( as p = 1 atm)

and mole reaction of water vapour, xw

=p�

�= pw

Since pw is very small, the saturation temperature of watervapour at pw is less than atmospheric temperature, tatm



Relative humidity: It is the ratio of actual mass ofwater vapour in a given volume of moist air to the massof water vapour in the same volume of saturated air atthe same temperature and pressure.

Relative humidity (RH ϕ ) can also defined as the ratioof partial pressure of water vapour, pw, in a mixture to thesaturation pressure, ps, of pure water, at the sametemperature of the mixture.

�� ϕ =��



If water is injected into unsaturated air in a container, water willevaporate, which will increase the moisture content of the air, and pw willincrease. This will continue till air becomes saturated at that temperature,and there will be no more evaporation of water. For saturated air, therelative humidity is 100%.

Assuming water vapour as an ideal gas�� = �� = ��ṜT and

�� = �� = ��ṜT

where V is the volume and T the temperature of air, the subscripts w ands indicating unsaturated and saturated states of air respectively.

ϕ=��

=��

��

=

��

��

��ℎ��ℎ��

=��

=��



Specific Humidity: or humidity ratio, W , is defined asthe mass of water vapour (or moisture) per unit mass ofdry air in a mixture of air and water vapour.

If G = mass of dry air

m = mass of water vapour

W =�

�

Specific humidity is the maximum when air is saturated attemperature T, or

�� = �� =��

�



If dry air and water vapour behave as ideal gases�� = �� = ��

Now specific humidity

W =�

�

=��

��

��

��

=��

��

�.��/��.��

�.��/��

= 0.622��

� − ��where p is the atmospheric pressure, pw and pa are the partialpressure of water vapor and dry air.

If pw is constant, W remains constant.

If air is saturated at temperature T

� = �� = 0.622��

� − ��where ps is the saturation pressure of water vapour at temperature T.



Degree of Saturation: The degree of saturation, μ, can bedefined as the ratio of the actual specific humidity and thesaturated specific humidity, both at the same temperature T.

μ =�

��

= �.��∗

��

�.��∗��

��

= ��

��∗��

��

ϕ=��

= 0, �� = 0, �� = 0,� = 0, �. �. ��

μ=0ϕ=100%, �� = ��,� = ��,μ=1

Therefore, μ varies between 0 and 1.


If

If


It is known that, the degree of saturation, μ, can be defined asthe ratio of the actual specific humidity and the saturatedspecific humidity, both at the same temperature T.

μ =�

��=

0.622 ∗��

� − ��

0.622 ∗��

� − ��

= ��

∗� − �� − ��

=��

∗�(1 −

�� )

�(1 −�� )

= ��

��∗(��

��)

(��)

= ϕ∗(��

��)

(��ϕ∗��)

Upon simplification……(see lecture notes)

ϕ=�

��(��)��



Dry Bulb Temperature: Dry bulb temperature (dbt) isthe temperature recorded by the thermometer with a drybulb.

Wet Bulb Temperature: Wet bulb temperature (wbt) isthe temperature recorded by a thermometer when thebulb is enveloped by a cotton wick saturated with water.

As the air stream flows past it, some water evaporates, takingthe latent heat from the water-soaked wick, thus decreasing itstemperature. Energy is then transferred to the wick from the air.When equilibrium condition is reached, there is a balancebetween energy removed from the water film by evaporation andenergy supplied to the wick by heat transfer, and thetemperature recorded is the wet bulb temperature.



Dew Point Temperature: It is the temperature of airrecorded by a thermometer, when the moisture (watervapour) present in it begins to condense. In other words,the dew point temperature is the saturation temperature(tsat) corresponding to the partial pressure of watervapour (pw).

Note: For saturated air, the dry bulb temperature, wet bulbtemperature and dew point temperature is same.

Dew Point Depression: It is the difference between thedry bulb temperature and dew point temperature of air.


Psychrometer: A psychrometer is an instrument whichmeasures both the dry bulb and the wet bulb temperatures of air.And ultimately humidity and other properties.

Adiabatic Saturation Temperature: Adiabatic saturationtemperature refers to a temperature at which air can be broughtto saturation state, adiabatically, by the evaporation of water intoflowing air.

The device used for this type of process is known as adiabatic saturator.

The adiabatic saturation temperature and the wet bulb temperature aretaken to be equal for all practical purposes.



AdiabaticSaturation Process

When unsaturated air flows over a long sheet of water in aninsulated chamber, the water evaporates, and the specifichumidity of the air increases.

Both the air and water are cooled as evaporation takes places.The process continues until the energy transferred from the airto the water is equal to the energy required to vaporize thewater.



Since the system is insulated and no work is done, thefirst law yields�ℎ�� + ��ℎ��

+ �� −�� ℎ��= �ℎ�� + ��ℎ��

where (m2 - m1) is the mass of water added, hf2 is theenthalpy of the liquid water at t2(= twb2), ha is the specificenthalpy of dry air, and hw is the specific enthalpy ofwater vapour in air. Dividing by G, and since hw2 = hg2

ℎ�� +��ℎ�� + �� −�� ℎ��= ℎ�� +��ℎ��

Solving for W1

�� =(ℎ��− ℎ��) +��(ℎ��

− ℎ��)

ℎ�� − ℎ��



=��

�� − �� +��ℎ��ℎ�� − ℎ��

Where W� =��

�=

��

�= 0.622

��

��

The enthalpy of the air-vapour mixture is given by�ℎ = �ℎ� +�ℎ�

where h is the enthalpy of the mixture per kg of dry air(it is not the specific enthalpy of the mixture)

ℎ = ℎ� +�ℎ�



Again, Let us consider the energy balance for the adiabaticsaturation process

ℎ�� +��ℎ�� + �� −�� ℎ��= ℎ�� +��ℎ��

Since ha + Whw = h kJ/kg dry air

ℎ� −��ℎ��= ℎ� −��ℎ��

where subscript 2 refers to the saturation state, and subscript 1denotes any state along the adiabatic saturation path. Therefore,

ℎ −�ℎ��= ��

Since Whf2 is small compared to h (of the order of 1 or 2%)

ℎ = ��

indicating that the enthalpy of the mixture remains constant duringan adiabatic saturation process.


Psychrometric Chart

It is a graphical representation of the various thermodynamic propertiesof moist air.

The psychrometric chart is very useful for finding out the properties ofair (which are required in the field of air conditioning) and eliminating lotof calculations.

There is a slight variation in the charts prepared by different air-conditioning manufactures but basically they are all alike.

The psychrometric chart is normally drawn for standard atmosphericpressure of 760 mm of Hg (or 1.01325 bar)


Psychrometric Chart


Psychrometric Process

These processes include simple heating (raising thetemperature), simple cooling (lowering the temperature),humidifying (adding moisture), and dehumidifying (removingmoisture).

Sometimes two or more of these processes are needed to bringthe air to a desired temperature and humidity level.


Carriers Equation

According to Carrier's equation, the partial pressure of watervapour,

�� = �� −(� − ��)(�� − ��)

1544 − 1.44��

ps= Saturation pressure corresponding to wet bulbtemperature (from steam tables),

P = Barometric/atmospheric pressure,

td = Dry bulb temperature, and

tw= Wet bulb temperature.


Self Study

Why a wet cloth dries faster in winter?

?

Why do you feel sweat in summer and dry inwinter?

?


Problem-1

Atmospheric air at 1.0132 bar has a dbt of 32°C and a wbt of26°C. Compute

(a) the partial pressure of water vapour,

(b) the specific humidity,

(c) the dew point temperature,

(d) the relative humidity,

(e) the degree of saturation,

(f) the density of the air in the mixture,

(g) the density of the vapour in the mixture, and

(h) the enthalpy of the mixture.

n.b: Enthalpy of the mixture,ℎ = ℎ� +�ℎ�= �� +�[ℎ� + 1.88(�� − ��)]


Problem-2

Consider a room that contains air at 1 atm, 35°C, and 40percent relative humidity. Using the 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.


Problem-3,4(Self Study)

An air-water vapour mixture enters an adiabatic saturator at30°C and leaves at 20°C, which is the adiabatic saturationtemperature. The pressure remains constant at 100 kPa.Determine the relative humidity and the humidity ratio of theinlet mixture.(P K Nag Example)

Sling psychrometer reads 40°C dbt and 36°C wbt. Find thehumidity ratio, relative humidity, dew point temperature,specific volume, and enthalpy of air. (P K Nag Exercise)


Adiabatic Mixing of Two Streams

This is a common problem in air conditioning, whereventilation air and some room air are mixed prior to processingit to the desired state (say, by cooling and dehumidification), andsupplying it to the conditioned space. The process is shown inFigure.


Adiabatic Mixing of Two Streams

The following equations hold good:

�� + �� = ��

�� + �� = ��W�

��ℎ� + ��ℎ� = ��h�

The points 1, 2 and 3 fall in a straight line, and the division of theline is inversely proportional to the ratio of the mass flow ratesi.e. (1-3)/(2-3) is equal to the ratio of flow rates G2/G1.

Now we can write

��

=�� −��

�� −��=ℎ� − ℎ�ℎ� − ℎ�


Problem-5Air at 20°C, 40% RH is mixed adiabatically with air at 40°C,

40% RH in the ratio of 1 kg of the former with 2 kg of the latter(on dry basis). Find the final condition of air. (P K NagExample).


Thank You


To get updated lecture notes, browse:http://www.kuet.ac.bd/me/sharifulmekuet/index.php?pg=student_corner

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Thermodynamics ME 2105 Credit: 4 - KUET · 2021. 1. 24. · Psychrometry The psychrometry is that...

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