Course content
1. Review of the Second Law of Thermodynamics
2. Internal Combustion Engines
3. Steam Power Plants
4. Refrigeration
2
Course Objectives
The student is expected to:
•
Appreciate and the understand the thermodynamic principles in relation to
the Second law and its distinction from the first law.
•
Understand the operating mechanisms of Internal Combustion Engines
•
Know and understand the parameters of interest with respect to Engine
Performance Parameters
•
Understand the operating mechanisms and performance indicators of Steam
Power Plants
•
Develop a basic understanding of the operations of refrigeration systems 3
Course references
•
J.B. Ott & J. Boerio-Goates (2011) Chemical Thermodynamics: Advanced
Applications
•
Sandler, Stanley I (2016); Chemical, Biochemical, And Engineering
Thermodynamics; John Wiley and Sons Inc.
•
G. Astarita (2013). Thermodynamics: An advanced Textbook for chemical
Engineers. Pleneum Press, New York
•
Michael J. Moran, Howard N. Shapiro, Fundamentals of Engineering
Thermodynamics. 5th Edition, John Wiley and Sons, 2006
4
Course organisation
• 4 hours regular lectures per week
• Mid-semester exam (40% of assessment)*
• Final examination (60% of assessment)*
• Academic/Technical discussions: Email at your convenience
5
Review of the Second Law of
Thermodynamics
6
Review of the Second Law of Thermodynamics
Distinction between the 1st and 2nd Laws
Quiz
What happens to the energy that
leaves this cup of coffee when it
cools down?
7
Review of the Second Law of Thermodynamics
Distinction between the 1st and 2nd Laws
•
It is common experience that a cup of hot coffee left in a cooler
room eventually cools off.
•
This process satisfies the first law of thermodynamics since the
amount of energy lost by the coffee is equal to the amount gained
by the surrounding air. But can the reverse occur?
•
The first law places no restriction on the direction of a process,
but satisfying the first law does not ensure that the process can
actually occur.
•
This inadequacy of the first law to identify whether a process can
take place is remedied by introducing another general principle,
the second law of thermodynamics.
8
Review of the Second Law of Thermodynamics
Distinction between the 1st and 2nd Laws
•
The use of the second law of thermodynamics is not limited
to identifying the direction of processes.
•
The second law also asserts that energy has quality as well
as quantity.
•
The first law is concerned with the quantity of energy and
the transformations of energy from one form to another with
no regard to its quality.
•
The second law provides the necessary means to determine
the quality as well as the degree of degradation of energy
during a process.
9
Review of the Second Law of Thermodynamics
Thermal Energy Reservoirs
•
In the development of the second law of thermodynamics, it is very convenient to
have a hypothetical body with a relatively large thermal energy capacity (mass x
specific heat)
•
This hypothetical body
that can supply or absorb
finite amounts of heat
without undergoing any
change in temperature.
10
Review of the Second Law of Thermodynamics
Thermal Energy Reservoirs
•
Such a body is called a thermal energy reservoir, or just a reservoir.
•
In practice, large bodies of water such as oceans, lakes, and rivers as well as the
atmospheric air can be modelled accurately as thermal energy reservoirs.
11
Review of the Second Law of Thermodynamics
Thermal Energy Reservoirs
•
The atmosphere, for example, does not warm up as a result of heat losses from
residential buildings in winter.
•
Likewise, waste energy dumped in large rivers by power plants do not cause any
significant change in water temperature.
12
Review of the Second Law of Thermodynamics
Thermal Energy Reservoirs
•
The air in a room, for example, can be treated as a
reservoir in the analysis of the heat dissipation from a TV
set in the room.
•
Since the amount of heat transfer from the TV set to the
room air is not large enough to have a noticeable effect on
the room air temperature.
•
Thermal energy reservoirs are often referred to as heat
reservoirs since they supply or absorb energy in the form
of heat.
•
A reservoir that supplies energy in the form of heat is
called a source, and one that absorbs energy in the form
of heat is called a sink.
13
Review of the Second Law of Thermodynamics
Heat Engines
•
Work can be converted to heat directly and completely as is
the case with a water heater
•
But converting heat to work requires the use of some special
devices called heat engines.
14
Review of the Second Law of Thermodynamics
Heat Engines
•
Heat engines differ but they share the following
characteristics:
•
They receive heat from a high-temperature source (solar
energy, oil furnace, nuclear reactor, etc.).
•
They convert part of this heat to work (usually in the form of a
rotating shaft).
•
They reject the remaining waste heat to a low-temperature
sink (the atmosphere, rivers, etc.).
•
They operate in a cycle.
15
Heat Engines
•
The term heat engine is often used in a
broader sense to include work-producing
devices.
•
Engines that involve internal combustion
such as gas turbines and car engines fall
into this category.
•
These devices operate in a mechanical
cycle but not in a thermodynamic cycle
since the working fluid (the combustion
gases) does not undergo a complete cycle.
16
Review of the Second Law of Thermodynamics
Heat Engines
•
Instead of being cooled to the initial temperature, the exhaust gases are purged
and replaced by fresh air-and-fuel mixture at the end of the cycle.
17
Review of the Second Law of Thermodynamics
Heat Engines
•
The work-producing device that best fits into the definition of a heat engine is
the steam power plant, which is an external-combustion engine.
18
Review of the Second Law of Thermodynamics
Heat Engines
•
The steam power plant is an external-combustion engine.
•
The combustion takes place outside the engine, and the thermal energy released
during this process is transferred to the steam as heat.
19
Review of the Second Law of Thermodynamics
Heat Engines
•
= amount of heat supplied to
steam boiler from a high temperature
source (furnace).
•
= amount of heat rejected from
steam in condenser to a low
temperature sink (the atmosphere,
river, etc.)
•
= amount of work delivered by
steam as it expands in turbine.
•
= amount of work required to
20
compress water to boiler pressure.
Review of the Second Law of Thermodynamics
Heat Engines
•
The net work can also be determined
from the heat transfer data alone.
•
The four components of the steam power
plant together with the connecting pipes,
always contain the same fluid (assuming
no steam leaks) and can be analyzed as a
closed system.
•
Therefore the net work output of the
system is also equal to the net heat
transfer to the system:
21
,
Review of the Second Law of Thermodynamics
Heat Engines
•
The net work output of this power
plant is simply the difference
between the total work output of
the plant and the total work input
,
22
Review of the Second Law of Thermodynamics
Thermal Efficiency of Heat Engines
•
is never zero i.e. only part of the heat
transferred to the heat engine is converted to
work.
•
The fraction of the heat input that is converted
to net work output is a measure of the
performance of a heat engine and is called the
thermal efficiency,
,
•
For heat engines, the desired output is the net
work output, and the required input is the
amount of heat supplied to the working fluid
23
Review of the Second Law of Thermodynamics
Thermal Efficiency of Heat Engines
•
Cyclic devices of practical interest such as heat engines
and refrigerators operate between a high-temperature
medium (reservoir) at temperature
and a lowtemperature medium (or reservoir) at temperature .
•
To bring uniformity to the treatment of heat engines,
refrigerators, and heat pumps, we define these two
quantities:
•
= magnitude of heat transfer between the cyclic device
and the high temperature medium at temperature
•
= magnitude of heat transfer between the cyclic
device and the low temperature medium at temperature
.
24
Review of the Second Law of Thermodynamics
Thermal Efficiency of Heat Engines
•
Thermal efficiency is a measure of how efficiently a heat
engine converts the heat that it receives to work.
•
Engineers are constantly trying to improve the
efficiencies of these heat engines since increased
efficiency means less fuel consumption and less
pollution.
•
The thermal efficiencies of work-producing devices are
relatively low.
25
Review of the Second Law of Thermodynamics
Thermal Efficiency of Heat Engines
•
The thermal efficiencies of work-producing devices are
relatively low.
•
Spark-ignition automobile engines – 25% (meaning
an automobile engine converts about 25% of the
chemical energy of the gasoline to mechanical work.
•
Diesel engines – 40% and
•
Large gas-turbine plants 60%
26
Review of the Second Law of Thermodynamics
Kelvin–Planck Statement
•
We have demonstrated that, even under ideal
conditions, no heat engine can convert all the heat it
receives to useful work.
•
This limitation on the thermal efficiency of heat engines
forms the basis for the Kelvin–Planck statement of the
second law of thermodynamics.
•
It states: It is impossible for any device that operates
on a cycle to receive heat from a single reservoir and
produce a net amount of work.
27
Review of the Second Law of Thermodynamics
Kelvin–Planck Statement
•
It can also be expressed as:
•
No heat engine can have a thermal efficiency of
100%, or
•
For a power plant to operate, the working fluid must
exchange heat with the environment as well as the
furnace.
•
Note that the impossibility of having a 100% efficient
heat engine is not due to friction or other dissipative
effects.
28
Review of the Second Law of Thermodynamics *
Reversible and Irreversible Processes
•
The second law of thermodynamics states that no
heat engine can have an efficiency of 100%.
•
What then is the highest efficiency that a heat
engine can possibly have?
29
Review of the Second Law of Thermodynamics *
Reversible and Irreversible Processes
•
Lets define an ideal (perfect) process first, which is called the
reversible process.
•
Once a cup of hot coffee cools, it will not heat up by
retrieving the heat it lost from the surroundings.
•
This process cannot reverse itself spontaneously and restore
the system to its initial state.
•
For this reason, they are classified as irreversible processes.
•
If it could, the surroundings, as well as the system (coffee),
would be restored to their original condition, and this
would be a reversible process.
30
Review of the Second Law of Thermodynamics
Reversible and Irreversible Processes
•
A reversible process is defined as a process that can be
reversed without leaving any trace on the surroundings.
•
This is possible only if the net heat and net work exchange
between the system and the surroundings is zero for the
combined (original and reverse).
•
Reversible processes actually do not occur in nature. They are
merely idealizations (fantasies) of actual processes.
•
It can be approximated by actual devices, but they can never be
achieved.
•
Then, why we are bothering with such fictitious processes!
31
Review of the Second Law of Thermodynamics
Reversible and Irreversible Processes
• Then, why we are
bothering with
such fictitious
processes!
32
Review of the Second Law of Thermodynamics
Reversible and Irreversible Processes
•
There are two reasons!
•
First, they are easy to analyse, since
a system passes through a series of
equilibrium states during a
reversible process;
•
Second, they serve as ideal (perfect)
models to which actual processes
can be compared.
33
Review of the Second Law of Thermodynamics
Reversible and Irreversible Processes
•
Engineers are interested in reversible processes because work-producing devices
such as car engines and gas or steam turbines deliver the most work when
reversible processes are used.
•
Work-consuming devices such as compressors, fans, and pumps consume the
least work when reversible processes are used instead of irreversible ones.
34
Review of the Second Law of Thermodynamics
Reversible and Irreversible Processes
•
The factors that cause a process to be irreversible are called irreversibilities.
•
They include
•
friction,
•
unrestrained expansion,
•
mixing of two fluids,
•
heat transfer across a fixed temperature difference,
•
electric resistance,
•
inelastic deformation of solids,
•
chemical reactions.
35
Review of the Second Law of Thermodynamics
Entropy
•
Remember the simple definition of energy is the
ability to do work.
•
Entropy is a measure of how much energy is not
available to do work.
•
Although all forms of energy are interconvertible,
and all can be used to do work, it is not always
possible, even in principle, to convert the entire
available energy into work.
36
Review of the Second Law of Thermodynamics
Entropy
•
We can see how entropy is defined by examining any
reversible process.
•
In reversible processes,
𝑳
𝑳
𝑳
𝑯
𝑯
𝑯
𝑳
𝑯
37
Review of the Second Law of Thermodynamics
Entropy
•
This ratio is designated as Entropy, S and is defined as
𝒓𝒆𝒗
•
where Q is the heat transfer, which is positive for heat transfer
into and negative for heat transfer out of,
•
and T is the absolute temperature at which the reversible
process takes place.
38
Review of the Second Law of Thermodynamics
Entropy
•
The definition of ΔS is valid strictly for reversible processes
however, we can find ΔS precisely even for real, irreversible
processes.
•
The reason is that the entropy S of a system, like internal energy
U, depends only on the state of the system and not how it
reached that condition.
39
Review of the Second Law of Thermodynamics
Entropy
•
If Entropy is a property of state, then the change in entropy ΔS of a system
between state 1 and state 2 is the same no matter how the change occurs.
•
We just need to find or imagine a reversible process that takes us from state 1 to
state 2 and calculate ΔS for that process.
•
That will be the change in entropy for any
process going from state 1 to state 2. (See
Figure)
40
Review of the Second Law of Thermodynamics
Entropy
•
Consider a hypothetical engine called a
Carnot engine which undergoes a
reversible process (Fig.).
•
Lets look at the change in entropy of a
Carnot engine and its heat reservoirs for
one full cycle.
41
Review of the Second Law of Thermodynamics
Entropy
•
The high-temp. reservoir has a loss of entropy
because heat is transferred out of it:
•
The low-temp. reservoir has a gain of entropy
because heat transfer occurs into it:
42
Review of the Second Law of Thermodynamics
Entropy
•
So the total change in entropy is
•
We know that for a Carnot engine (or any other
reversible process)
•
Therefore,
•
This result, which has general validity, means that
the total change in entropy for a system in any
reversible process is zero.
43
Review of the Second Law of Thermodynamics
Entropy
•
Overall, the system does not affect the entropy of its surroundings, since heat
transfer between them does not occur.
•
Thus the reversible process changes neither the total entropy of the system nor
the entropy of its surroundings.
•
Sometimes this is stated as follows: Reversible processes do not affect the total
entropy of the universe.
44
Review of the Second Law of Thermodynamics
Entropy
•
Real processes are not reversible so they do change total entropy. We can
use hypothetical reversible processes to determine the value of entropy in
real, irreversible processes.
•
Therefore for real processes,
•
Spontaneous heat transfer from hot to cold is an irreversible process.
•
Entropy increases in an irreversible (real) process. Let’s try and prove this
with an example.
45
Review of the Second Law of Thermodynamics
Entropy
Example 1
Calculate the total change in entropy if 4000 J of heat transfer
occurs from a high-temp. reservoir at Th = 600 K (327ºC) to a
low-temp. reservoir at Tc = 250 K(−23ºC), assuming there is
no temperature change in either reservoir. (Figure)
46
Review of the Second Law of Thermodynamics
Entropy
Solution 1
Statement:
• How can we calculate the change in entropy for an
irreversible process when
is valid only
for reversible processes?
•
Remember that the total change in entropy of the hot and
cold reservoirs will be the same whether a reversible or
irreversible process is involved in heat transfer from hot to
cold.
47
Review of the Second Law of Thermodynamics
Entropy
Solution 1 (cont’d)
Statement (cont’d)
• So we can calculate the change in
entropy of the high-temp. reservoir
for a hypothetical reversible process
in which 4000 J of heat transfer
occurs from it (Fig B);
•
Then we do the same for a
hypothetical reversible process in
which 4000 J of heat transfer occurs
to the low-temp. reservoir (Fig B).
48
Review of the Second Law of Thermodynamics
Entropy
Solution 1 (cont’d)
Statement (cont’d)
• This produces the same changes in the
hot and cold reservoirs that would
occur if the heat transfer were allowed
to occur irreversibly between them,
and so it also produces the same
changes in entropy.
49
Review of the Second Law of Thermodynamics
Entropy
Solution 1 (cont’d)
Analysis
• We now calculate the two changes in entropy. First, for the heat transfer from the
hot reservoir
•
For the cold reservoir,
•
Therefore, the total is
Note: There is an increase in entropy for the system undergoing this irreversible 50heat
transfer therefore energy has become unavailable to do work.
Review of the Second Law of Thermodynamics
Entropy
∆
, there is a larger change at lower temperatures.
∆
•
Since the change in entropy is
•
The decrease in entropy of the hot object is therefore less than the increase in
entropy of the cold object, producing an overall increase, just as seen in the
previous example.
•
Therefore the general conclusion is: there is an increase in entropy for any
system undergoing an irreversible process.
•
With respect to entropy, there are only two possibilities:
• entropy is constant for a reversible process, and
• it increases for an irreversible process.
51
Review of the Second Law of Thermodynamics**
Entropy
•
The second law of thermodynamics can be stated in terms of entropy as:
•
The total entropy of a system either increases or remains constant in any
process; it never decreases.
•
Entropy unlike energy is not conserved but increases in all real processes.
•
Reversible processes (such as in Carnot engines) are the processes in which the
most heat transfer to work takes place and are also the ones that keep entropy
constant.
•
Thus we are led to make a connection between entropy and the availability of
energy to do work.
52
Review of the Second Law of Thermodynamics
Entropy
•
What does a change in entropy mean, and why should we be interested in it?
•
One reason is that entropy is directly related to the fact that not all heat
transfer can be converted into work.
•
Lets carefully examine an example to prove it
53
Review of the Second Law of Thermodynamics
The Unavailability of Energy to Do Work
Example
Calculate the work output of an engine operating between temperatures of 600 K and
100 K for 4000 J of heat transfer to the engine.
Now suppose that the 4000 J of heat
transfer occurs first from the 600 K
reservoir to a 250 K reservoir
(without doing any work, and this
produces the increase in entropy
(9.33 J/K) calculated earlier) before
transferring into a Carnot engine
operating between 250 K and 100 K.
What work output is produced?
(Note Figure)
54
Review of the Second Law of Thermodynamics
The Unavailability of Energy to Do Work
Solution:
In both parts, we must first calculate the Carnot efficiency and then the work output.
,
;
,
;
Analysis
For the first part, Carnot efficiency is given by
Substituting the given temperatures yields
Now the work output can be calculated using the definition of efficiency for any55 heat
engine as given above.
Review of the Second Law of Thermodynamics
The Unavailability of Energy to Do Work
Solution:
Solving for W and substituting known terms gives
For the second part, similarly as the first, Carnot efficiency is
So that
∗
56
Review of the Second Law of Thermodynamics
The Unavailability of Energy to Do Work
Solution:
•
Note: There is 933 J less work from the same heat transfer in the second process.
The same heat transfer into two perfect engines produces different work outputs,
because the entropy change differs in the two cases.
•
In the second case, entropy is greater and less work is produced. Entropy is
therefore associated with the unavailability of energy to do work.
57
Review of the Second Law of Thermodynamics
The Unavailability of Energy to Do Work
•
When entropy increases, a certain amount of energy becomes permanently
unavailable to do work.
•
The energy is not lost, but its character is changed, so that some of it can never be
converted to doing work—that is, to an organized force acting through a distance.
•
For instance, in Example 11, 933 J less work was done after an increase in
entropy of 9.33 J/K occurred in the 4000 J heat transfer from the 600 K reservoir
to the 250 K reservoir.
58
Review of the Second Law of Thermodynamics
Order to Disorder
•
Entropy is related not only to the unavailability of energy to do work, it is also a
measure of disorder.
• When ice melts, it becomes more
disordered and less structured.
• The systematic arrangement of
molecules in a crystal structure is
replaced by a more random and less
orderly movement of molecules
without fixed locations or
orientations.
• Its entropy increases because heat
transfer occurs into it. Entropy is
therefore a measure of this disorder.
59
Review of the Second Law of Thermodynamics
Order to Disorder
•
Which is more disordered?
The glass of ice chips or the glass
•
of water?
For a glass of water the number of
molecules is countless.
The jumble of ice chips may look more
disordered in comparison to the glass of
water which looks uniform and
homogeneous.
•
But the ice chips place limits on the
number of ways the molecules can be
arranged.
•
The water molecules in the glass of water
can be arranged in many more ways; they
60
have greater "multiplicity" and therefore
greater entropy.
Review of the Second Law of Thermodynamics
Order to Disorder
Example 12
Find the increase in entropy of 1.00 kg of ice originally at 0º C (273 K) that is melted
to form water at 0º C.
Statement
As before, the change in entropy can be calculated from the definition of ΔS once we
find the energy Q needed to melt the ice.
Analysis
The change in entropy is defined as
Here Q is the heat transfer necessary to melt 1 kg of ice and is given by
,
where m is the mass and Lf is the latent heat of fusion. Lf=334 kJ/kg for water,
Therefore,
61
Review of the Second Law of Thermodynamics
Order to Disorder
Example 11
Analysis
Now the change in entropy is positive, since heat transfer occurs into the ice to cause
the phase change; therefore,
Note: This is a significant increase in entropy accompanying an increase in disorder.
62
Review of the Second Law of Thermodynamics
Order to Disorder
•
Lets look at another example, suppose we mix equal masses of water originally at
two different temperatures, say 20.0ºC and 40.0ºC. The result is water at an
intermediate temperature of 30.0ºC.
•
Three outcomes have resulted:
• entropy has increased,
• some energy has become unavailable to do work, and
• the system has become less orderly.
•
Let us examine these results.
63
Entropy
Order to Disorder
•
First, entropy has increased for the same reason that it did earlier.
•
Mixing the two bodies of water has the same effect as heat transfer from the hot
one and the same heat transfer into the cold one.
•
The mixing decreases the entropy of the hot water but increases the entropy of
the cold water by a greater amount, producing an overall increase in entropy.
64
Review of the Second Law of Thermodynamics
Order to Disorder
•
Second, once the two masses of water are mixed, there is only one temperature—
you cannot run a heat engine with them.
•
The energy that could have been used to run a heat engine is now unavailable to
do work.
•
Third, the mixture is less orderly, or less structured.
•
Rather than having two masses at different temperatures and with different
distributions of molecular speeds, we now have a single mass with a uniform
temperature.
•
These three results—entropy, unavailability of energy, and disorder—are not
65
only related but are in fact essentially equivalent.
Review of the Second Law of Thermodynamics
Order to Disorder
•
The entropy of a substance is lowest in the solid phase and
highest in the gas phase (Figure).
•
In the solid phase, the molecules of a substance
continually oscillate about their equilibrium positions, but
they cannot move relative to each other, and their position
at any instant can be predicted with good certainty.
•
In the gas phase, the molecules move about at random,
collide with each other, and change direction, making it
extremely difficult to predict accurately the microscopic
state of a system at any instant.
•
Associated with this molecular chaos is a high value of
entropy.
The level of molecular
disorder (entropy) of a
66
substance increases as it
melts or evaporates.
Review of the Second Law of Thermodynamics
Isentropic Processes
•
The entropy of a fixed mass can be changed by (1) heat transfer and (2)
irreversibilities.
•
Also the entropy of a fixed mass does not change during a process that is
internally reversible and adiabatic (Figure).
•
So a process during which the entropy remains
constant is called an isentropic process.
•
It is characterized by
•
i.e. a substance will have the same entropy value at
the end of the process as it does at the beginning if
the process is carried out in an isentropic manner.
67
Review of the Second Law of Thermodynamics
Isentropic Processes
•
Many engineering systems or devices such as pumps, turbines, nozzles, and
diffusers are essentially adiabatic in their operation.
•
They perform best when the irreversibilities, such as the friction associated with
the process, are minimized.
•
Therefore, an isentropic process can serve as an appropriate model for actual
processes.
•
Also, isentropic processes enable us to define efficiencies for processes to
compare the actual performance of these devices to the performance under
idealized conditions.
•
Note: A reversible adiabatic process is isentropic, but an isentropic process 68is
not necessarily a reversible adiabatic process.
Review of the Second Law of Thermodynamics
Does Entropy seem confusing?
•
Lets clarify further!
•
The quantity of energy is always preserved during an actual process (the first
law), but the quality is bound to decrease (the second law).
•
This decrease in quality is always accompanied by an increase in entropy.
69
Review of the Second Law of Thermodynamics
Does Entropy seem confusing?
•
As an example, based on what we calculated earlier;
•
Consider the transfer of 10 kJ of energy as heat from a hot medium to a cold one.
•
At the end of the process, we still have the 10 kJ of energy, but at a lower
temperature and thus at a lower quality.
•
Heat is, in essence, a form of disorganized energy, and some disorganization
(entropy) flows with heat.
70
Review of the Second Law of Thermodynamics
The Carnot Cycle**
•
We mentioned earlier that heat engines are
cyclic devices and that the working fluid of a
heat engine returns to its initial state at the end
of each cycle.
•
Work is done by the working fluid during one
part of the cycle and on the working fluid during
another part.
•
The difference between these two is the net
work delivered by the heat engine.
•
The efficiency of a heat-engine cycle greatly
71
depends on how the individual processes that
make up the cycle are executed.
Review of the Second Law of Thermodynamics
The Carnot Cycle
•
The net work and the cycle efficiency, can be maximized
by using processes that require the least amount of work
and deliver the most, that is, by using reversible
processes.
•
Therefore, it is no surprise that the most efficient cycles
are reversible cycles.
•
Reversible cycles cannot be achieved in practice because
the irreversibilities associated with each process cannot
be eliminated.
•
However, reversible cycles provide upper limits on the
72
performance of real cycles.
Review of the Second Law of Thermodynamics
The Carnot Cycle
•
Reversible heat engines and refrigerators that work on reversible cycles serve
as models to which actual heat engines and refrigerators can be compared.
•
One of the best known reversible cycle is the Carnot cycle, first proposed in
1824 by French engineer Sadi Carnot.
•
The theoretical heat engine that operates on the Carnot cycle is called the
Carnot heat engine.
•
The Carnot cycle is composed of four reversible processes
• two isothermal and two adiabatic
73
Review of the Second Law of Thermodynamics
The Carnot Cycle
•
Consider a closed system that consists of a gas contained in an adiabatic
piston–cylinder device (Figure).
•
The insulation of the cylinder head is such that it may be removed to bring the
cylinder into contact with reservoirs to provide heat transfer.
•
Let use this to describe the four reversible processes that make up the Carnot
cycle.
74
Review of the Second Law of Thermodynamics
The Carnot Cycle
Reversible Isothermal Expansion
(process 1-2, 𝑯 = constant)
• Initially (state 1), the temperature of the
gas is 𝑯 and the cylinder head is in
close contact with a source at temperature
𝑯.
•
The gas is allowed to expand slowly, doing work on the surroundings. As
the gas expands, the temperature of the gas tends to decrease.
•
But as soon as the temperature drops by an insignificant amount dT, some
heat is transferred from the reservoir into the gas, raising the gas
temperature to 𝑯 .
75
•
Thus, the gas temperature is kept constant at
𝑯.
Review of the Second Law of Thermodynamics
The Carnot Cycle
Reversible Isothermal Expansion
(process 1-2, 𝑯 = constant).
• Since the temperature difference
between the gas and the reservoir never
exceeds a differential amount dT, this is
a reversible heat transfer process.
•
It continues until the piston reaches
position 2.
•
The amount of total heat transferred to
the gas during this process is 𝑯 .
76
Review of the Second Law of Thermodynamics
The Carnot Cycle
Reversible Adiabatic Expansion
(process 2-3, temperature drops from 𝑯 to 𝑳 )
• At state 2, the reservoir that was in contact
with the cylinder head is removed and replaced
by insulation so that the system becomes
adiabatic.
•
The gas continues to expand slowly, doing work on the surroundings until its
temperature drops from 𝑯 to 𝑳 (state 3).
•
The piston is assumed to be frictionless and the process to be quasi-equilibrium
(partial equilibrium), so the process is reversible as well as adiabatic.
77
Review of the Second Law of Thermodynamics
The Carnot Cycle
Reversible Isothermal Compression
(process 3-4, 𝑳 constant).
• At state 3, the insulation at the cylinder
head is removed, and the cylinder is
brought into contact with a sink at
temperature 𝑳 .
•
Now the piston is pushed inward by an external force, doing work on the
gas.
•
As the gas is compressed, its temperature tends to rise.
•
But as soon as it rises by an infinitesimal amount dT, heat is transferred
from the gas to the sink, causing the gas temperature to drop to 𝑳 .
78
Review of the Second Law of Thermodynamics
The Carnot Cycle
Reversible Isothermal Compression
(process 3-4, 𝑳 constant).
• Thus, the gas temperature remains
constant at 𝑳 .
•
Since the temperature difference between
the gas and the sink never exceeds a
differential amount dT.
•
It continues until the piston reaches state 4.
•
The amount of heat rejected from the gas
during this process is 𝑳 .
79
Review of the Second Law of Thermodynamics
The Carnot Cycle
Reversible Adiabatic Compression
(process 4-1, temperature rises from 𝑳 to 𝑯 )
• State 4 is such that when the low-temperature
reservoir is removed, the insulation is put back
on the cylinder head,
•
The gas is then compressed in a reversible
manner, the gas returns to its initial state (state
1).
•
The temperature rises from to during this
reversible adiabatic compression process,
which completes the cycle.
80
Review of the Second Law of Thermodynamics
Carnot Principles
•
Two conclusions pertain to the thermal
efficiency of reversible and irreversible (i.e.,
actual) heat engines, and they are known as the
Carnot principles, expressed as follows:
•
The efficiency of an irreversible heat
engine is always less than the efficiency of
a reversible one operating between the
same two reservoirs.
•
The efficiencies of all reversible heat
engines operating between the same two
reservoirs are the same.
81
2. Internal Combustion
Engines
82
Internal Combustion Engines
Power cycle considerations
•
Most power-producing devices operate on cycles.
•
The power cycles encountered in actual devices are difficult to analyze because
of the presence of irreversibilities, such as friction.
•
To make the analysis of a cycle feasible, we remove irreversibilities in the
actual cycle to obtain a cycle that resembles the actual cycle closely but is
made up totally of internally reversible processes.
•
Such a cycle is called an ideal cycle.
•
This simple idealized model enables engineers to study the effects of the major
parameters that dominate the cycle without worrying about other details.
83
Internal Combustion Engines
Power cycle considerations
•
The numerical values obtained from
the analysis of an ideal cycle,
however, are not necessarily
representative of the actual cycles,
and care should be exercised in their
interpretation.
•
In our course we have simplified the
analysis of various power cycles of
practical interest to serve as the
starting point for a more in-depth
study in your careers when required.
84
Internal Combustion Engines
Power cycle considerations
•
Heat engines are designed for the purpose of converting thermal energy to
work, and their performance is expressed in terms of the thermal efficiency
•
Remember: thermal efficiency is the ratio of the net work produced by the
engine to the total heat input.
•
Remember also that heat engines that operate on a totally reversible cycle,
such as the Carnot cycle, have the highest thermal efficiency of all heat
engines operating between the same temperature levels.
•
That is, nobody can develop a cycle more efficient than the Carnot cycle.
85
Internal Combustion Engines
Power cycle considerations
•
Then the curious question naturally is:
•
If the Carnot cycle is the best possible cycle, why do we not use it as the model
cycle for all the heat engines instead of bothering with something else called
ideal cycles?
•
The answer to this question is related to the hardware.
•
Most cycles encountered in practice differ significantly from the Carnot cycle,
which makes it unsuitable as a realistic model.
•
Each ideal cycle is related to a specific work-producing device and is a perfect
version of the actual cycle.
86
Internal Combustion Engines
Power cycle considerations
•
The ideal cycles are internally reversible, but, unlike the Carnot cycle, they
are not necessarily externally reversible.
•
What does this mean?
•
A process is called internally reversible if no irreversibilities occur within the
boundaries of the system during the process.
•
A process is called externally reversible if no irreversibilities occur outside the
system boundaries during the process.
•
A process is called totally reversible, or simply reversible, if it involves no
irreversibilities within the system or its surroundings.
87
Internal Combustion Engines
Power cycle considerations
•
As an example, consider the transfer of heat to two identical systems that are
undergoing a constant-pressure (thus constant-temperature) phase-change process,
as shown in Fig.
•
Both processes are internally
reversible, since both take place
isothermally and both pass through
exactly the same equilibrium states.
•
The first process shown is externally
reversible also, since heat transfer for
this process takes place through an
infinitesimal (tiny) temperature
difference dT.
88
Internal Combustion Engines
Power cycle considerations
•
The second process, however, is
internally irreversible only, since
it involves heat transfer through a
finite temperature difference ΔT.
89
Internal Combustion Engines
Power cycle considerations
•
So when we say:
•
The ideal cycles are internally reversible, but, unlike the Carnot cycle, they are
not necessarily externally reversible.
•
We simply mean:
•
Ideal cycles may involve irreversibilities external to the system such as heat
transfer through a finite temperature difference.
•
Therefore, the thermal efficiency of an ideal cycle, in general, is less than that
of a totally reversible cycle operating between the same temperature limits.
•
90
However, it is still considerably higher than the thermal efficiency of an actual
cycle because of the perfections or idealizations utilized.
Internal Combustion Engines
Power cycle considerations
•
The idealizations or perfections (assumptions) commonly employed in the
analysis of power cycles include:
•
The cycle does not involve any friction. Therefore, the working fluid does
not experience any pressure drop as it flows in pipes or devices such as
heat exchangers.
•
All expansion and compression processes take place in a quasiequilibrium manner.
•
The pipes connecting the various components of a system are well
insulated, and heat transfer through them is negligible.
•
The changes in kinetic and potential energies of the working fluid are
negligible.
91
Internal Combustion Engines***
Power cycle considerations
•
•
So what is the role of the Carnot cycle in all this?
The real value of the Carnot cycle comes from it being a standard against
which the actual or the ideal cycles can be compared.
•
The thermal efficiency of the Carnot cycle is a function of the sink and source
temperatures only, and the thermal efficiency relation for the Carnot cycle
conveys an important message that is equally applicable to both ideal and
actual cycles, i.e.:
•
Thermal efficiency increases with an increase in the average temperature at
which heat is supplied to the system (source) or with a decrease in the average
temperature at which heat is rejected from the system (sink).
,
92
Internal Combustion Engines
Power cycle considerations
But there are some limitations in practice:
• The source and sink temperatures that can be used in practice are not without
limits.
•
These include:
•
The highest temperature (from the source) in the cycle is limited by the
maximum temperature that the components of the heat engine, such as the
piston or the turbine blades, can withstand.
•
The lowest temperature (from the sink) is limited by the temperature of the
cooling medium utilized in the cycle such as a lake, a river, or the atmospheric
air.
93
Internal Combustion Engines
Power cycle considerations
Also note the following considerations about the working fluid (air):
• In gas power cycles, the working fluid remains a gas throughout the entire
cycle.
•
Spark-ignition engines, diesel engines, and conventional gas turbines are
familiar examples of devices that operate on gas cycles.
•
In all these engines, energy is provided by burning a fuel within the system
boundaries i.e. they are internal combustion engines.
•
Because of this combustion process, the composition of the working fluid
changes from air and fuel to combustion products during the course of the
cycle.
94
Internal Combustion Engines
Power cycle considerations
Also note the following considerations about the working fluid (air):
•
Even though internal combustion engines operate on a mechanical cycle, the
working fluid does not undergo a complete thermodynamic cycle.
•
It is thrown out of the engine at some point in the cycle (as exhaust gases)
instead of being returned to the initial state.
•
This makes the actual gas power cycles rather complex.
95
Internal Combustion Engines
Power cycle considerations
•
To reduce the analysis of such cycles to a
manageable level, we utilize the following
approximations, commonly known as the airstandard assumptions:
•
The working fluid is air, which continuously
circulates in a closed loop and always behaves
as an ideal gas.
•
All the processes that make up the cycle are
internally reversible.
•
The combustion process is replaced by a heataddition process from an external source.
96
Internal Combustion Engines
Power cycle considerations
•
Air-standard assumptions (continued):
•
The exhaust process is replaced by a heatrejection process that restores the working
fluid to its initial state.
•
Air has constant specific heats whose values
are determined at room temperature (25°C)
97
Internal Combustion Engines
Overview of Reciprocating Engines
•
Despite its simplicity, the reciprocating engine
(basically a piston–cylinder device) is very
versatile and has a wide range of applications.
•
It is the driving force of the vast majority of
automobiles, trucks, ships, and electric power
generators.
•
The basic components of a reciprocating
engine are shown in the Figure.
98
Internal Combustion Engines
Overview of Reciprocating Engines
•
The piston reciprocates in the cylinder between
two fixed positions called the top dead center
(TDC)
• i.e. the position of the piston when it forms
the smallest volume in the cylinder
•
And the bottom dead center (BDC)
• i.e. the position of the piston when it forms
the largest volume in the cylinder.
•
The distance between the TDC and the BDC is
the largest distance that the piston can travel in
one direction, and it is called the stroke of the
engine.
99
Internal Combustion Engines
Overview of Reciprocating Engines
•
The diameter of the piston is called the bore.
•
The air or air–fuel mixture is drawn into the
cylinder through the intake valve, and the
combustion products are expelled from the
cylinder through the exhaust valve.
100
Internal Combustion Engines
Overview of Reciprocating Engines
•
The minimum volume formed in the
cylinder when the piston is at TDC
is called the clearance volume
(Figure).
•
The volume displaced by the piston
as it moves between TDC and BDC
is called the displacement volume.
101
Internal Combustion Engines
Overview of Reciprocating Engines
•
The ratio of the maximum volume
formed in the cylinder to the
minimum (clearance) volume is
called the compression ratio, r of the
engine:
•
Note that the compression ratio is a
volume ratio.
102
Internal Combustion Engines
Overview of Reciprocating Engines
•
Another important relationship between the
cylinder volumes is the mean effective
pressure.
•
The mean effective pressure can be used as
a parameter to compare the performances of
reciprocating engines of equal size.
•
The engine with a larger value of MEP
delivers more net work per cycle and thus
performs better.
103
Internal Combustion Engines
Overview of Reciprocating Engines
•
Reciprocating engines are classified as spark-ignition (SI) engines or
compression-ignition (CI) engines depending on how the combustion
process in the cylinder is initiated.
•
In SI engines, the combustion of the air–fuel mixture is initiated by a
spark plug.
•
In CI engines, the air–fuel mixture is self-ignited as a result of
compressing the mixture above its self-ignition temperature.
•
Lets discuss the Otto and Diesel cycles, which are the ideal cycles for the SI
and CI reciprocating engines, respectively.
104
Internal Combustion Engines
Otto Cycle
•
The Otto cycle is the ideal cycle for spark-ignition reciprocating engines.
•
It is named after Nikolaus A. Otto, who built a successful four-stroke engine
in 1876 in Germany.
•
In most spark-ignition engines, the piston executes four complete strokes
within the cylinder, and the crankshaft completes two revolutions for each
thermodynamic cycle.
•
These engines are called four-stroke internal combustion engines.
•
Lets examine a schematic of each stroke as well as a P-v diagram for an
actual four-stroke spark-ignition engine.
105
Internal Combustion Engines
Otto Cycle
•
Initially, both the intake and the exhaust valves are closed, and the piston is at
its lowest position (BDC).
•
During the compression stroke, the piston moves upward, compressing the air–
fuel mixture.
106
Internal Combustion Engines
Otto Cycle
•
Shortly before the piston reaches its highest position (TDC), the spark plug fires
and the mixture ignites, increasing the pressure and temperature of the system.
•
The high-pressure gases force the piston down, which in turn forces the
crankshaft to rotate, producing a useful work output during the expansion or
power stroke.
107
Internal Combustion Engines
Otto Cycle
•
At the end of this stroke, the piston is at its lowest position (the completion of
the first mechanical cycle), and the cylinder is filled with combustion products.
•
Now the piston moves upward one more time, purging the exhaust gases
through the exhaust valve (the exhaust stroke).
108
Internal Combustion Engines
Otto Cycle
•
It then moves down a second time, drawing in fresh air–fuel mixture through
the intake valve (the intake stroke).
109
Internal Combustion Engines
Otto Cycle
110
Internal Combustion Engines
Otto Cycle
•
The figure shown is the P-v diagram
indicating the path of the four-stroke
process.
•
Note that the pressure in the cylinder
is slightly above the atmospheric value
during the exhaust stroke and slightly
below during the intake stroke.
111
Internal Combustion Engines
Otto Cycle
•
Lets examine the Two-Stroke Engine
•
In two-stroke engines (usually found in
motorcycles), all four functions described
above are executed in just two strokes:
•
the power stroke and
•
the compression stroke.
112
Internal Combustion Engines
Otto Cycle
•
In two stroke engines, the
crankcase is sealed, and the
outward motion of the piston is
used to slightly pressurize the
air–fuel mixture in the crankcase
(Figure).
•
Also, the intake and exhaust
valves are replaced by openings
in the lower portion of the
cylinder wall.
113
Internal Combustion Engines
Otto Cycle
•
During the latter part of the power
stroke, the piston uncovers first the
exhaust port, allowing the exhaust
gases to be partially expelled.
•
It then uncovers the intake port,
allowing the fresh air–fuel mixture
to rush in and drive most of the
remaining exhaust gases out of the
cylinder.
•
This mixture is then compressed as
the piston moves upward during the
compression stroke and is
subsequently ignited by a spark plug.
114
Internal Combustion Engines
Otto Cycle
•
The two-stroke engines are generally
less efficient than their four-stroke
counterparts
•
This is because of the incomplete
expulsion of the exhaust gases and the
partial expulsion of the fresh air–fuel
mixture with the exhaust gases.
•
However, they are relatively simple and
inexpensive, and they have high powerto-weight and power-to-volume ratios.
•
This makes them suitable for
applications requiring small size and
weight such as for motorcycles, chain
saws, and lawn mowers
115
Internal Combustion Engines
Otto Cycle***
Thermodynamic analysis of Four Stroke Engine
•
The thermodynamic analysis of the actual fourstroke or two-stroke cycles can be simplified
significantly using the air-standard assumptions
(Figure).
•
The resulting cycle, which closely resembles the
actual operating conditions, is the ideal Otto
cycle.
•
It consists of four internally reversible processes
116
Internal Combustion Engines
Otto Cycle
Thermodynamic analysis of
Four Stroke Engine
•
It consists of four internally
reversible processes
•
1-2 Isentropic (reversible
adiabatic) compression
•
2-3 Constant-volume heat
addition
•
3-4 Isentropic expansion
•
4-1 Constant-volume heat
rejection
117
Internal Combustion Engines
Otto Cycle
Thermodynamic analysis of Four Stroke Engine
• The Otto cycle is executed in a closed system, and disregarding the changes in
kinetic and potential energies, the energy balance for any of the processes is
expressed, on a unit-mass basis,
•
Then the thermal efficiency of the ideal Otto cycle under the cold air standard
assumptions becomes
,
118
Internal Combustion Engines
Otto Cycle
Thermodynamic analysis of Four Stroke Engine
,
•
Where
•
•
•
is the compression ratio
is the specific heat ratio
Note: The amount of energy needed to raise the temperature of a unit mass
of a substance by one degree is called the specific heat at constant
119
volume 𝒗 for a constant-volume process and the specific heat at constant
pressure 𝒑 for a constant-pressure process.
Internal Combustion Engines
Otto Cycle
Thermodynamic analysis of Four Stroke Engine
• The earlier equations shows that the thermal efficiency of an ideal Otto cycle
depends on the compression ratio of the engine and the specific heat ratio of
the working fluid.
•
The thermal efficiency of the ideal Otto cycle therefore increases with both
the compression ratio and the specific heat ratio.
•
This is also true for the actual spark-ignition internal combustion engines
120
Internal Combustion Engines
Otto Cycle
Thermodynamic analysis of Four Stroke Engine
• A plot of thermal efficiency versus the
compression ratio is given in the Figure for k =
1.4, which is the specific heat ratio value of air
at room temperature.
•
For a given compression ratio, the thermal
efficiency of an actual spark-ignition engine
is less than that of an ideal Otto cycle.
•
This is because of the irreversibilities, such as
friction, and other factors such as incomplete
combustion.
121
Internal Combustion Engines
Otto Cycle
Thermodynamic analysis of Four Stroke Engine
• We can observe from the Figure that the
thermal efficiency curve is rather steep at low
compression ratios but flattens out starting
with a compression ratio value of about 8.
•
Therefore, the increase in thermal efficiency
with the compression ratio is not as obvious at
high compression ratios.
•
Also, when high compression ratios are used,
the temperature of the air–fuel mixture rises
above the auto-ignition temperature of the
fuel.
122
Internal Combustion Engines
Otto Cycle
Thermodynamic analysis of Four Stroke Engine
• The auto-ignition temperature is the
temperature at which the fuel ignites without
the help of a spark.
•
When the temperature of the air–fuel mixture
rises above the auto-ignition temperature of
the fuel during the combustion process, an
early and rapid burn of the fuel is caused.
•
This occurs at some point or points ahead of
the flame front, followed by almost
instantaneous inflammation of the end gas.
123
Internal Combustion Engines
Otto Cycle
Thermodynamic analysis of Four Stroke Engine
• This premature ignition of the fuel, called
auto-ignition, produces an audible noise,
which is called engine knock.
•
Auto-ignition in spark-ignition engines cannot
be tolerated because it hurts performance and
can cause engine damage.
•
The requirement that auto-ignition should not
be allowed places an upper limit on the
compression ratios that can be used in spark
ignition internal combustion engines.
124
Internal Combustion Engines
Otto Cycle*
Thermodynamic analysis of Four Stroke Engine
• An improvement of the thermal efficiency of
gasoline engines by utilizing higher
compression ratios (up to about 12) without
facing the auto-ignition problem is always
required.
•
This improvement has been made possible by
using gasoline blends that have good
antiknock characteristics.
•
The introduction of additivies into the fuel is
an inexpensive method of raising the octane
rating, which is a measure of the engine
knock resistance of a fuel.
125
Internal Combustion Engines
Diesel Cycle
•
The Diesel cycle is the ideal cycle for
Compression-Ignition (CI) reciprocating
engines.
•
The CI engine, first proposed by Rudolph
Diesel in the 1890s, is very similar to the SI
engine we have discussed
•
They differ mainly in the method of initiating
combustion.
126
Internal Combustion Engines
Diesel Cycle
•
In SI engines (gasoline engines), the air–fuel
mixture is compressed to a temperature that is
below the autoignition temperature of the fuel,
and the combustion process is initiated by
firing a spark plug.
•
In CI engines (diesel engines), the air is
compressed to a temperature that is above the
autoignition temperature of the fuel, and
combustion starts on contact as the fuel is
injected into this hot air.
•
Therefore, the spark plug and carburettor (used
in mixing air and fuel mist) are replaced by a
fuel injector in diesel engines (Figure).
127
Internal Combustion Engines
Diesel Cycle
•
In gasoline engines, a mixture of air and fuel is
compressed during the compression stroke,
and the compression ratios are limited by the
onset of autoignition or engine knock.
•
In diesel engines, only air is compressed
during the compression stroke, eliminating the
possibility of autoignition.
•
Therefore, diesel engines can be designed to
operate at much higher compression ratios,
typically between 12 and 24.
128
Internal Combustion Engines
Diesel Cycle
•
Not having to deal with the problem of
autoignition has another benefit: many of the
stringent requirements placed on the gasoline
can now be removed.
•
This means that fuels that are less refined (thus
less expensive) can be used in diesel engines.
•
The fuel injection process in diesel engines
starts when the piston approaches TDC and
continues during the first part of the power
stroke.
129
Internal Combustion Engines
Diesel Cycle
•
Therefore, the combustion process in these
engines takes place over a longer interval.
•
Because of this longer duration, the
combustion process in the ideal Diesel cycle is
approximated as a constant-pressure heataddition process.
•
This is the only process where the Otto and
the Diesel cycles differ.
•
The remaining three processes are the same
for both ideal cycles.
130
Internal Combustion Engines
Diesel Cycle
•
•
That is,
•
process 1-2 is isentropic compression,
•
3-4 is isentropic expansion, and
•
4-1 is constant-volume heat rejection.
The similarity between the two cycles is also
apparent from the P-v and T-s diagrams of the
Diesel cycle,.
131
Internal Combustion Engines
Diesel Cycle
•
The thermal efficiency of the ideal Diesel cycle under the cold-air standard
assumptions is
,
•
Where
•
is the compression ratio
•
is the specific heat ratio
•
is a new quantity called, the cutoff ratio, which is the ratio
132
between the cylinder volumes after and before the combustion process.
Internal Combustion Engines
Diesel Cycle
Note
• The ratio of the maximum volume
formed in the cylinder to the
minimum (clearance) volume is
called the compression ratio, r of the
engine:
•
Note that the compression ratio is a
volume ratio.
133
Internal Combustion Engines
Diesel Cycle
•
Looking at thermal efficiency of the ideal
Diesel cycle equation carefully, one would
notice that under the cold-air-standard
assumptions, the efficiency of a Diesel
cycle differs from the efficiency of an Otto
cycle by the quantity in the brackets.
•
This quantity is always greater than 1.
Therefore when both cycles operate on the
same compression ratio,
,
,
134
Internal Combustion Engines
Diesel Cycle
•
Remember, that diesel engines operate at much higher compression ratios
therefore are usually more efficient than the spark-ignition (gasoline) engines.
•
The diesel engines also burn the fuel more completely since they usually
operate at lower revolutions per minute and the air–fuel mass ratio is much
higher than spark-ignition engines.
•
Thermal efficiencies of large diesel engines range from about 35 to 40%.
135
Internal Combustion Engines
Diesel Cycle
•
The higher efficiency and lower fuel costs of diesel engines make them
attractive in applications requiring relatively large amounts of power
•
These applications include locomotive engines, emergency power generation
units, large ships, and heavy trucks.
136