Actual and Ideal Cycles, Carnot Cycle, Air-Standard
Assumptions, Reciprocating Engines
1
Ex- How does the thermal efficiency of an ideal cycle, in general, compare to that of a Carnot
cycle operating between the same temperature limits?
2
Ex- How does the thermal efficiency of an ideal cycle, in general, compare to that of a Carnot
cycle operating between the same temperature limits?
It is less than the thermal efficiency of a Carnot cycle.
The Carnot cycle is totally reversible, whereas the Ideal cycle is
internally reversible (it’s not externally reversible due to the finite
temperature difference during the heat transfer processes.
3
Ex- Can any ideal gas power cycle have a thermal efficiency greater than 55% when using thermal
energy reservoirs at 627℃ and 17 ℃ ?
4
Ex- Can any ideal gas power cycle have a thermal efficiency greater than 55% when using thermal
energy reservoirs at 627℃ and 17 ℃ ?
5
Ex- What does the area enclosed by the cycle represent on a P-v diagram? How about on a T-s
diagram?
6
Ex- What does the area enclosed by the cycle represent on a P-v diagram? How about on a T-s
diagram?
It represents the net work on both diagrams.
7
Ex- What is the difference between air-standard assumptions and the cold-air-standard
assumptions?
8
Ex- What is the difference between air-standard assumptions and the cold-air-standard
assumptions?
The cold air standard assumptions involves the additional
assumption that air can be treated as an ideal gas with constant
specific heats at room temperature.
9
Ex- How are the combustion and exhaust processes modeled under the air-standard
assumptions?
10
Ex- How are the combustion and exhaust processes modeled under the air-standard
assumptions?
Under the air standard assumptions, the combustion process is
modeled as a heat addition process, and the exhaust process as a
heat rejection process.
11
Ex- What are the air-standard assumptions?
12
Ex- What are the air-standard assumptions?
The air standard assumptions are:
(1) the working fluid is air which behaves as an ideal gas,
(2) All the processes are internally reversible,
(3) the combustion process is replaced by the heat addition process, and
(4) the exhaust process is replaced by the heat rejection process which returns the
working fluid to its original state.
13
Ex- What is the difference between the clearance volume and the displacement volume of
reciprocating engines?
14
Ex- What is the difference between the clearance volume and the displacement volume of
reciprocating engines?
The clearance volume is the minimum volume formed in the
cylinder whereas the displacement volume is the volume displaced
by the piston as the piston moves between the top dead center and
the bottom dead center.
15
Ex- Define the compression ratio for reciprocating engines.
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Ex- Define the compression ratio for reciprocating engines.
It is the ratio of the maximum to minimum volumes in the
cylinder.
17
Ex- How is the mean effective pressure for reciprocating engines defined?
18
Ex- How is the mean effective pressure for reciprocating engines defined?
The MEP is the fictitious pressure which, if acted on the piston
during the entire power stroke, would produce the same amount
of net work as that produced during the actual cycle.
19
Ex- Can the mean effective pressure of an automobile engine in operation be less than the
atmospheric pressure?
20
Ex- Can the mean effective pressure of an automobile engine in operation be less than the
atmospheric pressure?
Yes.
(MEP is a fictitious pressure)
21
Ex- As a car gets older, will its compression ratio change? How about the mean effective
pressure?
22
Ex- As a car gets older, will its compression ratio change? How about the mean effective
pressure?
Assuming no accumulation of carbon deposits on the piston face,
the compression ratio will remain the same (otherwise it will
increase). The mean effective pressure, on the other hand, will
decrease as a car gets older as a result of wear and tear.
23
Ex- What is the difference between spark-ignition (SI) and compression-ignition (CI) engines?
24
Ex- What is the difference between spark-ignition (SI) and compression-ignition (CI) engines?
The SI and CI engines differ from each other in the way
combustion is initiated; by a spark in SI engines, and by
compressing the air above the self-ignition temperature of the fuel
in CI engines.
25
Ex- Define the following terms related to reciprocating engines: stroke, bore, top dead center,
and clearance volume.
26
Ex- Define the following terms related to reciprocating engines: stroke, bore, top dead center,
and clearance volume.
Stroke is the distance between the TDC and the BDC.
Bore is the diameter of the cylinder.
TDC is the position of the piston when it forms the
smallest volume in the cylinder.
Clearance volume is the minimum volume formed in
the cylinder.
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Ex-
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Solution
(a)
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Ex-
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Solution
(a)
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34
Repeat the analysis of this problem for variable specific heats.
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Ex-
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Solution
(a)
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Otto Cycle
40
Ex- What four processes make up the ideal Otto cycle?
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Ex- What four processes make up the ideal Otto cycle?
The four processes that make up the Otto cycle are (1) isentropic
compression, (2) v = constant heat addition, (3) isentropic
expansion, and (4) v = constant heat rejection.
42
Ex- How do the efficiencies of the ideal Otto cycle and the Carnot cycle compare for the same
temperature limits? Explain.
43
Ex- How do the efficiencies of the ideal Otto cycle and the Carnot cycle compare for the same
temperature limits? Explain.
The ideal Otto cycle involves external irreversibilities, and thus it
has a lower thermal efficiency.
44
Ex- How is the rpm (revolutions per minute) of an actual four-stroke gasoline engine related to
the number of thermodynamic cycles? What would your answer be for a two-stroke engine?
45
Ex- How is the rpm (revolutions per minute) of an actual four-stroke gasoline engine related to
the number of thermodynamic cycles? What would your answer be for a two-stroke engine?
For actual four-stroke engines, the rpm is twice the number of
thermodynamic cycles;
for two stroke engines, it is equal to the number of thermodynamic
cycles.
46
Ex- Are the processes that make up the Otto cycle analyzed as closed-system or steady-flow
processes? Why?
47
Ex- Are the processes that make up the Otto cycle analyzed as closed-system or steady-flow
processes? Why?
They are analyzed as closed system processes because no mass
crosses the system boundaries during any of the processes.
48
Ex- How does the thermal efficiency of an ideal Otto cycle change with the compression ratio of
the engine and the specific heat ratio of the working fluid?
49
Ex- How does the thermal efficiency of an ideal Otto cycle change with the compression ratio of
the engine and the specific heat ratio of the working fluid?
It increases with both of them.
50
Ex- Why are high compression ratios not used in spark ignition engines?
51
Ex- Why are high compression ratios not used in spark ignition engines?
Because high compression ratios cause engine knock.
52
Ex- An ideal Otto cycle with a specified compression ratio is executed using (a) air, (b) argon, and
(c) ethane as the working fluid. For which case will the thermal efficiency be the highest? Why?
53
Ex- An ideal Otto cycle with a specified compression ratio is executed using (a) air, (b) argon, and
(c) ethane as the working fluid. For which case will the thermal efficiency be the highest? Why?
The thermal efficiency will be the highest for argon because it has
the highest specific heat ratio, k = 1.667.
54
Ex- What is the difference between fuel-injected gasoline engines and diesel engines?
55
Ex- What is the difference between fuel-injected gasoline engines and diesel engines?
The fuel is injected into the cylinder in both engines, but it is
ignited with a spark plug in gasoline engines.
56
Ex- An ideal Otto cycle has a compression ratio of 12, takes in air at 100 kPa and 20℃, and is
repeated 1000 times per minute. Using constant specific heats at room temperature, determine
the thermal efficiency of this cycle and the rate of heat input if the cycle is to produce 200 kW of
power.
57
Ex- An ideal Otto cycle has a compression ratio of 12, takes in air at 100 kPa and 20℃, and is
repeated 1000 times per minute. Using constant specific heats at room temperature, determine
the thermal efficiency of this cycle and the rate of heat input if the cycle is to produce 200 kW of
power.
58
Ex- The compression ratio of an air-standard Otto cycle is 9.5. Prior to the isentropic compression
process, the air is at 100 kPa, 35°C, and 600 cm3. The temperature at the end of the isentropic
expansion process is 800 K. Using specific heat values at room temperature, determine (a) the
highest temperature and pressure in the cycle; (b) the amount of heat transferred in, in kJ; (c) the
thermal efficiency; and (d) the mean effective pressure.
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Repeat the previous problem for different compression ratios:
r = 9.5, 10, 10.5, 11, 11.5, and 12
All other parameters in the problem are fixed.
Plot then the following variables versus r:
-work output,
-MEP
-T3 (maximum temperature in the cycle)
-P3 (maximum pressure in the cycle)
62
Ex- An ideal Otto cycle with air as the working fluid has a compression ratio of 8. The minimum
and maximum temperatures in the cycle are 300 and 1340 K. Accounting for the variation of
specific heats with temperature, determine (a) the amount of heat transferred to the air during
the heat-addition process, (b) the thermal efficiency, and (c) the thermal efficiency of a Carnot
cycle operating between the same temperature limits.
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Diesel Cycle
66
Ex- How does a diesel engine differ from a gasoline engine?
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Ex- How does a diesel engine differ from a gasoline engine?
A diesel engine differs from the gasoline engine in the way
combustion is initiated. In diesel engines combustion is initiated
by compressing the air above the self-ignition temperature of the
fuel whereas it is initiated by a spark plug in a gasoline engine.
68
Ex- How does the ideal Diesel cycle differ from the ideal Otto cycle?
69
Ex- How does the ideal Diesel cycle differ from the ideal Otto cycle?
The Diesel cycle differs from the Otto cycle in the heat addition
process only; it takes place at constant volume in the Otto cycle,
but at constant pressure in the Diesel cycle.
70
Ex- For a specified compression ratio, is a diesel or gasoline engine more efficient?
71
Ex- For a specified compression ratio, is a diesel or gasoline engine more efficient?
The gasoline engine.
72
Ex- Do diesel or gasoline engines operate at higher compression ratios? Why?
73
Ex- Do diesel or gasoline engines operate at higher compression ratios? Why?
Diesel engines operate at high compression ratios because the
diesel engines do not have the engine knock problem.
74
Ex- What is the cutoff ratio? How does it affect the thermal efficiency of a Diesel cycle?
75
Ex- What is the cutoff ratio? How does it affect the thermal efficiency of a Diesel cycle?
Cutoff ratio is the ratio of the cylinder volumes after and before
the combustion process. As the cutoff ratio decreases, the
efficiency of the diesel cycle increases.
76
Ex- An ideal Diesel cycle has a compression ratio of 18 and a cutoff ratio of 1.5. Determine the
maximum air temperature and the rate of heat addition to this cycle when it produces 200 hp of
power; the cycle is repeated 1200 times per minute; and the state of the air at the beginning of
the compression is 95 kPa and 17℃. Use constant specific heats at room temperature.
77
78
Ex- An ideal Diesel cycle has a maximum cycle temperature of 2000℃ and a cutoff ratio of 1.2.
The state of the air at the beginning of the compression is P1 = 95 kPa and T1 = 15 ℃. This cycle
is executed in a four stroke, eight-cylinder engine with a cylinder bore of 10 cm and a piston
stroke of 12cm. The minimum volume enclosed in the cylinder is 5% of the maximum cylinder
volume. Determine the power produced by this engine when it operated at 1600 rpm. Use
constant specific heats at room temperature.
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Ex- An air-standard Diesel cycle has a compression ratio of 18.2. Air is at 27℃ and 100 kPa at the
beginning of the compression process and at 1700 K at the end of the heat addition process.
Accounting for the variation of specific heats with temperature, determine (a) the cutoff ratio, (b)
the heat rejection per unit mass, and (c) the thermal efficiency.
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83
Ex- Repeat the previous problem but using constant specific heats.
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Ideal and Actual Gas-Turbine (Brayton) Cycles
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The Simple Ideal Brayton Cycle
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Deviation of Actual Gas-Turbine Cycles from Idealized Ones
92
An Actual Gas-Turbine Cycle
Assuming a compressor efficiency of 80 percent and a turbine efficiency of 85 percent,
determine (a) the back work ratio, (b) the thermal efficiency, and (c) the turbine exit
temperature of the gas-turbine cycle discussed in the previous Example.
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96
Ex- Why are back ratios relatively high in gas turbine engines ?
97
Ex- Why are back ratios relatively high in gas turbine engines ?
In gas turbine engines a gas is compressed, and thus the
compression work requirements are very large since the
steady-flow work is proportional to the specific volume.
98
Ex- What four processes make up the simple ideal Brayton cycle ?
99
Ex- What four processes make up the simple ideal Brayton cycle ?
They are (1) isentropic compression (in a compressor), (2) P =
constant heat addition, (3) isentropic expansion (in a turbine), and
(4) P = constant heat rejection.
100
Ex- For fixed maximum and minimum temperatures, what is the effect of pressure ratio on (a)
the thermal efficiency and (b) the net work output of a simple ideal Brayton cycle ?
101
Ex- For fixed maximum and minimum temperatures, what is the effect of pressure ratio on (a)
the thermal efficiency and (b) the net work output of a simple ideal Brayton cycle ?
For fixed maximum and minimum temperatures, (a) the thermal
efficiency increases with pressure ratio, (b) the net work first
increases with pressure ratio, reaches a maximum, and then
decreases.
102
Ex- What is the back work ratio ? What are typical back work ratio values for gas-turbine
engines?
103
Ex- What is the back work ratio ? What are typical back work ratio values for gas-turbine
engines?
Back work ratio is the ratio of the compressor (or pump) work
input to the turbine work output. It is usually between 0.40 and
0.6 for gas turbine engines.
104
Ex- A simple ideal Brayton cycle with air as the working fluid has a pressure ratio of 10. The air
enters the compressor at 290 and the turbine at 1100 K. Accounting for the variation of specific
heats with temperature, determine (a) the air temperature at the compressor exit, (b) the back
work ratio, and (c) the thermal efficiency.
105
106
Ex- A simple Brayton cycle using air as the working fluid has a pressure ratio of 8. The minimum
and maximum temperatures in the cycle are 310 and 1160 K. Assuming an isentropic efficiency of
75 percent for the compressor and 82 percent for the turbine, determine (a) the air temperature
at the turbine exit, (b) the net work output, and (c) the thermal efficiency.
107
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109
Ex- A simple ideal Brayton cycle operates with air with minimum and maximum temperatures of
27℃ and 727℃. It is designed so that the maximum cycle pressure is 2000 kPa and the minimum
cycle pressure is 100 kPa. Determine the net work produced per unit mass of air each time this
cycle is executed and the cycle’s thermal efficiency. Use constant specific heats at room
temperature.
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111
Ex- Repeat the previous exercise given the isentropic efficiency of the turbine is 90%.
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113
Ex- A stationary gas-turbine power plant operates on a simple ideal Brayton cycle with air as the
working fluid. The air enters the compressor at 95 kPa and 290 K and the turbine at 760 kPa and
1100 K. Heat is transferred to air at a rate of 35000 kJ/s. Determine the power delivered by this
plant (a) assuming constant specific heats at room temperature and (b) accounting for the
variation of specific heats with temperature.
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