UNESCO
UNESCO-NIGERIA TECHNICAL &
VOCATIONAL EDUCATION
REVITALISATION PROJECT
PROJECT-PHASE II
NATIONAL DIPLOMA IN
MECHANICAL ENGINEERI
ENGINEERING
NG TECHNOLOGY
THERMODYNAMICS 1
(THEORY)
COURSE CODE: MEC122
YEAR II- SEMESTER 2
TABLE OF CONTENTS
Week1
1.1 What is thermodynamics?
1.1.2 Application areas of thermodynamics
1.1.3 Basic terminologies of thermodynamics
1.2.1 Boyle’s law
1.2.2 Charle’s law
Week 2
1.3.1 Temperature
1.3.2 Difference between temperature and heat
1.4 Zeroth law of thermodynamics (law number zero)
1.5 Thermometric substances
1.6. Temperature Scales
Week 3
1.7 Solved problems
1.8 First law of thermodynamics
1.9 Non-flow energy equation (NFEE)
1.10 Steady flow energy equation (SFEE)
Week 4
1.11 Example 1.9.1: Application of NFEE
1.12 Example 1.10.1: Application of SFEE
Week 5
2.0 Thermodynamics processes
2.1 Isochoric or isometric process:
2.2 Isobaric process:
2.3 Isothermal process:
2.4 Adiabatic process: this is a process during which there is no heat flow.
2.5 Polytropic process
Week 6
2.6 Work
2.7 Isochoric or isometric work transfer
2.8 Isobaric work transfer
2.9 Isothermal work transfer
2.10 Adiabatic work transfer
2.11 Polytropic work transfer
2.12 Example 2.9.1 On isothermal process
2.13 Example 2.10.1 on adiabatic process
2.14 Example 2.11.1 on polytropic process
Week 7
3.1 What is Steam?
3.1.1 Tripple point
3.1.2 Ice
3.1.3 Water
3.1.4 Enthalpy of water, liquid enthalpy or sensible heat (hf) of water
3.2 Steam
3.3 Enthalpy of evaporation or latent heat (hfg)
3.3.1 Enthalpy of saturated steam, or total heat of saturated steam
3.4 Saturated steam tables
Week 8
3.5 Dryness fraction
3.6 The steam phase diagram
3.7.1 Flash steam
Week 9
4.1 Fuels
4.1.1 Solid fuels
4.1.2 Liquid fuels
4.1.3 Gaseous fuels
4.2 Combustion
4.3 Complete and incomplete combustion
4.4 Stoichiometric combustion
4.5 Air-fuel ratio
Week 10
5.2 Modes of heat transfer
5.2.1 Conduction
5.2.2 Convection
5.2.3 Radiation
5.3 Conductors and insulators
5.4 Fourier’s law
5.5 Newton’s law of cooling
5.6 Heat exchangers
5.7 Forced convection
5.8 Black body radiation
Week 11
5.9 Emissivity
5.9.1 Radiation configuration factor
5.9.2 Example 5.4.1 on conduction:
Week 12
6.1 Refrigeration
6.1.1 Historical applications
6.1.2 Current applications of refrigeration
6.3 Hydrocarbon refrigerants
6.4 Hydrocarbon refrigerant safety
6.5. Methods of refrigeration
6.6 Non-cyclic refrigeration
6.7 Heat pump and refrigeration cycle
Week 13
6.3.1 Classification of refrigeration cycle
Week 14
6.4.1 Air conditioning
6.5.2 Humidity control
6.5.3 Health implications
Week 15
6.6.1 How Does an Air Conditioner Work?
6.6.3 Energy use
6.6.4 Automobile air conditioners
6.6.5 Portable air conditioners
WEEK 1 THERMODYNAMICS I
MEC I22
Learning objectives: - understanding thermodynamic principles
1.1 WHAT IS THERMODYNAMICS?
Thermodynamics can be defined as the science of energy. That is, it is concerned with energy
and energy transformation.
The name thermodynamics is derived from the Greek words therme (heat) and dynamis (power),
which is most descriptive of the early efforts to convert heat into power. Today the same name is
broadly interpreted to include all aspect of energy and energy transformations, including power
production, refrigeration and relationships among the properties of matter.
Although the principles of thermodynamics have been in existence since the creation of the
universe, thermodynamics did not emerge as a science until the construction of the first
successful atmospheric steam engines in England by Thomas Savery in 1697 and Thomas
Newcomen in 1712.these engines were very slow and inefficient, but they opened the way for
the development of a new science.
The first and second laws of thermodynamics emerged simultaneously in the 1850s, primarily
out of the works of William Rankin, Rudolph Clausius, and Lord Kelvin. The thermodynamics
was used in a publication by Lord Kelvin in 1849. The first book on thermodynamics was
written in 1859 by William Rankin; a professor at the university of Glasgow.
1.1.2
APPLICATION AREAS OF THERMODYNAMICS
One does not need to go very far to see some application areas of thermodynamics. These areas
are right where one lives. An ordinary house is, in some respects, an exhibition hall filled with
wonders of thermodynamics. Many ordinary household utensils and appliances are designed, in
whole or in part, by using the principle of thermodynamics. Some examples include the heating
and air-conditioning systems, the refrigerator, the pressure cooker, the water heater, the shower,
the iron, the computer, the TV. On a larger scale thermodynamics plays a major part in the
design and analysis of automotive engines, rockets, jet engines, and power plants. Human body
is also an interesting application area of thermodynamics.
1.1.3
BASIC TERMINOLOGIES OF THERMODYNAMICS
cience has a unique vocabulary associated with it, thermodynamics is no
exception.
Every science
Below are the definitions of some of the terminologies frequently used in thermodynamics:
1 System: this is a quantity of matter or a region in space chosen for st
study.
udy. The mass or region
outside the system is called the surroundings. The real or imaginary surface that separates the
system from its surroundings is called the boundary.
Systems may be considered to be closed or open, depending on whether a fixed volume or a
fixed mass is chosen for study.
Fig 1.1.3.1: A closed system
Fig1.1.3.2: A Four stroke (i.c.) engine (a closed system)
2
Control volume:: this is an open system where there is mass flow across the boundary.
Examples of control volume are compressor, turbine, pump, boiler, condenser, nozzle, etc.
Fig 1.1.3.3: An open system
Fig 1.1.3.4: Example of an open system: the blower
3
Control surface: this is the boundary of control volume. Both mass and energy can cross
control surface.
4
Isolated system: this is a kind of system in which both mass and energy are disallowed to
cross the boundary. When a system is isolated, it is not affected by its surroundings.
Nevertheless, changes may occur within the system that can be detected with measuring
devices.
5
State: this the condition of a system as defined by its properties.
Fig 1.1.3.4: state of a system
6
Property: this is any observable characteristic of a system which depends on the state of the
system. Below are some of thermodynamics properties commonly in use
(i)
Temperature (T): this is the degree of hotness or coldness of a body. Its SI unit is
Celsius 0C (formerly called Centigrade) and its English unit is the Fahrenheit 0F .
The thermodynamics unit of temperature is the Kelvin k.
T (K) = T (0C) + 273.15
(ii)
(1.1)
Pressure (P): is the force exerted by a fluid per unit area. The SI unit of pressure is
Newton’s per square meter (N/m2), which is called a Pascal (pa). That is :
1pa = 1 N/m2
1kpa= 1000pa
Two other common pressure units are the bar and standard atmosphere:
1 bar = 10 5 pa =0.1 Mpa =100kpa
1 atm = 101,325 pa =101.325 kpa = 1.01325 bars.
(iii)
Volume (V): the SI unit of volume is m3.
1 m3 = 1000 L = 10 6 cm3
The above three properties are easily measurable; the remaining properties are
related mathematically to them.
(iv) Internal energy (U): this is the energy associated with the internal state of a system. It
represents the kinetic and potential energies of the molecules, atoms, and subatomic particles that
constitute the system on a microscopic scale.
dU = mcvdT
Where:
(1.2)
m - mass kg
Cv – specific heat capacity at constant volume (J/kgks)
dT- temperature difference k
The unit of U is thus: kJ.
(V)
Enthalpy (H): This is commonly referred to as the heat content of a system.
Mathematically:
H = U +PV
(1.3)
That is:
Enthalpy = Internal energy + pressure x volume
Or,
h = u + pv
(1.4)
That is:
Specific enthalpy = specific internal energy + pressure x specific volume
The unit of enthalpy is kJ. Or kJ/kg (for specific enthalpy)
Note:
1 kpa . m3 = 1 kJ
1 kpa . m3/kg = 1 kJ/kg
1 bar. m3 = 100 kJ
1 Mpa . m3 = 1000 kJ
1 psi . ft3 = 0.18505 Btu
The above five properties are going to be used in this study of thermodynamics in 100 level.
However, entropy is another property which is associated with the second law of
thermodynamics it is dealt with in 200 level.
7
Process: this is an operation that changes the state of a system. During a process, system
interacts with its surroundings so as to exchange heat and work.
1.2.1 Boyle’s law
This law was formulated by Robert s Boyle in 1662. It states that, ‘the absolute pressure of a
given mass of a perfect gas varies inversely as its volume, when the temperature remains
constant.
Mathematically,
∞ or,
The more useful form of the equation is
P1v1 = p2v2 = p3v3 =..... = constant
(1.5)
1.2.2 Charles’ law
This law was formulated by a Frenchman Jacques A.C. Charles in about 1787. It states that, ‘the
volume of a given mass of a perfect gas varies directly as its absolute temperature, when the
absolute pressure remains constant.
Mathematically
∞
Or
(1.6)
WEEK 2 THERMODYNAMICS I
MEC I22
Learning objectives: - understanding temperature and temperature scales
1.3.1 Temperature
Temperature is a measure of the molecular activity of a substance. The greater the movement of
molecules, the higher the temperature. It is a relative measure of how "hot" or "cold" a substance
is and can be used to predict the direction of heat transfer.
The subject of temperature investigation is called thermometry.
1.3.2 Difference between temperature and heat
Heat is a form of energy and may be converted into other forms of energy. Heat is measured in
units of energy that is joules.
Temperature describes the degree of ‘hotness’ or ‘coldness’ of a body or medium. It is a means
of specifying the ‘level’ of the sensation caused by heat energy, not the quantity of heat energy.
1.4 Zeroth law of thermodynamics (law number zero)
This law is concerned with thermal equilibrium. It states that ‘if two bodies, say A and B, are
separately in thermal equilibrium with a third body, C, then they must be in thermal equilibrium
to each other.’
Thermal equilibrium means there is no change of state and hence the zeroth law implies that the
bodies A, B and C will all be at the same temperature and, furthermore, that all bodies in thermal
equilibrium will be at the same temperature.
1.5 Thermometric substances
Thermometric substance is any substance that has a property which varies appreciably with
temperature change.
Examples of thermometric substances are: (1) Mercury, its thermometric property is its volume.
The volume of mercury varies with temperature change; (2) Platinum wire. The thermometric
property of platinum wire is its electrical resistance. The electrical resistance of platinum wire
changes with temperature change. Other thermometric substances include: alcohol, bimetallic
strips, e.t.c.
1.6. Temperature Scales
The two temperature scales normally employed for measurement purposes are the Fahrenheit (F)
and Celsius (C) scales. These scales are based on a specification of the number of increments
between the freezing point and boiling point of water at standard atmospheric pressure. The
Celsius scale has 100 units between these points, and the Fahrenheit scale has 180 units. The
zero points on the scales are arbitrary.
The freezing point of water was selected as the zero point of the Celsius scale. The coldest
temperature achievable with a mixture of ice and salt water was selected as the zero point of the
Fahrenheit scale. The temperature at which water boils was set at 100 on the Celsius scale and
212 on the Fahrenheit scale. The relationship between the scales is represented by the following
equations.
°F = 32.0 + (9/5)°C
(2.1)
°C = (°F - 32.0)(5/9)
(2.2)
It is necessary to define an absolute temperature scale having only positive values. The absolute
temperature scale that corresponds to the Celsius scale is called the Kelvin (K) scale, and the
absolute scale that corresponds to the Fahrenheit scale is called the Rankine (R) scale. The zero
points on both absolute scales represent the same physical state. This state is where there is no
molecular motion of individual atoms. The relationships between the absolute and relative
temperature scales are shown in the following equations.
°R = °F + 460
(2.3)
°K = °C + 273
(2.4)
The conversion of one temperature scale to another is sometimes required at nuclear facilities,
and the operator should be acquainted with the process. The following two examples will be
helpful.
WEEK 3 THERMODYNAMICS I
MEC I22
1.7 SOLVED PROBLEMS
Example 1.10.1: Temperature Scale Conversion
What is the Rankine equivalent of 80°C?
Solution:
°F = (9/5) °C + 32
= (9/5)(80) + 32
= 176 °F
°R = °F + 460
= 176 + 460
= 636 °R
Example 1.10.2: Temperature Scale Conversion
What is the Kelvin equivalent of 80°F?
Solution:
°C = (5/9) (°F - 32)
= (5/9) (80 - 32)
= 26.7°C
°K = °C + 273
= 26.7 + 273
= 299.7 °K
Exercise:
1 The deep body temperature of a healthy person is 370C. What is this temperature in Kelvin?
Answer: 310k
2. Consider a system whose temperature is 180C. Express this temperature in R, K, and F.
3. The temperature of a system rises by 450C, during heating process. Express this temperature
rise in Kelvin.
Answer: 45k
4 the temperature of a system drops by 100F during cooling process. Express this drop in
temperature in K, R, and 0C.
1.11 Example on determination of temperature when the thermometric property values at certain
fixed points are given and a scale of temperature is prescribed.
A platinum thermo- resistive element is to be used to determine the temperature of a laboratory;
the thermometer has a temperature scale of:
Rt =
(a + b log
10
t
)
Where Rt is the resistance at temperature t, and Ro the resistances at ice point, and a and b are
constants. At steam point (t=1000C), the resistance of the thermometer is 2.4Ω, at ice point
(t=00C), the resistance is 0.8Ω. What will be the temperature of the laboratory if the
thermometer indicates 1.6 Ω in the lab?
SOLUTION:
GIVEN: R100
= 2.4Ω, R0= 0.8Ω, Rt= 1.6Ω
From,
Rt =
(a + b log
10
)
t ,
2.4 =a+ blog10(100)
(1)
0.8= a + blog10(0)
(2)
Now, blog10(0) = 0; therefore, a = 0.8.
Thus,
2.4 = 0.8 + blog10(100)
2.4 – 0.8 = 2b,
1.6 = 2b,
=0.8
The temperature scale is therefore:
Rt = 0.8+ 0.8 log10t
Since Rt = 1.6Ω,
Therefore 1.6 = 0.8 +0.8 log10t
Therefore t= 100C
1.8 First law of thermodynamics
The first law of thermodynamics gives a quantitative expression to the principle of conservation
of energy. In words, it says that the total energy change of a closed system is equal to the heat
transferred to the system minus the work done by the system.
Mathematically:
∆E = Q − W
(3.1)
The total energy change ∆E can be split into several terms, each representing the change in
energy of a particular form:
∆E = ∆E K + ∆E P + ∆U
(3.2)
Where: ∆E K , is the change in kinetic energy, ∆E P is the change in potential energy, and ∆ U
is the change in internal energy. By definition,
∆E K =
(
1
2
2
m c 2 − c1
2
)
(3.3)
∆E P = mg ( z 2 − z1 )
(3.4)
∆ U = m(u2 − u1 )
(3.5)
Where u is the specific internal energy, c is the velocity, z is the elevation above a datum level,
m is the mass of the system, and g is the acceleration due to gravity.
Combining equation (3.1) and (3.2) , yields:
∆E K + ∆E P + ∆U = Q − W
(3.6)
Combining equations (3.3), (3.4), (3.5), and (3.6), gives:
Q −W =
(
)
1
2
m c 2 2 − c1 + mg ( z2 − z1 ) + m(u2 − u1 )
2
(3.7)
1.9 Non-flow energy equation (NFEE)
A non-flow process is that in which a constant mass is undergoing change of state in a closed
system where changes in potential energy and kinetic energy are negligible.
Consider a system of fixed mass of constant kinetic and potential energy, equation (3.7) therefore
reduces to:
Q − W = m(u2 − u1 )
(3.8)
Or,
Q − W = U 2 − U1
(3.9)
Where U, is the internal energy of the system.
1.10 Steady flow energy equation (SFEE)
Steady flow process is the one in which matter enters and leaves through openings in the control
surface at a steady rate.
To obtain SFEE we have to add flow energy to equation (3.2) and hence equation (3.7).
Flow energy the energy required to push the fluid element into or out of the control volume.
Flow energy = pV = mpv
(3.10)
Where: v is the specific volume.
Therefore equation (3.7) writes:
Q −W =
(
)
1
2
m c 2 2 − c1 + mg ( z 2 − z1 ) + m(u 2 − u1 ) + m( p 2 v 2 − p1v1 )
2
(3.11)
(
)
Q& − W& 1 2
2
= c 2 − c1 + g ( z 2 − z1 ) + (( p 2 v 2 + u 2 ) − ( p1v1 + u1 ))
m&
2
(3.12)
From equation (1.4), h = pv +u
(
)
Q& − W& 1 2
2
= c 2 − c1 + g ( z 2 − z1 ) + (h2 − h1 )
m&
2


Q& − W&
c2
∴
= ∆ h +
+ gz 
m&
2


Or better perhaps
∴

Q& − W&
c2
gz 
= ∆ h +
+

2000 1000 
m&

(3.13)
(3.14)
Week 4
1.11 Example 1.13.1: Application of NFEE
1. A system undergoes a process in which the heat transfer to the system is 45kJ and
the work done by the system is evaluated at 47000Nm. Calculate the increase in the
system energy.
Solution:
Using sign convention, we write:
Q = +45000J, W = +47000J
Applying the non-flow energy equation
Q − W = U 2 − U1
+45000 - +47000 =U2 -U1
U2 –U1= - 2000J
The increase in the system energy is -2KJ. This corresponds, therefore, to a decrease in
system energy of 2KJ.
Example 1.13.2
2. In the cylinder of an air motor the compressed air has a specific internal energy
400kJ/kg at the beginning of the expansion and a specific internal energy of 200kJ/kg
after expansion. Calculate the heat transfer to or from the cylinder when the work
done by the air during the expansion is 100kJ/kg.
Solution:
Here,
u1 = 400kJ/kg, u2 = 200kJ/kg, W = +100kJ/kg.
Applying NFEE:
Q − W = U 2 − U1
Q – 100 = 200 – 400
Q = - 200 + 100 =- 100 KJ/kg
The negative sign means that heat is rejected to the surroundings which is numerically
equal to 100kJ/kg.
1.12 Example 1.14.1: Application of SFEE
3. During a steady flow process 600kg/h of fluid passes through an apparatus in which
the inlet pipe is 2m above the exit pipe. Properties at inlet and exit are as follows:
Pressure p
500kN/m2
200kN/m2
Velocity c
40 m/s
250 m/s
Specific internal energy u
100 kJ/kg
50KJ/kg
Specific volume v
0.1 m3/kg
0.3 m3/kg
If the heat transfer by radiation from the apparatus is 105kJ/h. what is the power
developed? Take g =9.81m/s2
Solution:
Applying SFEE:

c2
gz 
Q& − W& = m& ∆ h +
+

2000 1000 

− 10 5
Q& =
= −27.78 KW
3600
6000
m& =
= 1.67kg / s
3600
h = u + pv
∴ h1 = u1 + p1v1 = 100 + 500 x0.1 = 150kJ / kg
h2 = u 2 + p 2 v 2 = 50 + 200 x0.3 = 110kJ / kg
∴ ∆h = h2 − h1 = 100 − 150 = −40kJkg
c2
250 2 − 40 2
=
= 30.45kJ / kg
2000
2000
∆gz 9.81(− 2)
=
= −0.01962kJ / kg
1000
1000
∆
Substituting in the SFEE, we have:
− 27.78 − W& = 1.67(− 40 + 30.45 − 0.0192 )
− 27.78 − W& = −15.98
W& = −11.8 KW
Example 1.14.2
4. Steam enters a turbine with a velocity of 16m/s and specific enthalpy 2950kJ/kg. The steam
leaves the turbine with a velocity and specific enthalpy 2530kJ/kg. The heat lost to the
surroundings as the steam passes through the turbine is 25kJ/kg. The steam flow rate is
32400kg/hr. determine the work output from the turbine in kilowatt.
Solution:
Given: C1 = 16m/s, h1 = 2950 kJ/kg, C2 = 37m/s, h2 = 2530 kJ/kg,
Q = - 25kJ/kg,
m = 32400kg/hr = 32400/3600 = 9 kg/s

Q& − W&
c2
gz 
∴
= ∆ h +
+

m&
2000 1000 

Here the potential energy term is neglected, therefore the equation reduces to:


Q& − W&
c2
= ∆ h +
+
m&
2000 

− 25 − w& 
37 2 − 16 2 
= 2530 − 2950 +

9
2000 

∴
− 25 − w& = 9[− 420 + 0.5565]
− 25 − w& = 9[− 419.4435]
∴ w& = 3750kJ / kg
QUIZS
1.
A closed system undergoes a process in which the heat transfer to the system is 25kJ
and the work done by the system is evaluated at 27kNm. Calculate the change in the
system energy.
2. In the cylinder of an air motor the compressed air has an internal energy of 500kJ at
the beginning of the expansion and an internal energy of 200kJ after expansion.
Calculate the heat transfer to or from the cylinder when the work done by the air
during the expansion is 100kJ.
WEEK 5 THERMODYNAMICS I
MEC I22
Learning objectives: - understanding various types of thermodynamic processes.
2.0 THERMODYNAMICS PROCESSES
As stated earlier, process refers to an operation that alters the state of a system. We now
analyze some of the most commonly encountered thermodynamic processes:
2.1
Isochoric or isometric process: this is a process during which volume remains
constant. For this process: V = constant
(4.1)
2.2
Isobaric process: this is a constant pressure process. For isobaric:
P = constant
2.3
(4.2)
Isothermal process: this is a process during which temperature remains constant. It
obeys the law:
Pv = c
(4.3)
That is
p1v1 = p 2 v 2
Example 2.3.1
0.02 m3 of a perfect gas at temperature of 400 0C, expands reversibly and
isothermally from a pressure of 200 kpa to 5 kpa. Find:
(a) The final volume; (b) The mass of the gas.
Solution:
Give: v1 = 0.02m3; p1 = 200kpa; p2 = 5kpa; T1= T2 = 400+273 = 673 k;
J/kgk. V2=?; m =?
This is isothermal problem, therefore we use:
R = 286
p1v1 = p 2 v 2
∴ v2 =
p1v1
p2
∴ v2 =
200 x10 3 x0.02
= 0.8m 3
3
5 x10
To get the mass m, of the gas we use:
p1v1 = mRT
∴m =
p1v1
RT1
∴ m = 200 x10 3 x0.02 /(286 x673) = 0.02kg
2.4
Adiabatic process: this is a process during which there is no heat flow. There are two
ways a process can be adiabatic: Either the system is well insulated so that only a
negligible amount of heat can pass through the boundary, or both the system and its
surroundings are at the same temperature; therefore they are in thermal equilibrium.
Adiabatic process obeys the law:
pv γ = c
p1v1
γ
= p 2 v2
γ
(4.5)
γ is called the adiabatic index
γ =
CP
; where
CV
Cp is the specific heat capacity at constant pressure
Cv is the specific heat capacity at constant volume
(4.5)
R = Cp - Cv
(4.6)
Example 2.4.1
A perfect gas at 1.2 KN/m2 and temperature 125 0C occupies a volume of 0.36m3;
the gas is compressed adiabatically to a pressure of 1.05 bar. Find:
(a) Its final volume; (b) Its final temperature. Take Cp =1005 J/kgk and
Cv = 710J/kgk
Solution:
Give: V1 = 0.036 m3, P1 =1.2 KN/m2 ,T1 =1250C +273 = 398 K, P2 =1.05x105
This is adiabatic problem. To get V2, we use:
γ
p1 v1 = p 2 v 2
Now γ =
Cp
Cv
 PV γ 1 
V2 =  1

 P2 
1/ γ
=
γ
1005
= 1.41
710
1.2 X 10 3 X 0.361.41 
=

1.05 X 10 5


0.707
= 0.015m 3
To get the final temperature T2, we use:
p1v1 p 2 v 2
=
T1
T2
∴ T2 =
2.5
P2V2T1 1.05 X 10 5 X 0.015 X 398
=
= 1480 K
P1V1
1.2 X 10 3 X 0.36
Polytropic process: During expansion or compression processes of real
pressure and volume are often related by:
gases,
pvn = c.
(4.7)
Where n is called the polytropic index. This kind of process is called polytropic
process. Many processes in practice are polytropic. In polytropic process there is both
temperature change and heat flow.
Example 2.5.1
A certain amount of gas is compressed to half of its original volume from a
temperature of 2500C; its pressure increased from 450 kN/m2 to 1.2MN/m2. Find the
index of compression and the final temperature.
Solution:
Let V1 be the initial volume
V2 =1/2V1, P1= 450kN/m2; P2 = 1.2MN/m2 T1 = 250+273 = 523k
Now this is a polytropic process:
P1Vn1= P2Vn2
To get n, we make n the subject of the equation:
V1
n
V2
n
=
P2
P1
n
 V1 
P
  = 2
P1
 V2 
V
log 1
 V2
n

P
 = log 2
 P1

V
n log 1
 V2




P 
 = log 2 

 P1 
P 
log 2 
1.2 x106
log 450
P1 
log(2.67 )

x103
n=
=
=
= 1.42
log(2 )
 V1 
 V1 

log  log
 V2 
 1 / 2V1 
(
)
To get the final temperature we use:
p1v1 p 2 v 2
=
T1
T2
∴ T2 =
P2V2T1 1.2 X 10 6 X 1 / 2 XV1 X 523
=
= 697.33K
P1V1
450 X 10 3 XV1
WEEK 6 THERMODYNAMICS I
MEC I22
Learning objectives: - understanding work transfer and various modes so work
transfer
2.6 WORK
Work, like heat, is an energy interaction between a system and its surroundings. As
mentioned earlier, energy can cross the boundary of a closed system in the form of heat or
work. Therefore, if the energy crossing the boundary of a closed system is not heat, it must
be work. Work is the energy transfer associated with force acting through a distance. A rising
piston, a rotating shaft, and an electric wire crossing the system boundaries are all associated
with work interactions.
The work done during a process between states 1 and 2 is denoted by W1,2 or simply W. In
elementary mechanics, the work done by a constant force F on a body displaced a distance s
in the direction of the force is given by:
W = FS
(5.1)
If the force F is not constant, the work is obtained by adding (i.e. integrating) the differential
amounts of work,
W1, 2 = ∫ 1 Fds
2
(5.2)
Now consider a gas enclosed in a piston-cylinder device, the initial pressure of the gas is p,
the total volume is V, and the cross-sectional area of the piston is A. If the piston is allowed
to move a distance ds in a quasi-equilibrium manner, the differential work done during this
process is:
δw = Fds = pAds = pdv
(5.3)
The total boundary work done during the entire process as the piston moves is obtained by
adding all the differential works from the initial state to the final state:
∴W1, 2 = ∫ 1 pdv
2
(5.4)
This is the fundamental equation for mechanical work transfer.
We now use the above equation to evaluate the work transfers for the five processes
earlier mentioned.
2.7 Isochoric or isometric work transfer
For isochoric or isometric process v = c
Therefore from equation (5.2),
∴W1, 2 = ∫ 1 pdv
2
Since V = C, V1 = V2
∴ dv = 0
∴ w1, 2 = ∫ 1 p.0 = 0
2
(5.5)
∴ w1, 2 = 0
2.8 Isobaric work transfer
For isobaric, p = c
Therefore from equation (5.4),
W1, 2 = ∫ 1 pdv
2
but p = c
∴W1, 2 = ∫ 1 cdv = c ∫ 1 dv = c[v ]1
2
2
∴ w1, 2 = c[v 2 − v1 ] = p[v 2 − v1 ]
2
(5.6)
2.9 Isothermal work transfer
We said before that, for isothermal:
Pv = c
∴p=
c
v
c
2
dv = c[ln v ]1
v
v
p
= pv[ln v 2 − ln v 2 ] = pv ln 2 = pv ln 1
v1
p2
∴ w1, 2 = ∫ 1 pdv = ∫ 1
2
∴ w1, 2
2
(5.7)
2.10 Adiabatic work transfer
Adiabatic process obeys:
pv γ = c
c
∴ p = γ = cv −γ
v
From equation (5.4),
γ
w1, 2 = ∫ 1 pdv = ∫ 1 cv − dv = c ∫ 1 v − γ dv
2
2
2
w1, 2
 v 2 −γ +1 − v1 −γ +1 
 v −γ +1  2
= c

 = c
1− γ
 − γ + 1 1


w1, 2
 v 2 −γ +1 − v1 −γ +1  p 2 v 2 − p1v1
= pv 
=
1−γ
1− γ


γ
(5.8)
2.11
Polytropic work transfer
For polytropic, pvn = c
With similar method for pv γ = c above, the work transfer for polytropic
is:
w1, 2 =
p 2 v2 − p1v1
1− n
(5.9)
Table 2.12: summary
held constan
t
isothermal
isobaric
isochoric
adiabatic
temperature
pressure
volume
heat
W = -P∆V
0
W = ∆U
combined
gas law
PV diagrams
W = - ∫P
dV
expanding
+
W=mRTln(V2÷V1)]
case
compresse
d
Q
- temp dec
+ temp inc
Q = -W
Q = mCP∆T
Q = mCV∆T
0
∆U
- temp
dec
+ temp
inc
0
∆U = mCV∆T
∆U = mCV∆T
∆U = mCV∆T
∆U = Q + W
∆U = Q + W
∆U = Q + W
∆U = Q + W
∆U = 0
Q = -W
mCV∆T = mCP∆T
- P∆V
∆U = Q
∆U = W
1st Law
as the gas
expands, heat
must be added
since no work is since no heat can
since P∆V =
done, the
be added or
mR∆T
internal energy
removed, any
of the gas
mCV∆T = mCP∆T
work done is at
- mR∆T
increases with
the expense of
CP - CV = R
the addition of
the internal
heat
energy of the gas
Example 2.9.1 On isothermal process
0.65kg of a gas expands isothermally from a volume of 0.02m3 and pressure 950 Kpa to
a pressure of 380 Kpa. Calculate (a) its final volume, (b) the work done. Take R to be 286
J/kgk.
Solution:
Given: m =0.65kg, v1 =0.02m3, p1 = 950 kN/m2, p2 = 380 kN/m2, R =286 J/kgk
To get T1, we use:
Pv = mRT
∴ T1 =
p1v1 950 X 10 3 X 0.02
=
= 102K
mR
0.65 X 286
Since it is isothermal, T2 = T1 =102 K.
To get v2, we use:
∴ v2 =
p1v1 = p2v2
p1v1 950 x0.02
=
= 0.05m 3
p2
380
To get the work done we use:
w1, 2 = pv ln
v2
v
= p1v1 ln 2
v1
v1
= 950 x10 3 x0.02 ln
0.05
= 17410 J
0.02
Example 2.10.1 on adiabatic process
A gas whose temperature and pressure were respectively 3000C and 1.8 MN/m2 expands
isentropically to a temperature of 1800C and a pressure of 800kpa. Calculate the work
done by the gas. Take Cv = 718 J/kgk, and Cp = 1008 J/kgk.
Solution:
Given: T1 = 3000C, P1 = 1.8MN/m2, T2 = 1800C, P2 = 800kpa, Cp = 1008 J/kgk,
Cv = 718 J/kgk
To get work done we use:
w1, 2 =
R (T2 − T1 )
1− γ
So we have to look for R and γ
R = Cp - Cv = 1008 -718 = 290J/kgk
Now γ =
∴ w1, 2 =
Cp
Cv
=
1008
= 1 .4
718
290(180 − 300 )
= 87 kJ
1 − 1 .4
Example 2.11.1 on polytropic process
A certain perfect gas is compressed to one-third of its initial volume, from a pressure of
450 kN/m2, to 2.0 MN/m2, according to the law pv1.3 = C. its initial temperature was
2000C. Calculate the final temperature and the work done. Take R to be 285J/kgk
Solution:
Given: V2 = 1/3 V1, P1 = 450KN/m2, P2 = 2.0 MN/ m2, T1 = 200+273 = 473k,
n = 1.3
To get the final temperature T2, we use:
T2 = ?
p1v1 p 2 v 2
=
T1
T2
P2V2T1 2.0 X 10 6 X 1 / 3 XV1 X 473
∴ T2 =
=
= 701K
P1V1
450 X 10 3 XV1
w1, 2 =
R(T2 − T1 ) 285(701 − 473)
=
= 216.354kJ
1− n
1 − 1.3
WEEK 7 THERMODYNAMICS I
MEC I22
Learning objectives: - understanding the existence of water in three different states and its
heat contents
3.1 What is Steam?
A better understanding of the properties of steam may be achieved by understanding the general
molecular and atomic structure of matter, and applying this knowledge to ice, water and steam.
A molecule is the smallest amount of any element or compound substance still possessing all the
chemical properties of that substance which can exist. Molecules themselves are made up of
even smaller particles called atoms, which define the basic elements such as hydrogen and
oxygen.
The specific combinations of these atomic elements provide compound substances. One such
compound is represented by the chemical formula H2O, having molecules made up of two atoms
of hydrogen and one atom of oxygen.
The reason water is so plentiful on the earth is because hydrogen and oxygen are amongst the
most abundant elements in the universe. Carbon is another element of significant abundance, and
is a key component in all organic matter.
Most mineral substances can exist in the three physical states (solid, liquid and vapour) which
are referred to as phases. In the case of H2O, the terms ice, water and steam are used to denote
the three phases respectively.
The molecular structure of ice, water, and steam is still not fully understood, but it is convenient
to consider the molecules as bonded together by electrical charges (referred to as the hydrogen
bond). The degree of excitation of the molecules determines the physical state (or phase) of the
substance.
3.1.1 TRIPPLE POINT
All the three phases of a particular substance can only coexist in equilibrium at a certain
temperature and pressure, and this is known as its triple point.
The triple point of H2O, where the three phases of ice, water and steam are in equilibrium, occurs
at a temperature of 273.16 K and an absolute pressure of 0.006 112 bar. This pressure is very
close to a perfect vacuum. If the pressure is reduced further at this temperature, the ice, instead of
melting, sublimates directly into steam.
3.1.2 ICE
In ice, the molecules are locked together in an orderly lattice type structure and can only vibrate.
In the solid phase, the movement of molecules in the lattice is a vibration about a mean bonded
position where the molecules are less than one molecular diameter apart.
The continued addition of heat causes the vibration to increase to such an extent that some
molecules will eventually break away from their neighbors, and the solid starts to melt to a liquid
state. At atmospheric pressure, melting occurs at 0°C. Changes in pressure have very little effect
on the melting temperature, and for most practical purposes, 0°C can be taken as the melting
point. However, it has been shown that the melting point of ice falls by 0.0072°C for each
additional atmosphere of pressure. For example, a pressure of 13.9 bar g would be needed to
reduce the melting temperature by 0.1°C.
Heat that breaks the lattice bonds to produce the phase change while not increasing the
temperature of the ice, is referred to as enthalpy of melting or heat of fusion. This phase change
phenomenon is reversible when freezing occurs with the same amount of heat being released
back to the surroundings.
For most substances, the density decreases as it changes from the solid to the liquid phase.
However, H2O is an exception to this rule as its density increases upon melting, which is why ice
floats on water.
3.1.3 WATER
In the liquid phase, the molecules are free to move, but are still less than one molecular diameter
apart due to mutual attraction; and collisions occur frequently. More heat increases molecular
agitation and collision, raising the temperature of the liquid up to its boiling temperature.
3.1.4 Enthalpy of water, liquid enthalpy or sensible heat (hf) of water
This is the heat energy required to raise the temperature of water from a datum point of 0°C to its
current temperature.
At this reference state of 0°C, the enthalpy of water has been arbitrarily set to zero. The enthalpy
of all other states can then be identified, relative to this easily accessible reference state.
Sensible heat was the term once used, because the heat added to the water produced a change in
temperature. However, the accepted terms these days are liquid enthalpy or enthalpy of water.
At atmospheric pressure (0 bar g), water boils at 100°C, and 419 kJ of energy are required to heat
1 kg of water from 0°C to its boiling temperature of 100°C. It is from these figures that the value
for the specific heat capacity of water (cp) of 4.19 kJ/kg °C is derived for most calculations
between 0°C and 100°C.
3.2 STEAM
As the temperature increases and the water approaches its boiling condition, some molecules
attain enough kinetic energy to reach velocities that allow them to momentarily escape from the
liquid into the space above the surface, before falling back into the liquid.
Further heating causes greater excitation and the number of molecules with enough energy to
leave the liquid increases. As the water is heated to its boiling point, bubbles of steam form
within it and rise to break through the surface.
Considering the molecular structure of liquids and vapors, it is logical that the density of steam is
much less than that of water, because the steam molecules are further apart from one another.
The space immediately above the water surface thus becomes filled with less dense steam
molecules.
When the number of molecules leaving the liquid surface is more than those re-entering, the
water freely evaporates. At this point it has reached boiling point or its saturation temperature, as
it is saturated with heat energy.
If the pressure remains constant, adding more heat does not cause the temperature to rise any
further but causes the water to form saturated steam. The temperature of the boiling water and
saturated steam within the same system is the same, but the heat energy per unit mass is much
greater in the steam.
At atmospheric pressure the saturation temperature is 100°C. However, if the pressure is
increased, this will allow the addition of more heat and an increase in temperature without a
change of phase.
Therefore, increasing the pressure effectively increases both the enthalpy of water, and the
saturation temperature. The relationship between the saturation temperature and the pressure is
known as the steam saturation curve (see Figure 7.1).
Fig. 7.1 Steam saturation curve
Water and steam can coexist at any pressure on this curve, both being at the saturation
temperature. Steam at a condition above the saturation curve is known as superheated steam:
If the steam is able to flow from the boiler at the same rate that it is produced, the addition of
further heat simply increases the rate of production. If the steam is restrained from leaving the
boiler, and the heat input rate is maintained, the energy flowing into the boiler will be greater
than the energy flowing out. This excess energy raises the pressure, in turn allowing the
saturation temperature to rise, as the temperature of saturated steam correlates to its pressure.
3.3 Enthalpy of evaporation or latent heat (hfg)
This is the amount of heat required to change the state of water at its boiling temperature, into
steam. It involves no change in the temperature of the steam/water mixture, and all the energy is
used to change the state from liquid (water) to vapors (saturated steam).
The old term latent heat is based on the fact that although heat was added, there was no change in
temperature. However, the accepted term is now enthalpy of evaporation.
Like the phase change from ice to water, the process of evaporation is also reversible. The same
amount of heat that produced the steam is released back to its surroundings during condensation,
when steam meets any surface at a lower temperature.
This may be considered as the useful portion of heat in the steam for heating purposes, as it is
that portion of the total heat in the steam that is extracted when the steam condenses back to
water.
3.3.1 Enthalpy of saturated steam, or total heat of saturated steam
This is the total energy in saturated steam, and is simply the sum of the enthalpy of water and the
enthalpy of evaporation.
(7.1)
Where:
hg = Total enthalpy of saturated steam (Total heat) (kJ/kg)
hf = Liquid enthalpy (Sensible heat) (kJ/kg)
hfg = Enthalpy of evaporation (Latent heat) (kJ/kg)
The enthalpy (and other properties) of saturated steam can easily be referenced using the
tabulated results of previous experiments, known as steam tables.
3.4 SATURATED STEAM TABLES
The steam tables list the properties of steam at varying pressures. They are the results of actual
tests carried out on steam. Table 6.1 shows the properties of dry saturated steam at atmospheric
pressure - 0 bar g.
Table 7.1 Properties of saturated steam at atmospheric pressure
Example 7.1
At atmospheric pressure (0 bar g), water boils at 100°C, and 419 kJ of energy are required to heat
1 kg of water from 0°C to its saturation temperature of 100°C. Therefore the specific enthalpy of
water at 0 bar g and 100°C is 419 kJ/kg, as shown in the steam tables (see Table 6.2).
Another 2 257 kJ of energy are required to evaporate 1 kg of water at 100°C into 1 kg of steam at
100°C. Therefore at 0 bar g the specific enthalpy of evaporation is 2 257 kJ/kg, as shown in the
steam tables (see Table 6.2).
However, steam at atmospheric pressure is of a limited practical use. This is because it cannot be
conveyed under its own pressure along a steam pipe to the point of use.
Note: Because of the pressure/volume relationship of steam, (volume is reduced as pressure is
increased) it is usually generated in the boiler at a pressure of at least 7 bar g. The generation of
steam at higher pressures enables the steam distribution pipes to be kept to a reasonable size.
As the steam pressure increases, the density of the steam will also increase. As the specific
volume is inversely related to the density, the specific volume will decrease with increasing
pressure.
Figure 6.2 shows the relationship of specific volume to pressure. This highlights that the greatest
change in specific volume occurs at lower pressures, whereas at the higher end of the pressure
scale there is much less change in specific volume.
Fig. 7.2 Steam pressure/specific volume relationship
The extract from the steam tables shown in Table 6.2 shows specific volume, and other data
related to saturated steam. At 7 bar g, the saturation temperature of water is 170°C. More heat
energy is required to raise its temperature to saturation point at 7 bar g than would be needed if
the water were at atmospheric pressure. The table gives a value of 721 kJ to raise 1 kg of water
from 0°C to its saturation temperature of 170°C.
The heat energy (enthalpy of evaporation) needed by the water at 7 bar g to change it into steam
is actually less than the heat energy required at atmospheric pressure. This is because the specific
enthalpy of evaporation decreases as the steam pressure increases.
However, as the specific volume also decreases with increasing pressure, the amount of heat
energy transferred in the same volume actually increases with steam pressure.
WEEK 8 THERMODYNAMICS I
MEC I22
Learning objectives: - understanding the dryness fraction of steam
3.5 DRYNESS FRACTION
Steam with a temperature equal to the boiling point at that pressure is known as dry saturated
steam. However, to produce 100% dry steam in an industrial boiler designed to produce saturated
steam is rarely possible, and the steam will usually contain droplets of water.
In practice, because of turbulence and splashing, as bubbles of steam break through the water
surface, the steam space contains a mixture of water droplets and steam.
Steam produced in any shell-type boiler (see Block 3), where the heat is supplied only to the
water and where the steam remains in contact with the water surface, may typically contain
around 5% water by mass.
If the water content of the steam is 5% by mass, then the steam is said to be 95% dry and has a
dryness fraction of 0.95.
The actual enthalpy of evaporation of wet steam is the product of the dryness fraction ( ) and the
specific enthalpy (hfg) from the steam tables. Wet steam will have lower usable heat energy than
dry saturated steam.
(8.1)
Therefore:
(8.2)
Because the specific volume of water is several orders of magnitude lower than that of steam, the
droplets of water in wet steam will occupy negligible space. Therefore the specific volume of
wet steam will be less than dry steam:
(8.3)
Where vg is the specific volume of dry saturated steam.
Example 3.6.1
Steam at a pressure of 6 bar g having a dryness fraction of 0.94 will only contain 94% of the
enthalpy of evaporation of dry saturated steam at 6 bar g. The following calculations use figures
from steam tables:
3.6 The steam phase diagram
The data provided in the steam tables can also be expressed in a graphical form. Figure 7.1
illustrates the relationship between the enthalpy and temperature of the various states of water
and steam; this is known as a phase diagram.
Fig. 3.7.1 Temperature enthalpy phase diagram
As water is heated from 0°C to its saturation temperature, its condition follows the saturated
water line until it has received all of its liquid enthalpy, hf, (A- B).
If further heat continues to be added, the water changes phase to a water/vapour mixture and
continues to increase in enthalpy while remaining at saturation temperature ,hfg, (B-C).
As the water/vapour mixture increases in dryness, its condition moves from the saturated liquid
line to the saturated vapour line. Therefore at a point exactly halfway between these two states,
the dryness fraction ( ) is 0.5. Similarly, on the saturated steam line the steam is 100% dry.
Once it has received all of its enthalpy of evaporation, it reaches the saturated steam line. If it
continues to be heated after this point, the pressure remains constant but the temperature of the
steam will begin to rise as superheat is imparted (C-D).
The saturated water and saturated steam lines enclose a region in which a water/vapour mixture
exists - wet steam. In the region to the left of the saturated water line only water exists, and in the
region to the right of the saturated steam line only superheated steam exists.
The point at which the saturated water and saturated steam lines meet is known as the critical
point. As the pressure increases towards the critical point the enthalpy of evaporation decreases,
until it becomes zero at the critical point. This suggests that water changes directly into saturated
steam at the critical point.
Above the critical point the steam may be considered as a gas. The gaseous state is the most
diffuse state in which the molecules have an almost unrestricted motion, and the volume
increases without limit as the pressure is reduced.
The critical point is the highest temperature at which water can exist. Any compression at
constant temperature above the critical point will not produce a phase change.
Compression at constant temperature below the critical point however, will result in liquefaction
of the vapour as it passes from the superheated region into the wet steam region.
The critical point occurs at 374.15°C and 221.2 bar for steam. Above this pressure the steam is
termed supercritical and no well-defined boiling point applies.
3.7.1 FLASH STEAM
The term 'flash steam' is traditionally used to describe steam issuing from condensate receiver
vents and open-ended condensate discharge lines from steam traps. How can steam be formed
from water without adding heat?
Flash steam occurs whenever water at high pressure (and a temperature higher than the saturation
temperature of the low-pressure liquid) is allowed to drop to a lower pressure. Conversely, if the
temperature of the high-pressure water is lower than the saturation temperature at the lower
pressure, flash steam cannot be formed. In the case of condensate passing through a steam trap; it
is usually the case that the upstream temperature is high enough to form flash steam. See Figure
3.7.1.1
Fig. 3.7.1.1 Flash steam formed because T1 > T2
Consider a kilogram of condensate at 5 bar g and a saturation temperature of 159°C passing
through a steam trap to a lower pressure of 0 bar g. The amount of energy in one kilogram of
condensate at saturation temperature at 5 bar g is 671 kJ. In accordance with the first law of
thermodynamics, the amount of energy contained in the fluid on the low-pressure side of the
steam trap must equal that on the high-pressure side, and constitutes the principle of conservation
of energy.
Consequently, the heat contained in one kilogram of low-pressure fluid is also 671 kJ. However,
water at 0 bar g is only able to contain 419 kJ of heat, subsequently there appears to be an
imbalance of heat on the low-pressure side of 671 - 419 = 252 kJ, which, in terms of the water,
could be considered as excess heat.
This excess heat boils some of the condensate into what is known as flash steam and the boiling
process is called flashing. Therefore, the one kilogram of condensate which existed as one
kilogram of liquid water on the high pressure side of the steam trap now partly exists as both
water and steam on the low-pressure side.
The amount of flash steam produced at the final pressure (P2) can be determined using Equation
7.4:
( 8.4)
Where:
P1 =Initial pressure Final Pressure, hf=Liquid enthalpy (kJ/kg)
hfg = Enthalpy of evaporation (kJ/kg)
Example 3.7.1 The case where the high pressure condensate temperature is higher than the
low pressure saturation temperature.
Consider a quantity of water at a pressure of 5 bar g, containing 671 kJ/kg of heat energy at its
saturation temperature of 159°C. If the pressure was then reduced down to atmospheric pressure
(0 bar g), the water could only exist at 100°C and contain 419 kJ/kg of heat energy. This
difference of 671 - 419 = 252 kJ/kg of heat energy, would then produce flash steam at
atmospheric pressure.
The proportion of flash steam produced can be thought of as the ratio of the excess energy to the
enthalpy of evaporation at the final pressure.
Example 3.7.2 the case where the high pressure condensate temperature is lower than the
low pressure saturation temperature.
Consider the same conditions as in Example 7.1 with the exception that the high-pressure
condensate temperature is at 90°C, that is, sub-cooled below the atmospheric saturation
temperature of 100°C. Note: It is not usually practical for such a large drop in condensate
temperature from its saturation temperature (in this case 159°C to 90°C); it is simply being used
to illustrate the point about flash steam not being produced under such circumstances.
In this case, the sub-saturated water table will show that the liquid enthalpy of one kilogram of
condensate at 5 bar g and 90°C is 377 kJ. As this enthalpy is less than the enthalpy of one
kilogram of saturated water at atmospheric pressure (419 kJ), there is no excess heat available to
produce flash steam. The condensate simply passes through the trap and remains in a liquid state
at the same temperature but lower pressure, atmospheric pressure in this case. See Figure 2.2.5.
Fig.3.7.1.2 No flash steam formed because T 1 < T 2
The vapour pressure of water at 90°C is 0.7 bar absolute. Should the lower condensate pressure
have been less than this, flash steam would have been produced.
The principles of conservation of energy and mass between two process states
The principles of the conservation of energy and mass allow the flash steam phenomenon to be
thought of from a different direction.
Consider the conditions in Example 7.1
1 kg of condensate at 5 bar g and 159°C produces 0.112 kg of flash steam at atmospheric
pressure. This can be illustrated schematically in Figure 2.2.6. The total mass of flash and
condensate remains at 1 kg.
Fig.3.7.1.3 The principle of energy conservation between two process states
The principle of energy conservation states that the total energy in the lower-pressure state must
equal the total energy in the higher-pressure state. Therefore, the amount of heat in the flash
steam and condensate must equal that in the initial condensate of 671 kJ.
Steam tables give the following information:
Total enthalpy of saturated water at atmospheric pressure (hf) = 419 kJ/kg
Total enthalpy in saturated steam at atmospheric pressure (hg) = 2 675 kJ/kg
Therefore, at the lower pressure state of 0 bar g,
Total enthalpy in the water = 0.888 kg x 419 kJ / kg = 372 kJ (A)
Total enthalpy in the steam = 0.112 kg x 2 675 kJ / kg = 299 kJ (B)
Total enthalpy in condensate and steam at the lower pressure = A + B = 671 kJ
Therefore, according to the steam tables, the enthalpy expected in the lower-pressure state is the
same as that in the higher-pressure state, thus proving the principle of consersavation of energy
holds.
WEEK 9 THERMODYNAMICS I
MEC I22
Learning objectives: - understanding fuel, types of fuel and heat contents of
fuel
4.1 Fuels
Fuel is any material that is burned or altered in order to obtain energy. Fuel releases its energy
either through a chemical reaction means, such as combustion, or nuclear means, such as nuclear
fission or nuclear fussion.
Types of fuel
(i)
(ii)
(iii)
Solid fuels
Liquid fuels
Gaseous fuels
4.1.1 SOLID FUELS
These refer to various types of solid substances that are used as fuel to produce energy and
provide heating, usually released through combustion. Solid fuels include wood, charcoal, peat,
coal.
4.1.2 LIQUID FUELS
These include kerosene, gasoline (petrol), paint thinner, airplane fuel, e.t.c. Most liquid fuels are
very volatile (that is they can explode when in contact with fire)
4.1.3 GASEOUS FUELS
A gaseous fuel is a combustible gas that can be burned in a furnace or an engine. Gaseous fuels
are stored naturally beneath the earth in many parts of the world, often in the vicinity of oil field.
Where natural gas is not available, gaseous fuel may be manufactured, by thermal treatment of
coal or oil. Gaseous fuel may be divided into four classes: natural gas, producer gas, water gas
and coal gas.
TABLE 4.1: Volume Analyses of some fuel-gas mixtures (%)
Coal gas
CO
9
H2
53.6
CH4
25
C 2 H6
_
C3H8 C4H10 O2
_
3
.4
CO2
3
N2
6
(town
gas)
Producer
gas
Blast
furnace
gas
Natural
gas(uk)
Natural
gas(u.s.a.)
Natural
gas
(u.s.s.r)
29
12
2.6
0.4
_
_
_
4
52
27
2
_
_
_
_
_
11
60
1
_
93
_
3
_
_
_
3
_
_
80
_
_
_
_
2
_
1
93
_
_
_
2
0.5
3.5
4.2 COMBUSTION
A chemical reaction during which a fuel is oxidized and a large quantity of energy is released is
called combustion. The oxidizer most often used is in combustion processes is air because it is
free and readily available
On a mole basis, dry air is composed of 20.9 % oxygen, 78.1% nitrogen, 0.9% argon, and small
amount of carbon dioxide, helium, neon, and hydrogen. In the analysis of combustion processes,
the argon in the air is treated as nitrogen, and the gases that exist in trace amounts are
disregarded. Then the dry air can be approximated as 21% oxygen and 79 %nitrogen by mole
numbers. Therefore each one mole of oxygen entering a combustion chamber will be
accompanied by 0.79/0.21 = 3.76 mol of nitrogen. That is,
1 kmol O2 +3.76 kmol N2 = 4.76 kmol air
4.3 COMPLETE AND INCOMPLETE COMBUSTION
A combustion process is complete if all the carbon in the fuel burns to CO2, all the hydrogen
burns to H2O, and all the sulphur (if any) burns to SO2. That is all the combustible components
of a fuel are burned to completion during a complete combustion process. Conversely, the
combustion process is incomplete if the combustion products contain any unburned fuel or
components such as C, H2, CO, or OH.
Insufficient oxygen is the obvious reason for incomplete combustion, but is not the only one.
Incomplete combustion occurs even when more oxygen is present in the combustion chamber
than is needed for complete combustion. This may be attributed to insufficient mixing in the
combustion chamber during the limited time that the fuel and the oxygen are in contact
4.4 STOICHIOMETRIC COMBUSTION
The minimum amount of air needed for complete combustion of a fuel is called the
stoichiometric or theoretical combustion of the fuel. For example, the theoretical combustion of
methane is
CH4 + 2(O2 +3.76N2) → CO2 +2H2O +7.52N2
Notice that the products of combustion contain no unburned methane and no C, H2, CO, OH, or
free O2
4.5 AIR-FUEL RATIO
A frequently used quantity in the analysis of combustion processes to quantify the amounts of
fuel and air is the air-fuel ratio AF. It is usually expressed on mass basis and is defined as the
ratio of the mass of air to the mass of fuel for a combustion process. That is,
AF =
m air
m fuel
The mass m of a substance is related to the number of moles N through the relation m = NM,
where M is the molar mass.
The air-fuel ratio can also be expressed on a mole basis as the ratio of the mole numbers of air to
the mole numbers of fuel. The reciprocal of air-fuel ratio is called the fuel-air ratio.
WEEK 10 THERMODYNAMICS I
MEC I22
Learning objectives: - understanding modes of heat transfer
5.2 MODES OF HEAT TRANSFER
5.2.1 Conduction
Heat can be conducted between two bodies which are in contact with each other; heat "flows"
from one to the other.
•
•
Materials which conduct heat well are called conductors of heat. Electrical
conductors (such as metals) are good conductors of heat.
Materials which do not conduct heat well are called insulators. Electrical
insulators (for example, wood or glass) are usually good insulators of heat.
Materials with low density, such as air or foamed plastic, are normally also good
insulators unless they happen to be electrical conductors. To prevent heat from
moving from one place to another, we usually place an insulator between.
Once a good insulator becomes hot, however, it stays that way for a long time, because it is
difficult for the material to lose heat by conduction. Think of a hot ceramic pan and a hot metal
pan: which cools faster?
Fig 5.2.1.1: how conduction and convection occur
5.2.2 Convection
This is a different kind of heat transfer than conduction. In conduction, heat itself is moving; in
convection, hot portions of a fluid move through the body of the fluid. The hot fluid mixes with
the cold fluid, and heat is transferred more quickly than by conduction.
What we commonly call a "rolling boil" results from convection. Hot fluids rise through
surrounding, cooler fluid because they are less dense; cooler fluids sink through warmer fluids
because they are denser. This causes circular motion of the fluid away from a source of heat.
Convection in water drives ocean currents; convection in air drives weather patterns; and
convection of molten rock inside the earth is thought to drive plate tectonics.
Fig 5.2.2.1: how convection takes place
Convection leads to the counterintuitive fact that good insulators (like air) can transfer heat
efficiently as long as the air is allowed to move freely. Trapped air, as between panes of a
double window, cannot transfer heat well because it cannot mix with air of a different
temperature.
5.2.3 Radiation
Radiation is the simplest means of heat transfer. Heat radiation is carried not by moving atoms
(as in conduction or convection) but by electromagnetic waves. Radiation is the only way that
heat can move through a vacuum, and is the reason that even a closed thermos bottle (which has
a vacuum between the inner and outer parts) will eventually come to the same temperature as its
surroundings.
Heat transfer is most efficient by convection, then by conduction; radiation is the least efficient
and slowest means of heat transfer. Low efficiency of heat transfer means that vacuums make
excellent insulation.
5.3 Conductors and insulators
Thermal Conductors are materials that conduct thermal energy from one point to another.
Insulators on the other hand do not heat. The rate at which a material conducts thermal energy
depends on its thermal conductivity, k. Thus good thermal conductors have high thermal
conductivities and insulators have low thermal conductivities. The unit of thermal conductivity is
W/mk. For example Aluminium is a good conductor (k = 237 W/mk) whereas Glass fiber is an
insulator (k = 0.043W/mk).
5.4 FOURIER’S LAW
Fourier stated that the rate of heat conducted through a layer of constant thickness ∆x is
proportional to the temperature difference ∆T across the layer and the area A normal to the
direction of heat transfer, and is inversely proportional to the thickness of the layer.
(9.1)
K is the coefficient of thermal conductivity (W/mk).
5.5 NEWTON’S LAW OF COOLING
The rate of heat transfer by convection , is determined from Newton’s law of cooling,
expressed as:
= hA ( Ts –Tf)
(9.2)
Where h is the convective heat transfer coefficient, (W/m2k), A the solid surface area through
which the heat transfer takes place, Ts is the surface temperature, and Tf is bulk fluid temperature
away from the surface.
5.6 HEAT EXCHANGERS
Heat exchangers are devices that are used to transfer thermal energy from one fluid to another
without mixing the two fluids.
The transfer of thermal energy between fluids is one of the most important and frequently used
processes in engineering. The transfer of heat is usually accomplished by means of a device
known as a heat exchanger. Common applications of heat exchangers in the nuclear field include
boilers, fan coolers, cooling water heat exchangers, and condensers.
The basic design of a heat exchanger normally has two fluids of different temperatures separated
by some conducting medium. The most common design has one fluid flowing through metal
tubes and the other fluid flowing around the tubes. On either side of the tube, heat is transferred
by convection. Heat is transferred through the tube wall by conduction.
Heat exchangers may be divided into several categories or classifications. In the most commonly
used type of heat exchanger, two fluids of different temperature flow in spaces separated by a
tube wall. They transfer heat by convection and by conduction through the wall. This type is
referred to as an "ordinary heat exchanger," as compared to the other two types classified as
"regenerators" and "cooling towers."
5.7 Forced convection
The term forced convection is used if this motion and mixing is caused by an outside force, such
as a pump. The transfer of heat from a hot water radiator to a room is an example of heat transfer
by natural convection. The transfer of heat from the surface of a heat exchanger to the bulk of a
fluid being pumped through the heat exchanger is an example of forced convection.
Heat transfer by convection is more difficult to analyze than heat transfer by conduction because
no single property of the heat transfer medium, such as thermal conductivity, can be defined to
describe the mechanism. Heat transfer by convection varies from situation to situation (upon the
fluid flow conditions), and it is frequently coupled with the mode of fluid flow. In practice,
analysis of heat transfer by convection is treated empirically (by direct observation).
Convection heat transfer is treated empirically because of the factors that affect the stagnant film
thickness: Fluid velocity, Fluid viscosity, Heat flux, Surface roughness,
Type of flow, (single-phase/two-phase).
Convection involves the transfer of heat between a surface at a given temperature (Ts) and fluid
at a bulk temperature (Tb). The exact definition of the bulk temperature (Tb) varies depending on
the details of the situation. For flow adjacent to a hot or cold surface, Tb is the temperature of the
fluid "far" from the surface. For boiling or condensation, Tb is the saturation temperature of the
fluid. For flow in a pipe, Tb is the average temperature measured at a particular cross-section of
the pipe.
5.8 BLACK BODY RADIATION
A body that emits the maximum amount of heat for its absolute temperature is called a black
body. Radiant heat transfer rate from a black body to its surroundings can be expressed by the
following equation.

= σ AT4

Where:
= heat transfer rate (W)
σ = Stefan-Boltzmann constant (5.67x10-8 W/m2k-4)
A = surface area (m2)
T = temperature (k)
(9.3)
Two black bodies that radiate toward each other have a net heat flux between them. The net flow
rate of heat between them is given by
= A (T41- T42 )
(9.4)
Where:
A = surface area of the first body (m2)
T1 = temperature of the first body (k)
T2 = temperature of the second body (k)
All bodies above absolute zero temperature radiate some heat. The sun and earth both radiate
heat toward each other. This seems to violate the Second Law of Thermodynamics, which states
that heat cannot flow from a cold body to a hot body. The paradox is resolved by the fact that
each body must be in direct line of sight of the other to receive radiation from it. Therefore,
whenever the cool body is radiating heat to the hot body, the hot body must also be radiating heat
to the cool body. Since the hot body radiates more heat (due to its higher temperature) than the
cold body, the net flow of heat is from hot to cold.
WEEK 11 THERMODYNAMICS I
MEC I22
Learning objectives: - understanding the emissivity of bodies in radiation
5.9 Emissivity
Real objects do not radiate as much heat as a perfect black body. They radiate less heat than a
black body and are called gray bodies. To take into account the fact that real objects are gray
bodies, the above equation is modified to be of the following form:
= є AT4
Where:
(10.1)
 є = emissivity of the gray body (dimensionless)
Emissivity is simply a factor by which we multiply the black body heat transfer to take into
account that the black body is the ideal case. Emissivity is a dimensionless number and has a
maximum value of 1.0.
5.9.1 Radiation Configuration Factor
Radiative heat transfer rate between two gray bodies can be calculated by the equation stated
below.
= є A (T14 –T 24 )
(10.2)
Where:
є = is the emissivity factor, which depends on the emissivities of both objects
(Dimensionless) configuration factor is usually found in a text book for the given situation.
Once the configuration factor is obtained, the overall net heat flux can be determined. Radiant
heat flux should only be included in a problem when it is greater than 20% of the problem.
Example 5.4.1 on conduction:
Calculate the heat conducted per unit area through a solid surface of coefficient of thermal
conductivity 0.72W/mk and 25mm thickness when the temperature difference between the inner
and outer surfaces is 40k.
SOLUTION:
Applying Fourier’s law
∆T
Q& = KA
∆X
Where: k = 0.72 W/mk, ∆x = 0.025m, ∆T = 40k
/A = (0.72W/mk x 40k)/0.025m = 1152 W/m2
Example 5.4.2 On convection
Calculate the transfer by convection between a hot solid surface of cross-sectional area 0.225m2
at temperature 800C and a fluid at temperature 300C. The convective heat transfer coefficient
between the surface and the fluid is 125 W/m2k.
SOLUTION:
Applying Newton’s law of cooling
= hA(ts-tf)
Where: h = 125W/m2k, A = 0.225m2, ts = 800C, tf = 300C.
= 125W/m2k x 0.225m2x (80-30)k = 1406.25 W
Example 5.4.3 on Radiation
Calculate the radiant heat between the floor (1.5 m x 1.5 m) of a furnace and the roof, if
the two are located 4m apart. The floor and roof temperatures are 1093°C and 315°C,
respectively. Assume that the floor and the roof have black surfaces. Take є = 0.31
Solution:
A1 = A2 = (1.5 m) (1.5 m) = 2.25 m2
T1 = 1093oC+ 273 = 1366 K
T2 = 315oC + 273 = 588 K
1-2 = A є (T14 - T24)
= 5.67x10-8 W/m2k-4 x2.25m2x 0.31 (13664-5884)
=132,971.2175W
WEEK 12 THERMODYNAMICS I
MEC I22
Learning objectives: - understanding the concept of
refrigeration
6.1 Refrigeration
Refrigeration is the process of removing heat from an enclosed space, or from a substance, and
moving it to a place where it is unobjectionable. The primary purpose of refrigeration is lowering
the temperature of the enclosed space or substance and then maintaining that lower temperature.
The term cooling refers generally to any natural or artificial process by which heat is dissipated.
The process of artificially producing extreme cold temperatures is referred to as cryogenics.
Cold is the absence of heat, hence in order to decrease a temperature, one "removes heat", rather
than "adding cold."
6.1.1 Historical applications
Ice harvesting
The use of ice to refrigerate and thus preserve food goes back to prehistoric times. Through the
ages, the seasonal harvesting of snow and ice was a regular practice of most of the ancient
cultures: Chinese, Hebrews, Greeks, Romans, and Persians. Ice and snow were stored in caves or
dugouts lined with straw or other insulating materials. The Persians stored ice in pits called
yakhchals. Rationing of the ice allowed the preservation of foods over the warm periods. This
practice worked well down through the centuries, with icehouses remaining in use into the
twentieth century.
In the 16th century, the discovery of chemical refrigeration was one of the first steps toward
artificial means of refrigeration. Sodium nitrate or potassium nitrate, when added to water,
lowered the water temperature and created a sort of refrigeration bath for cooling substances. In
Italy, such a solution was used to chill wine.
During the first half of the 19th century, ice harvesting became big business in America. New
Englander Frederic Tudor, who became known as the "Ice King", worked on developing better
insulation products for the long distance shipment of ice, especially to the tropics.
6.1.2 Current applications of refrigeration
Probably the most widely-used current applications of refrigeration are for
(1) The air-conditioning of private homes and public buildings,
(2) The refrigeration of foodstuffs in homes, restaurants and large storage warehouses.
6.2 Refrigeration in commerce and manufacturing,
(1) Refrigeration is used to liquefy gases like oxygen, nitrogen, propane and methane for
example.
(2) In compressed air purification, it is used to condense water vapor from compressed air to
reduce its moisture content.
(3) In oil refineries, chemical plants, and petrochemical plants, refrigeration is used to
maintain certain processes at their required low temperatures (for example, in the
alkylation of butenes and butane to produce a high octane gasoline component).
(4) Metal workers use refrigeration to temper steel and cutlery.
(5) In transporting temperature-sensitive foodstuffs and other materials by trucks, trains,
airplanes and sea-going vessels, refrigeration is a necessity.
(6) Dairy products are constantly in need of refrigeration, and it was only discovered in the
past few decades that eggs needed to be refrigerated during shipment rather than waiting
to be refrigerated after arrival at the grocery store.
(7) Meats, poultry and fish all must be kept in climate-controlled environments before being
sold. Refrigeration also helps keep fruits and vegetables edible longer.
6.3 HYDROCARBON REFRIGERANTS
Hydrocarbons are an environmentally friendly, non-toxic, non-ozone-depleting replacement for
obsolete Chlorofluorocarbons CFCs importation and production of which were banned from
December 31, 1995. Hydrocarbon refrigerants are naturally occurring substances obtained when
oil and gas are produced and are:
o
Safe to use with proper handling.
o
o
o
Highly efficient, reducing energy use in refrigeration and air conditioning
systems.
Able to replace CFC RI 2; CFC R22, and HFC RI 34a refrigerants in existing,
systems without components or oils having to be changed.
Economical - low purchase price as well as lower system running costs.
Hydrocarbon refrigerants have been in use since 1867, and, in conjunction with ammonia, were
the most widely used refrigerants prior to the introduction of chemical refrigerants in the 1930s.
Australia is a major producer of hydrocarbons, which are processed for a wide range of
applications, such as fuels, lubricants, plastics and chemicals. Hydrocarbon gases are used
extensively as pressure pack propellants: for portable and static energy purposes: and now as
replacements for chemical refrigerants.
6.4 HYDROCARBON REFRIGERANT SAFETY
Like many commonly used commodities such as petrol, natural gas and electricity, the use of HC
refrigerants requires common sense and observance of adequate safety procedures. It is
important to understand the volume of hydrocarbon refrigerant involved m motor vehicle air
conditioning and refrigeration system applications. A typical car air conditioning system contains
about a coffee cup full of liquid refrigerant, and a small refrigerator contains about an eggcup
full.
In all applications hydrocarbon refrigerants are much safer for the consumer than chemical
refrigerants, most of which degrade producing toxic by products following accidental release in
the presence of an adequate heat source.
6.5. Methods of refrigeration
Methods of refrigeration can be classified as non-cyclic, cyclic and thermoelectric.
6.6 Non-cyclic refrigeration
In these methods, refrigeration can be accomplished by melting ice or by subliming dry ice.
These methods are used for small-scale refrigeration such as in laboratories and workshops, or in
portable coolers.
Ice owes its effectiveness as a cooling agent to its constant melting point of 0 °C (32 °F). In
order to melt, ice must absorb 333.55 kJ/kg, (approx. 144 Btu/lb) of heat. Foodstuffs maintained
at this temperature or slightly above have an increased storage life. Solid carbon dioxide, known
as dry ice, is used also as a refrigerant. Having no liquid phase at normal atmospheric pressure, it
sublimes directly from the solid to vapor phase at a temperature of -78.5 °C (-109.3 °F). Dry ice
is effective for maintaining products at low temperatures during the period of sublimation.
6.7 Heat pump and refrigeration cycle
This consists of a refrigeration cycle, where heat is removed from a low-temperature space or
source and rejected to a high-temperature sink with the help of external work, and its inverse, the
thermodynamic power cycle. In the power cycle, heat is supplied from a high-temperature source
to the engine, part of the heat being used to produce work and the rest being rejected to a lowtemperature sink.
A refrigeration cycle describes the changes that take place in the refrigerant as it alternately
absorbs and rejects heat as it circulates through a refrigerator. It is also applied to HVACR work,
when describing the "process" of refrigerant flow through an HVACR unit, whether it is a
packaged or split system.
Heat naturally flows from hot to cold. Work is applied to cool a living space or storage volume
by pumping heat from a lower temperature heat source into a higher temperature heat sink.
Insulation is used to reduce the work and energy required to achieve and maintain a lower
temperature in the cooled space. The operating principle of the refrigeration cycle was described
mathematically by Sadi Carnot in 1824 as a heat engine.
The most common types of refrigeration systems use the reverse-Rankine vapor-compression
refrigeration cycle although absorption heat pumps are used in
WEEK 13 THERMODYNAMICS I
MEC I22
Learning objectives: - understanding the classification of refrigeration cycles.
6.3.1 CLASSIFICATION OF REFRIGERATION CYCLE
Cyclic refrigeration can be classified as:
1. Vapor cycle, and
2. Gas cycle
Vapor cycle refrigeration can further be classified as:
1. Vapor compression refrigeration
2. Vapor absorption refrigeration
The vapor-compression cycle is used in most household refrigerators as well as in many large
commercial and industrial refrigeration systems. Figure 1 provides a schematic diagram of the
components of a typical vapor-compression refrigeration system.
Figure 6.3.1: Vapor compression refrigeration
The thermodynamics of the cycle can be analyzed on a diagram as shown in Figure 2. In this
cycle, a circulating refrigerant such as Freon enters the compressor as a vapor. From point 1 to
point 2, the vapor is compressed at constant entropy and exits the compressor superheated.
superheated From
point 2 to point 3 and on to point 4, the superheated vapor travels through the condenser which
first cools and removes the superheat and then conden
condenses
ses the vapor into a liquid by removing
additional heat at constant pressure and temperature. Between points 4 and 5, the liquid
refrigerant goes through the expansion
pansion valve (also called a throttle valve) where its pressure
abruptly decreases, causing flash evaporation and auto-refrigeration
refrigeration of, typically, less than half
of the liquid.
Figure 6.3.2: Temperature–Entropy diagram
That results in a mixture of liquid and vapor at a lower temperature and pressure as shown at
point 5. The cold liquid-vapor mixture then travels through the evaporator coil or tubes and is
completely vaporized by cooling the warm air (from the space being refrigerated) being blown
by a fan across the evaporator coil or tubes. The resulting refrigerant vapor returns to the
compressor inlet at point 1 to complete the thermodynamic cycle.
The above discussion is based on the ideal vapor-compression refrigeration cycle, and does not
take into account real-world effects like frictional pressure drop in the system, slight
thermodynamic irreversibility during the compression of the refrigerant vapor, or non-ideal gas
behavior (if any).
More information about the design and performance of vapor-compression refrigeration systems
is available in the classic "Perry's Chemical Engineers' Handbook".
Vapor absorption cycle
In the early years of the twentieth century, the vapor absorption cycle using water-ammonia
systems was popular and widely used but, after the development of the vapor compression cycle,
it lost much of its importance because of its low coefficient of performance (about one fifth of
that of the vapor compression cycle). Nowadays, the vapor absorption cycle is used only where
waste heat is available, where heat is derived from solar collectors, or electricity is unavailable.
The absorption cycle is similar to the compression cycle, except for the method of raising the
pressure of the refrigerant vapor. In the absorption system, the compressor is replaced by an
absorber which dissolves the refrigerant in a suitable liquid, a liquid pump which raises the
pressure and a generator which, on heat addition, drives off the refrigerant vapor from the highpressure liquid. Some work is required by the liquid pump but, for a given quantity of
refrigerant, it is much smaller than needed by the compressor in the vapor compression cycle. In
an absorption refrigerator, a suitable combination of refrigerant and absorbent is used. The most
common combinations are ammonia (refrigerant) and water (absorbent), and water (refrigerant)
and lithium bromide (absorbent).
Gas cycle
When the working fluid is a gas that is compressed and expanded but doesn't change phase, the
refrigeration cycle is called a gas cycle. Air is most often this working fluid. As there is no
condensation and evaporation intended in a gas cycle, components corresponding to the
condenser and evaporator in a vapor compression cycle are the hot and cold gas-to-gas heat
exchangers in gas cycles.
The gas cycle is less efficient than the vapor compression cycle because the gas cycle works on
the reverse Brayton cycle instead of the reverse Rankine cycle. As such the working fluid does
not receive and reject heat at constant temperature. In the gas cycle, the refrigeration effect is
equal to the product of the specific heat of the gas and the rise in temperature of the gas in the
low temperature side. Therefore, for the same cooling load, a gas refrigeration cycle will require
a large mass flow rate and would be bulky.
Because of their lower efficiency and larger bulk, air cycle coolers are not often used nowadays
in terrestrial cooling devices. The air cycle machine is very common, however, on gas turbinepowered jet aircraft because compressed air is readily available from the engines' compressor
sections. These jet aircraft's cooling and ventilation units also serve the purpose of pressurizing
the aircraft.
Thermoelectric refrigeration
Thermoelectric cooling uses the Peltier effect to create a heat flux between the junctions of two
different types of materials. This effect is commonly used in camping and portable coolers and
for cooling electronic components and small instruments.
Magnetic refrigeration
Magnetic refrigeration, or adiabatic demagnetization, is a cooling technology based on the
magneto-caloric effect, an intrinsic property of magnetic solids. The refrigerant is often a
paramagnetic salt, such as cerium magnesium nitrate. The active magnetic dipoles in this case
are those of the electron shells of the paramagnetic atoms.
A strong magnetic field is applied to the refrigerant, forcing its various magnetic dipoles to align
and putting these degrees of freedom of the refrigerant into a state of lowered entropy. A heat
sink then absorbs the heat released by the refrigerant due to its loss of entropy. Thermal contact
with the heat sink is then broken so that the system is insulated, and the magnetic field is
switched off. This increases the heat capacity of the refrigerant, thus decreasing its temperature
below the temperature of the heat sink.
Because few materials exhibit the required properties at room temperature, applications have so
far been limited to cryogenics and research.
Other methods
Other methods of refrigeration include the air cycle machine used in aircraft; the vortex tube
used for spot cooling, when compressed air is available; and thermo acoustic refrigeration using
sound waves in a pressurized gas to drive heat transfer and heat exchange.
Unit of refrigeration
Domestic and commercial refrigerators may be rated in kJ/s, or Btu/h of cooling. Commercial
refrigerators in the US are mostly rated in tons of refrigeration, but elsewhere in kW. One ton of
refrigeration capacity can freeze one short ton of water at 0 °C (32 °F) in 24 hours. Based on
that:
Latent heat of ice (i.e., heat of fusion) = 333.55 kJ/kg ≈ 144 Btu/lb
One short ton = 2000 lb
Heat extracted = (2000)(144)/24 hr = 288000 Btu/24 hr = 12000 Btu/hr = 200 Btu/min
1 ton refrigeration = 200 Btu/min = 3.517 kJ/s = 3.517 kW
A much less common definition is: 1 tonne of refrigeration is the rate of heat removal required to
freeze a metric ton (i.e., 1000 kg) of water at 0 °C in 24 hours. Based on the heat of fusion being
333.55 kJ/kg, 1 tonne of refrigeration = 13,898 kJ/h = 3.861 kW. As can be seen, 1 tonne of
refrigeration is 10% larger than 1 ton of refrigeration.
Most residential air conditioning units range in capacity from about 1 to 5 tons of refrigeration.
WEEK 14 THERMODYNAMICS I
MEC I22
Learning objectives: - understanding the concept of air conditioning systems
4.1 Air conditioning
The term air conditioning refers to the cooling and dehumidification of indoor air for thermal
comfort. In a broader sense, the term can refer to any form of cooling, heating, ventilation or
disinfection that modifies the condition of air. An air conditioner (AC or A/C in North American
English, or HVAC in British, Singapore and Australian English) is an appliance, system, or
mechanism designed to stabilize the air temperature and humidity within an area (used for
cooling as well as heating depending on the air properties at a given time), typically using a
refrigeration cycle but sometimes using evaporation, most commonly for comfort cooling in
buildings and motor-cars.
Air conditioning engineers broadly divide air conditioning applications into comfort and process.
Comfort applications aim to provide a building indoor environment that remains relatively
constant in a range preferred by humans despite changes in external weather conditions or in
internal heat loads.
Fig 6.5.1.1: air conditioning system
Air conditioning makes deep plan buildings feasible, for otherwise they'd have to be built
narrower or with light wells so that inner spaces receive sufficient outdoor air via natural
ventilation. Air conditioning also allows buildings to be taller since wind speed increases
significantly with altitude making natural ventilation impractical for very tall buildings. Comfort
applications for various building types are quite different and may be categorized as
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Low-Rise Residential buildings, including single family houses, duplexes, and small
apartment buildings
High-Rise Residential buildings, such as tall dormitories and apartment blocks
Commercial buildings, which are built for commerce, including offices, malls, shopping
centers, restaurants, etc.
Institutional buildings, which includes hospitals, governmental, academic, and so on.
Industrial spaces where thermal comfort of workers is desired.
In addition to buildings, air conditioning can be used for many types of transportation - motorcars and other land vehicles, trains, ships, aircraft, and spacecraft.
Process applications aim to provide a suitable environment for a process being carried out,
regardless of internal heat and humidity loads and external weather conditions. Although often in
the comfort range, it is the needs of the process that determine conditions, not human preference.
Process applications include these:
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Hospital operating theatres, in which air is filtered to high levels to reduce infection risk
and the humidity controlled to limit patient dehydration. Although temperatures are often
in the comfort range, some specialist procedures such as open heart surgery require low
temperatures (about 18 °C, 64 °F) and others such as neonatal relatively high
temperatures (about 28 °C, 82 °F).
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Clean rooms for the production of integrated circuits, pharmaceuticals, and the like, in
which very high levels of air cleanliness and control of temperature and humidity are
required for the success of the process.
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Facilities for breeding laboratory animals. Since many animals normally only reproduce
in spring, holding them in rooms at which conditions mirror spring all year can cause
them to reproduce year-round.
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Aircraft air conditioning. Although nominally aimed at providing comfort for passengers
and cooling of equipment, aircraft air conditioning presents a special process because of
the low air pressure outside the aircraft
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Data processing centers
Textile factories
Physical testing facilities
Plants and farm growing areas
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Nuclear facilities
Chemical and biological laboratories
Mines
Industrial environments
Food cooking and processing areas
In both comfort and process applications the objective may be to not only control temperature,
but also humidity, air quality and air movement from space to space.
6.5.2 Humidity control
Refrigeration air conditioning equipment usually reduces the humidity of the air processed by the
system. The relatively cold (below the dew-point) evaporator coil condenses water vapor from
the processed air, (much like an ice-cold drink will condense water on the outside of a glass),
sending the water to a drain and removing water vapor from the cooled space and lowering the
relative humidity. Since humans perspire to provide natural cooling by the evaporation of
perspiration from the skin, drier air (up to a point) improves the comfort provided. The comfort
air conditioner is designed to create a 40% to 60% relative humidity in the occupied space. In
food retailing establishment’s large open chiller cabinets act as highly effective air
dehumidifying units.
A specific type of air conditioner that is used only for dehumidifying is called a dehumidifier. A
dehumidifier is different from a regular air conditioner in that both the evaporator and condenser
coils are placed in the same air path, and the entire unit is placed in the environment that is
intended to be conditioned (in this case dehumidified), rather than requiring the condenser coil to
be outdoors. Having the condenser coil in the same air path as the evaporator coil produces
warm, dehumidified air. The evaporator (cold) coil is placed first in the air path, dehumidifying
the air exactly as a regular air conditioner does. The air next passes over the condenser coil rewarming the now dehumidified air. Note that the terms "condenser coil" and "evaporator coil" do
not refer to the behavior of water in the air as it passes over each coil; instead they refer to the
phases of the refrigeration cycle. Having the condenser coil in the main air path rather than in a
separate, outdoor air path (as in a regular air conditioner) results in two consequences-- the
output air is warm rather than cold, and the unit is able to be placed anywhere in the environment
to be conditioned, without a need to have the condenser outdoors.
Unlike a regular air conditioner, a dehumidifier will actually heat a room just as an electric
heater that draws the same amount of power (watts) as the dehumidifier. A regular air
conditioner transfers energy out of the room by means of the condenser coil, which is outside the
room (outdoors). This is a thermodynamic system where the room serves as the system and
energy is transferred out of the system. Conversely with a dehumidifier, no energy is transferred
out of the thermodynamic system (room) because the air conditioning unit (dehumidifier) is
entirely inside the room. Therefore all of the power consumed by the dehumidifier is energy that
is input into the thermodynamic system (the room), and remains in the room (as heat).
Dehumidifiers are commonly used in cold, damp climates to prevent mold growth indoors,
especially in basements. They are also sometimes used in hot, humid climates for comfort
because they reduce the humidity which causes discomfort (just as a regular air conditioner, but
without cooling the room).
6.5.3 Health implications
A poorly maintained air-conditioning system can occasionally promote the growth and spread of
microorganisms, such as Legionella pneumophila, the infectious agent responsible for
Legionnaires' disease, or hemophilic actinomycetes, but as long as the air conditioner is kept
clean these health hazards can be avoided. Conversely, air conditioning, including filtration,
humidification, cooling, disinfection, etc., can be used to provide a clean, safe, hypoallergenic
atmosphere in hospital operating rooms and other environments where an appropriate
atmosphere is critical to patient safety and well-being. Air conditioning can have a positive effect
on sufferers of allergies and asthma.
In serious heat waves, air conditioning can save the lives of the elderly. Some local authorities
even set up public cooling centers for the benefit of those without air conditioning at home.
Poorly operating air conditioning systems can generate sound levels that contribute to hearing
loss, if exposures are endured over a long term. These levels are similar to the exposure of living
near a busy highway or airport for a considerable length of time. Properly functioning air
conditioners are much quieter.
In many people, the air flow (draught) caused by an otherwise clean air conditioning system of a
car may cause acute sinusitis.
WEEK 15 THERMODYNAMICS I
MEC I22
Learning objectives: - understanding how air conditioning unit works
6.6.1 How Does an Air Conditioner Work?
Air conditioners and refrigerators work the same way. Instead of cooling just the
small, insulated space inside of a refrigerator, an air conditioner cools a room, a
whole house, or an entire business.
Air conditioners use chemicals that easily convert from a gas to a liquid and back
again. This chemical is used to transfer heat from the air inside of a home to the
outside air.
The machine has three main parts. They are a compressor, a condenser and an
evaporator. The compressor and condenser are usually located on the outside air
portion of the air conditioner. The evaporator is located on the inside the house,
sometimes as part of a furnace. That's the part that heats your house.
The working fluid arrives at the compressor as a cool, low-pressure gas. The
compressor squeezes the fluid. This packs the molecule of the fluid closer together.
The closer the molecules are together, the higher its energy and its temperature.
The working fluid leaves the compressor as a hot, high pressure gas and flows into
the condenser. If you looked at the air conditioner part outside a house, look for the
part that has metal fins all around. The fins act just like a radiator in a car and helps
the heat go away, or dissipate, more quickly.
When the working fluid leaves the condenser, its temperature is much cooler and it
has changed from a gas to a liquid under high pressure. The liquid goes into the
evaporator through a very tiny, narrow hole. On the other side, the liquid's pressure
drops. When it does it begins to evaporate into a gas.
As the liquid changes to gas and evaporates, it extracts heat from the air around it.
The heat in the air is needed to separate the molecules of the fluid from a liquid to a
gas.
The evaporator also has metal fins to help in exchange the thermal energy with the
surrounding air.
By the time the working fluid leaves the evaporator, it is a cool, low pressure gas. It
then returns to the compressor to begin its trip all over again.
Connected to the evaporator is a fan that circulates the air inside the house to blow
across the evaporator fins. Hot air is lighter than cold air, so the hot air in the room
rises to the top of a room.
There is a vent there where air is sucked into the air conditioner and goes down
ducts. The hot air is used to cool the gas in the evaporator. As the heat is removed
from the air, the air is cooled. It is then blown into the house through other ducts
usually at the floor level.
This continues over and over and over until the room reaches the temperature you
want the room cooled to. The thermostat senses that the temperature has reached the
right setting and turns off the air conditioner. As the room warms up, the thermostat
turns the air conditioner back on until the room reaches the temperature.
6.6.2 Heat Pump
Imagine that you took an air conditioner and flipped it
around so that the hot coils were on the inside and the cold
coils were on the outside. Then you would have a heater. It
turns out that this heater works extremely well. Rather than
burning a fuel, what it is doing is "moving heat."
A heat pump is an air conditioner that contains a valve that lets it switch between
"air conditioner" and "heater." When the valve is switched one way, the heat pump
acts like an air conditioner, and when it is switched the other way it reverses the
flow of the liquid inside the heat pump and acts like a heater.
Heat pumps can be extremely efficient in their use of energy. But one problem with
most heat pumps is that the coils in the outside air collect ice. The heat pump has to
melt this ice periodically, so it switches itself back to air conditioner mode to heat up
the coils. To avoid pumping cold air into the house in air conditioner mode, the heat
pump also lights up burners or electric strip heaters to heat the cold air that the air
conditioner is pumping out. Once the ice is melted, the heat pump switches back to
heating mode and turns off the burners.
6.6.3 Energy use
It should be noted that in a thermodynamically closed system, any energy input into the
system that is being maintained at a set temperature (which is a standard mode of
operation for modern air conditioners) requires that the energy removal rate from the air
conditioner increase. This increase has the effect that for each unit of energy input into
the system (say to power a light bulb in the closed system) requires the air conditioner to
remove that energy. In order to do that the air conditioner must increase its consumption
by the inverse of its efficiency times the input unit of energy. As an example, presume
that inside the closed system a 100 watt light bulb is activated, and the air conditioner has
an efficiency of 200%. The air conditioner's energy consumption will increase by 50
watts to compensate for this, thus making the 100 W light bulb utilize a total of 150 W of
energy.
Note that it is typical for air conditioners to operate at "efficiencies" of significantly
greater than 100%.
6.6.4 Automobile air conditioners
Air conditioner systems are designed to allow the driver and or passengers feel more
comfortable during uncomfortably warm humid or hot trips in a vehicle. Cars in hot
climates often are fitted with air conditioning. There has been much debate and
discussion on what the usage of an air conditioner does to the gas mileage of a vehicle.
Factors such as wind resistance aerodynamics and engine power and weight have to be
factored into finding the true variance between using the air conditioning system and not
using it when figuring out difference in actual gas mileage. Other factors on the impact
on the engine and an overall engine heat increase can have a impact on the cooling
system of the vehicle.
6.6.5 Portable air conditioners
A portable air conditioner is one on wheels that can be easily transported inside a home
or office. They are currently available with capacities of about 6,000 to 60,000 BTU/h
(1,800 to 18,000 watts output) and with and without electric resistance heaters. Portable
true air conditioners come in two forms, split and hose. Evaporative coolers, sometimes
called conditioners, are also portable.
Air-cooled portable air conditioners are compressor-based refrigerant systems that use air
to exchange heat, in the same way as a car or typical household air conditioner. With this
type of system the air is dehumidified as it is cooled. They collect water condensed from
the cooled air, and produce hot air which must be vented outside of the cooled area (they
transfer heat from the air in the cooled area to air which must be vented).
A split system has an indoor unit on wheels connected to an outdoor unit via flexible
pipes, similar to a permanently fixed installed unit.
A single-duct unit draws air out of the room to cool its condenser, and then vents it
outside. This air is replaced by hot air from outside or other rooms, thus reducing
efficiency. Modern units run on approximately 1 to 3 ratio i.e., to produce 3 kW of
cooling this will use 1 kW of electricity. A dual-duct unit draws air from outside to cool
its condenser instead of from inside the room, and thus is more efficient than most singleduct units.
As a rule of thumb, 400 square feet (37 m²) can be cooled per 12,000 BTU/h (3.5 kW or
one ton of air conditioning) by a refrigerative air conditioner. However, other factors will
affect the total heat load.
Evaporative air coolers, sometimes called air conditioners, do not have a compressor or
condenser. Instead liquid water is evaporated, releasing the vapor into the cooled area.
Evaporating water absorbs a significant amount of heat, the latent heat of vaporization,
cooling the air—humans and other animals use the same mechanism to cool themselves
by sweating. Disadvantages are that unless ambient humidity is low (dry climate) cooling
is limited and the cooled air is very humid and can feel clammy. They have the advantage
of needing no hoses to vent heat outside the cooled area, making them truly portable; and
they are cheaper to install and use much less energy than refrigerative air conditioners.