9–1C Why is the Carnot cycle not suitable as an ideal cycle for all power-producing cyclic devices?
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9–2C
How does the thermal efficiency of an ideal cycle, in general, compare
to that of a Carnot cycle operating between the same temperature limits?
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9–3C What does the area enclosed by the cycle represent on a P-v diagram? How about on a T-s diagram?
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9–4C What is the difference between air-standard assumptions and the cold-air-standard assumptions?
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9–5C How are the combustion and exhaust processes modeled under the air-standard assumptions?
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9–6C What are the air-standard assumptions?
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9–7C What is the difference between the clearance volume and the displacement volume of reciprocating engines?
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9–8C Define the compression ratio for reciprocating engines.
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9–9C How is the mean effective pressure for reciprocating engines defined?
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9–10C Can the mean effective pressure of an automobile engine in operation be less than the atmospheric pressure?
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9–11C As a car gets older, will its compression ratio change? How about the mean effective pressure?
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9–12C What is the difference between spark-ignition and compression-ignition engines?
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9–13C Define the following terms related to reciprocating engines: stroke, bore, top dead center, and clearance volume.
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9–14
An air-standard cycle with variable specific heats is executed in a
closed system and is composed of the following four processes: 1-2
Isentropic compression from 100 kPa and 27°C to 800 kPa 2-3 v constant
heat addition to 1800 K 3-4 Isentropic expansion to 100 kPa 4-1 P
constant heat rejection to initial state (a) Show the cycle on P-v and
T-s diagrams. (b) Calculate the net work output per unit mass. (c)
Determine the thermal efficiency.
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9–15
Reconsider Problem 9–14. Using EES (or other) software, study the
effect of varying the temperature after the constant-volume heat
addition from 1500 K to 2500 K. Plot the net work output and thermal
efficiency as a function of the maximum temperature of the cycle. Plot
the T-s and P-v diagrams for the cycle when the maximum temperature of
the cycle is 1800 K.
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9–16
An air-standard cycle is executed in a closed system and is composed of
the following four processes: 1-2 Isentropic compression from 100 kPa
and 27°C to 1 MPa 2-3 P constant heat addition in amount of 2800 kJ/kg
3-4 v constant heat rejection to 100 kPa 4-1 P constant heat
rejection to initial state (a) Show the cycle on P-v and T-s diagrams.
(b) Calculate the maximum temperature in the cycle. (c) Determine the
thermal efficiency. Assume constant specific heats at room temperature.
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9–17E
An air-standard cycle with variable specific heats is executed in a
closed system and is composed of the following four processes: 1-2 v
constant heat addition from 14.7 psia and 80°F in the amount of 300
Btu/lbm 2-3 P constant heat addition to 3200 R 3-4 Isentropic
expansion to 14.7 psia 4-1 P constant heat rejection to initial state
(a) Show the cycle on P-v and T-s diagrams. (b) Calculate the total heat
input per unit mass. (c) Determine the thermal efficiency. Answers: (b)
612.4 Btu/lbm, (c) 24.2 percent
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9–18E Repeat Problem 9–17E using constant specific heats at room temperature.
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9–19
An air-standard cycle is executed in a closed system with 0.004 kg of
air and consists of the following three processes: 1-2 Isentropic
compression from 100 kPa and 27°C to 1 MPa 2-3 P constant heat
addition in the amount of 2.76 kJ 3-1 P c1v + c2 heat rejection to
initial state (c1 and c2 are constants) (a) Show the cycle on P-v and
T-s diagrams. (b) Calculate the heat rejected. (c) Determine the thermal
efficiency. Assume constant specific heats at room temperature.
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9–20
An air-standard cycle with variable specific heats is executed in a
closed system with 0.003 kg of air and consists of the following three
processes: 1-2 v = constant heat addition from 95 kPa and 17°C to 380
kPa 2-3 Isentropic expansion to 95 kPa 3-1 P = constant heat rejection
to initial state (a) Show the cycle on P-v and T-s diagrams. (b)
Calculate the net work per cycle, in kJ. (c) Determine the thermal
efficiency.
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9–21 Repeat Problem 9–20 using constant specific heats at room temperature.
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9–22
Consider a Carnot cycle executed in a closed system with 0.003 kg of
air. The temperature limits of the cycle are 300 and 900 K, and the
minimum and maximum pressures that occur during the cycle are 20 and
2000 kPa. Assuming constant specific heats, determine the net work
output per cycle.
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9–23
An air-standard Carnot cycle is executed in a closed system between the
temperature limits of 350 and 1200 K. The pressures before and after
the isothermal compression are 150 and 300 kPa, respectively. If the net
work output per cycle is 0.5 kJ, determine (a) the maximum pressure in
the cycle, (b) the heat transfer to air, and (c) the mass of air. Assume
variable specific heats for air.
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9–24 Repeat Problem 9–23 using helium as the working fluid.
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9–25
Consider a Carnot cycle executed in a closed system with air as the
working fluid. The maximum pressure in the cycle is 800 kPa while the
maximum temperature is 750 K. If the entropy increase during the
isothermal heat rejection process is 0.25 kJ/kg . K and the net work
output is 100 kJ/kg, determine (a) the minimum pressure in the cycle,
(b) the heat rejection from the cycle, and (c) the thermal efficiency of
the cycle. (d) If an actual heat engine cycle operates between the same
temperature limits and produces 5200 kW of power for an air flow rate
of 90 kg/s, determine the second law efficiency of this cycle.
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9–26C What four processes make up the ideal Otto cycle?
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9–27C How do the efficiencies of the ideal Otto cycle and the Carnot cycle compare for the same temperature limits? Explain.
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9–28C
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?
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9–29C Are the processes that make up the Otto cycle analyzed as closed-system or steady-flow processes? Why?
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9–30C
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?
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9–31C Why are high compression ratios not used in sparkignition engines?
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9–32C
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?
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9–33C What is the difference between fuel-injected gasoline engines and diesel engines?
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9–34
An ideal Otto cycle has a compression ratio of 8. At the beginning of
the compression process, air is at 95 kPa and 27°C, and 750 kJ/kg of
heat is transferred to air during the constant-volume heat-addition
process. Taking into account the variation of specific heats with
temperature, determine (a) the pressure and temperature at the end of
the heataddition process, (b) the net work output, (c) the thermal
efficiency, and (d) the mean effective pressure for the cycle.
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9–35
Reconsider Problem 9–34. Using EES (or other) software, study the
effect of varying the compression ratio from 5 to 10. Plot the net work
output and thermal efficiency as a function of the compression ratio.
Plot the T-s and P-v diagrams for the cycle when the compression ratio
is 8.
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9–36 Repeat Problem 9–34 using constant specific heats at room temperature.
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9–37
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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9–38
Repeat Problem 9–37, but replace the isentropic expansion process by a
polytropic expansion process with the polytropic exponent n 1.35.
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9–39E
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 540
and 2400 R. 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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9–40E Repeat Problem 9–39E using argon as the working fluid.
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9–41
A four-cylinder, four-stroke, 2.2-L gasoline engine operates on the
Otto cycle with a compression ratio of 10. The air is at 100 kPa and
60°C at the beginning of the compression process, and the maximum
pressure in the cycle is 8 MPa. The compression and expansion processes
may be modeled as polytropic with a polytropic constant of 1.3. Using
constant specific heats at 850 K, determine (a) the temperature at the
end of the expansion process, (b) the net work output and the thermal
efficiency, (c) the mean effective pressure, (d) the engine speed for a
net power output of 70 kW, and (e) the specific fuel consumption, in
g/kWh, defined as the ratio of the mass of the fuel consumed to the net
work produced. The air–fuel ratio, defined as the amount of air divided
by the amount of fuel intake, is 16.
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9–42C How does a diesel engine differ from a gasoline engine?
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9–43C How does the ideal Diesel cycle differ from the ideal Otto cycle?
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9–44C For a specified compression ratio, is a diesel or gasoline engine more efficient?
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9–45C Do diesel or gasoline engines operate at higher compression ratios? Why?
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9–46C What is the cutoff ratio? How does it affect the thermal efficiency of a Diesel cycle?
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9–47
An air-standard Diesel cycle has a compression ratio of 16 and a cutoff
ratio of 2. At the beginning of the compression process, air is at 95
kPa and 27°C. Accounting for the variation of specific heats with
temperature, determine (a) the temperature after the heat-addition
process, (b) the thermal efficiency, and (c) the mean effective
pressure. Answers: (a) 1724.8 K, (b) 56.3 percent, (c) 675.9 kPa
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9–48 Repeat Problem 9–47 using constant specific heats at room temperature.
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9–49E
An air-standard Diesel cycle has a compression ratio of 18.2. Air is at
80°F and 14.7 psia at the beginning of the compression process and at
3000 R at the end of the heataddition 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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9–50E Repeat Problem 9–49E using constant specific heats at room temperature.
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9–51
An ideal diesel engine has a compression ratio of 20 and uses air as
the working fluid. The state of air at the beginning of the compression
process is 95 kPa and 20°C. If the maximum temperature in the cycle is
not to exceed 2200 K, determine (a) the thermal efficiency and (b) the
mean effective pressure. Assume constant specific heats for air at room
temperature. Answers: (a) 63.5 percent, (b) 933 kPa
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9–52
Repeat Problem 9–51, but replace the isentropic expansion process by
polytropic expansion process with the polytropic exponent n 1.35.
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9–53
Reconsider Problem 9–52. Using EES (or other) software, study the
effect of varying the compression ratio from 14 to 24. Plot the net work
output, mean
effective pressure, and thermal efficiency as a function of the
compression ratio. Plot the T-s and P-v diagrams for the cycle when the
compression ratio is 20.
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9–54
A four-cylinder two-stroke 2.4-L diesel engine that operates on an
ideal Diesel cycle has a compression ratio of 17 and a cutoff ratio of
2.2. Air is at 55°C and 97 kPa at the beginning of the compression
process. Using the cold-airstandard assumptions, determine how much
power the engine will deliver at 1500 rpm.
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9–55 Repeat Problem 9–54 using nitrogen as the working fluid.
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9–56
The compression ratio of an ideal dual cycle is 14. Air is at 100 kPa
and 300 K at the beginning of the compression process and at 2200 K at
the end of the heat-addition process. Heat transfer to air takes place
partly at constant volume and partly at constant pressure, and it
amounts to 1520.4 kJ/kg. Assuming variable specific heats for air,
determine (a) the fraction of heat transferred at constant volume and
(b) the thermal efficiency of the cycle.
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9–57
Reconsider Problem 9–56. Using EES (or other) software, study the
effect of varying the compression ratio from 10 to 18. For the
compression ratio equal to 14, plot the T-s and P-v diagrams for the
cycle.
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9–58
Repeat Problem 9–56 using constant specific heats at room temperature.
Is the constant specific heat assumption reasonable in this case?
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9–59
A six-cylinder, four-stroke, 4.5-L compression-ignition engine operates
on the ideal diesel cycle with a compression ratio of 17. The air is at
95 kPa and 55°C at the beginning of the compression process and the
engine speed is 2000 rpm. The engine uses light diesel fuel with a
heating value of 42,500 kJ/kg, an air–fuel ratio of 24, and a combustion
efficiency of 98 percent. Using constant specific heats at 850 K,
determine (a) the maximum temperature in the cycle and the cutoff ratio
(b) the net work output per cycle and the thermal efficiency, (c) the
mean effective pressure, (d) the net power output, and (e) the specific
fuel consumption, in g/kWh, defined as the ratio of the mass of the fuel
consumed to the net work produced.
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9–60C
Consider the ideal Otto, Stirling, and Carnot cycles operating between
the same temperature limits. How would you compare the thermal
efficiencies of these three cycles?
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9–61C
Consider the ideal Diesel, Ericsson, and Carnot cycles operating
between the same temperature limits. How would you compare the thermal
efficiencies of these three cycles?
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9–62C What cycle is composed of two isothermal and two constant-volume processes?
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9–63C How does the ideal Ericsson cycle differ from the Carnot cycle?
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9–64E
An ideal Ericsson engine using helium as the working fluid operates
between temperature limits of 550 and 3000 R and pressure limits of 25
and 200 psia. Assuming a mass flow rate of 14 lbm/s, determine (a) the
thermal efficiency of the cycle, (b) the heat transfer rate in the
regenerator, and (c) the power delivered.
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9–65
Consider an ideal Ericsson cycle with air as the working fluid executed
in a steady-flow system. Air is at 27°C and 120 kPa at the beginning of
the isothermal compression process, during which 150 kJ/kg of heat is
rejected. Heat transfer to air occurs at 1200 K. Determine (a) the
maximum pressure in the cycle, (b) the net work output per unit mass of
air, and (c) the thermal efficiency of the cycle.
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9–66
An ideal Stirling engine using helium as the working fluid operates
between temperature limits of 300 and 2000 K and pressure limits of 150
kPa and 3 MPa. Assuming the mass of the helium used in the cycle is 0.12
kg, determine (a) the thermal efficiency of the cycle, (b) the amount
of heat transfer in the regenerator, and (c) the work output per cycle.
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9–67C Why are the back work ratios relatively high in gasturbine engines?
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9–68C What four processes make up the simple ideal Brayton cycle?
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9–69C
For fixed maximum and minimum temperatures, what is the effect of the
pressure ratio on (a) the thermal efficiency and (b) the net work output
of a simple ideal Brayton cycle?
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9–70C What is the back work ratio? What are typical back work ratio values for gas-turbine engines?
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9–71C
How do the inefficiencies of the turbine and the compressor affect (a)
the back work ratio and (b) the thermal efficiency of a gas-turbine
engine?
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9–72E
A simple ideal Brayton cycle with air as the working fluid has a
pressure ratio of 10. The air enters the compressor at 520 R and the
turbine at 2000 R. 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.
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9–73
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.
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9–74
Reconsider Problem 9–73. Using EES (or other) software, allow the mass
flow rate, pressure ratio, turbine inlet temperature, and the isentropic
efficiencies of the turbine and compressor to vary. Assume the
compressor inlet pressure is 100 kPa. Develop a general solution for the
problem by taking advantage of the diagram window method for supplying
data to EES software.
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9–75 Repeat Problem 9–73 using constant specific heats at room temperature.
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9–76
Air is used as the working fluid in a simple ideal Brayton cycle that
has a pressure ratio of 12, a compressor inlet temperature of 300 K, and
a turbine inlet temperature of 1000 K. Determine the required mass flow
rate of air for a net power output of 70 MW, assuming both the
compressor and the turbine have an isentropic efficiency of (a) 100
percent and (b) 85 percent. Assume constant specific heats at room
temperature. Answers: (a) 352 kg/s, (b) 1037 kg/s
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9–77
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 35,000 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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9–78
Air enters the compressor of a gas-turbine engine at 300 K and 100 kPa,
where it is compressed to 700 kPa and 580 K. Heat is transferred to air
in the amount of 950 kJ/kg before it enters the turbine. For a turbine
efficiency of 86 percent, determine (a) the fraction of the turbine work
output used to drive the compressor and (b) the thermal efficiency.
Assume variable specific heats for air.
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9–79 Repeat Problem 9–78 using constant specific heats at room temperature.
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9–80E
A gas-turbine power plant operates on a simple Brayton cycle with air
as the working fluid. The air enters the turbine at 120 psia and 2000 R
and leaves at 15 psia and 1200 R. Heat is rejected to the surroundings
at a rate of 6400 Btu/s, and air flows through the cycle at a rate of 40
lbm/s. Assuming the turbine to be isentropic and the compresssor to
have an isentropic efficiency of 80 percent, determine the net power
output of the plant. Account for the variation of specific heats with
temperature.
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9–81E For what compressor efficiency will the gas-turbine power plant in Problem 9–80E produce zero net work?
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9–82
A gas-turbine power plant operates on the simple Brayton cycle with air
as the working fluid and delivers 32 MW of power. The minimum and
maximum temperatures in the cycle are 310 and 900 K, and the pressure of
air at the compressor exit is 8 times the value at the compressor
inlet. Assuming an isentropic efficiency of 80 percent for the
compressor and 86 percent for the turbine, determine the mass flow rate
of air through the cycle. Account for the variation of specific heats
with temperature.
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9–83 Repeat Problem 9–82 using constant specific heats at room temperature.
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9–84
A gas-turbine power plant operates on the simple Brayton cycle between
the pressure limits of 100 and 1200 kPa. The working fluid is air, which
enters the compressor at 30°C at a rate of 150 m3/min and leaves the
turbine at 500°C. Using variable specific heats for air and assuming a
compressor isentropic efficiency of 82 percent and a turbine isentropic
efficiency of 88 percent, determine (a) the net power output, (b) the
back work ratio, and (c) the thermal efficiency.
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9–85C How does regeneration affect the efficiency of a Brayton cycle, and how does it accomplish it?
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9–86C
Somebody claims that at very high pressure ratios, the use of
regeneration actually decreases the thermal efficiency of a gas-turbine
engine. Is there any truth in this claim? Explain.
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9–87C Define the effectiveness of a regenerator used in gas-turbine cycles.
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9–88C
In an ideal regenerator, is the air leaving the compressor heated to
the temperature at (a) turbine inlet, (b) turbine exit, (c) slightly
above turbine exit?
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9–89C
In 1903, Aegidius Elling of Norway designed and built an 11-hp gas
turbine that used steam injection between the combustion chamber and the
turbine to cool the combustion gases to a safe temperature for the
materials available at the time. Currently there are several gas-turbine
power plants that use steam injection to augment power and improve
thermal efficiency. For example, the thermal efficiency of the General
Electric LM5000 gas turbine is reported to increase from 35.8 percent in
simple-cycle operation to 43 percent when steam injection is used.
Explain why steam injection increases the power output and the
efficiency of gas turbines. Also, explain how you would obtain the
steam.
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9–90E
The idea of using gas turbines to power automobiles was conceived in
the 1930s, and considerable research was done in the 1940s and 1950s to
develop automotive gas turbines by major automobile manufacturers such
as the Chrysler and Ford corporations in the United States and Rover in
the United Kingdom. The world’s first gas-turbinepowered automobile, the
200-hp Rover Jet 1, was built in 1950 in the United Kingdom. This was
followed by the production of the Plymouth Sport Coupe by Chrysler in
1954 under the leadership of G. J. Huebner. Several hundred
gasturbine-powered Plymouth cars were built in the early 1960s for
demonstration purposes and were loaned to a select group of people to
gather field experience. The users had no complaints other than slow
acceleration. But the cars were never mass-produced because of the high
production (especially material) costs and the failure to satisfy the
provisions of the 1966 Clean Air Act. A gas-turbine-powered Plymouth car
built in 1960 had a turbine inlet temperature of 1700°F, a pressure
ratio of 4, and a regenerator effectiveness of 0.9. Using isentropic
efficiencies of 80 percent for both the compressor and the turbine,
determine the thermal efficiency of this car. Also, determine the mass
flow rate of air for a net power output of 95 hp. Assume the ambient air
to be at 540 R and 14.5 psia.
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9–91
The 7FA gas turbine manufactured by General Electric is reported to
have an efficiency of 35.9 percent in the simple-cycle mode and to
produce 159 MW of net power. The pressure ratio is 14.7 and the turbine
inlet temperature is 1288°C. The mass flow rate through the turbine is
1,536,000 kg/h. Taking the ambient conditions to be 20°C and 100 kPa,
determine the isentropic efficiency of the turbine and the compressor.
Also, determine the thermal efficiency of this gas turbine if a
regenerator with an effectiveness of 80 percent is added.
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9–92
Reconsider Problem 9–91. Using EES (or other) software, develop a
solution that allows different isentropic efficiencies for the
compressor and turbine and study the effect of the isentropic
efficiencies on net work done and the heat supplied to the cycle. Plot
the T-s diagram for the cycle.
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9–93
An ideal Brayton cycle with regeneration has a pressure ratio of 10.
Air enters the compressor at 300 K and the turbine at 1200 K. If the
effectiveness of the regenerator is 100 percent, determine the net work
output and the thermal efficiency of the cycle. Account for the
variation of specific heats with temperature.
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9–94
Reconsider Problem 9–93. Using EES (or other) software, study the
effects of varying the isentropic efficiencies for the compressor and
turbine and regenerator effectiveness on net work done and the heat
supplied to the cycle for the variable specific heat case. Plot the T-s
diagram for the cycle.
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9–95 Repeat Problem 9–93 using constant specific heats at room temperature.
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9–96
A Brayton cycle with regeneration using air as the working fluid has a
pressure ratio of 7. The minimum and maximum temperatures in the cycle
are 310 and 1150 K. Assuming an isentropic efficiency of 75 percent for
the compressor and 82 percent for the turbine and an effectiveness of 65
percent for the regenerator, determine (a) the air temperature at the
turbine exit, (b) the net work output, and (c) the thermal efficiency.
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9–97
A stationary gas-turbine power plant operates on an ideal regenerative
Brayton cycle (P = 100 percent) with air as the working fluid. Air
enters the compressor at 95 kPa and 290 K and the turbine at 760 kPa and
1100 K. Heat is transferred to air from an external source at a rate of
75,000 kJ/s. Determine the power delivered by this plant (a) assuming
constant specific heats for air at room temperature and (b) accounting
for the variation of specific heats with temperature.
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9–98
Air enters the compressor of a regenerative gas-turbine engine at 300 K
and 100 kPa, where it is compressed to 800 kPa and 580 K. The
regenerator has an effectiveness of 72 percent, and the air enters the
turbine at 1200 K. For a turbine efficiency of 86 percent, determine (a)
the amount of heat transfer in the regenerator and (b) the thermal
efficiency. Assume variable specific heats for air.
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9–99 Repeat Problem 9–98 using constant specific heats at room temperature.
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9–100
Repeat Problem 9–98 for a regenerator effectiveness of 70 percent.
Brayton Cycle with Intercooling, Reheating, and Regeneration
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9–101C Under what modifications will the ideal simple gas-turbine cycle approach the Ericsson cycle?
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9–102C
The single-stage compression process of an ideal Brayton cycle without
regeneration is replaced by a multistage compression process with
intercooling between the same pressure limits. As a result of this
modification, (a) Does the compressor work increase, decrease, or remain
the same? (b) Does the back work ratio increase, decrease, or remain
the same? (c) Does the thermal efficiency increase, decrease, or remain
the same?
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9–103C
The single-stage expansion process of an ideal Brayton cycle without
regeneration is replaced by a multistage expansion process with
reheating between the same pressure limits. As a result of this
modification, (a) Does the turbine work increase, decrease, or remain
the same? (b) Does the back work ratio increase, decrease, or remain the
same? (c) Does the thermal efficiency increase, decrease, or remain the
same?
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9–104C
A simple ideal Brayton cycle without regeneration is modified to
incorporate multistage compression with intercooling and multistage
expansion with reheating, without changing the pressure or temperature
limits of the cycle. As a result of these two modifications, (a) Does
the net work output increase, decrease, or remain the same? (b) Does the
back work ratio increase, decrease, or remain the same? (c) Does the
thermal efficiency increase, decrease, or remain the same? (d) Does the
heat rejected increase, decrease, or remain the same?
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9–105C
A simple ideal Brayton cycle is modified to incorporate multistage
compression with intercooling, multistage expansion with reheating, and
regeneration without changing the pressure limits of the cycle. As a
result of these modifications, (a) Does the net work output increase,
decrease, or remain the same? (b) Does the back work ratio increase,
decrease, or remain the same? (c) Does the thermal efficiency increase,
decrease, or remain the same? (d) Does the heat rejected increase,
decrease, or remain the same?
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9–106C
For a specified pressure ratio, why does multistage compression with
intercooling decrease the compressor work, and multistage expansion with
reheating increase the turbine work?
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9–107C
In an ideal gas-turbine cycle with intercooling, reheating, and
regeneration, as the number of compression and expansion stages is
increased, the cycle thermal efficiency approaches (a) 100 percent, (b)
the Otto cycle efficiency, or (c) the Carnot cycle efficiency.
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9–108
Consider an ideal gas-turbine cycle with two stages of compression and
two stages of expansion. The pressure ratio across each stage of the
compressor and turbine is 3. The air enters each stage of the compressor
at 300 K and each stage of the turbine at 1200 K. Determine the back
work ratio and the thermal efficiency of the cycle, assuming (a) no
regenerator is used and (b) a regenerator with 75 percent effectiveness
is used. Use variable specific heats.
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9–109
Repeat Problem 9–108, assuming an efficiency of 80 percent for each
compressor stage and an efficiency of 85 percent for each turbine stage.
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9–110
Consider a regenerative gas-turbine power plant with two stages of
compression and two stages of expansion. The overall pressure ratio of
the cycle is 9. The air enters each stage of the compressor at 300 K and
each stage of the turbine at 1200 K. Accounting for the variation of
specific heats with temperature, determine the minimum mass flow rate of
air needed to develop a net power output of 110 MW.
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9–111 Repeat Problem 9–110 using argon as the working fluid. Jet-Propulsion Cycles
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9–112C What is propulsive power? How is it related to thrust?
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9–113C What is propulsive efficiency? How is it determined?
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9–114C
Is the effect of turbine and compressor irreversibilities of a turbojet
engine to reduce (a) the net work, (b) the thrust, or (c) the fuel
consumption rate?
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9–115E
A turbojet is flying with a velocity of 900 ft/s at an altitude of
20,000 ft, where the ambient conditions are 7 psia and 10°F. The
pressure ratio across the compressor is 13, and the temperature at the
turbine inlet is 2400 R. Assuming ideal operation for all components and
constant specific heats for air at room temperature, determine (a) the
pressure at the turbine exit, (b) the velocity of the exhaust gases, and
(c) the propulsive efficiency.
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9–116E Repeat Problem 9–115E accounting for the variation of specific heats with temperature.
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9–117
A turbojet aircraft is flying with a velocity of 320 m/s at an altitude
of 9150 m, where the ambient conditions are 32 kPa and -32°C. The
pressure ratio across the compressor is 12, and the temperature at the
turbine inlet is 1400 K. Air enters the compressor at a rate of 60 kg/s,
and the jet fuel has a heating value of 42,700 kJ/kg. Assuming ideal
operation for all components and constant specific heats for air at room
temperature, determine (a) the velocity of the exhaust gases, (b) the
propulsive power developed, and (c) the rate of fuel consumption.
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9–118 Repeat Problem 9–117 using a compressor efficiency of 80 percent and a turbine efficiency of 85 percent.
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9–119
Consider an aircraft powered by a turbojet engine that has a pressure
ratio of 12. The aircraft is stationary on the ground, held in position
by its brakes. The ambient air is at 27°C and 95 kPa and enters the
engine at a rate of 10 kg/s. The jet fuel has a heating value of 42,700
kJ/kg, and it is burned completely at a rate of 0.2 kg/s. Neglecting the
effect of the diffuser and disregarding the slight increase in mass at
the engine exit as well as the inefficiencies of engine components,
determine the force that must be applied on the brakes to hold the plane
stationary.
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9–120
Reconsider Problem 9–119. In the problem statement, replace the inlet
mass flow rate by an inlet volume flow rate of 9.063 m3/s. Using EES (or
other) software, investigate the effect of compressor inlet temperature
in the range of –20 to 30°C on the force that must be applied to the
brakes to hold the plane stationary. Plot this force as a function in
compressor inlet temperature.
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9–121
Air at 7°C enters a turbojet engine at a rate of 16 kg/s and at a
velocity of 300 m/s (relative to the engine).Air is heated in the
combustion chamber at a rate 15,000 kJ/s and it leaves the engine at
427°C. Determine the thrust produced by this turbojet engine. (Hint:
Choose the entire engine as your control volume.)
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9–122
Determine the total exergy destruction associated with the Otto cycle
described in Problem 9–34, assuming a source temperature of 2000 K and a
sink temperature of 300 K. Also, determine the exergy at the end of the
power stroke.
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9–123
Determine the total exergy destruction associated with the Diesel cycle
described in Problem 9–47, assuming a source temperature of 2000 K and a
sink temperature of 300 K. Also, determine the exergy at the end of the
isentropic compression process.
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9–124E
Determine the exergy destruction associated with the heat rejection
process of the Diesel cycle described in Problem 9–49E, assuming a
source temperature of 3500 R and a sink temperature of 540 R. Also,
determine the exergy at the end of the isentropic expansion process.
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9–125
Calculate the exergy destruction associated with each of the processes
of the Brayton cycle described in Problem 9–73, assuming a source
temperature of 1600 K and a sink temperature of 290 K.
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9–126
Determine the total exergy destruction associated with the Brayton
cycle described in Problem 9–93, assuming a source temperature of 1800 K
and a sink temperature of 300 K. Also, determine the exergy of the
exhaust gases at the exit of the regenerator.
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9–127
Reconsider Problem 9–126. Using EES (or other) software, investigate
the effect of varying the cycle pressure ratio from 6 to 14 on the total
exergy destruction for the cycle and the exergy of the exhaust gas
leaving the regenerator. Plot these results as functions of pressure
ratio. Discuss the results.
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9–128
Determine the exergy destruction associated with each of the processes
of the Brayton cycle described in Problem 9–98, assuming a source
temperature of 1260 K and a sink temperature of 300 K. Also, determine
the exergy of the exhaust gases at the exit of the regenerator. Take
Pexhaust = P0 = 100 kPa.
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9–129
A gas-turbine power plant operates on the simple Brayton cycle between
the pressure limits of 100 and 700 kPa. Air enters the compressor at
30°C at a rate of 12.6 kg/s and leaves at 260°C. A diesel fuel with a
heating value of 42,000 kJ/kg is burned in the combustion chamber with
an air–fuel ratio of 60 and a combustion efficiency of 97 percent.
Combustion gases leave the combustion chamber and enter the turbine
whose isentropic efficiency is 85 percent. Treating the combustion gases
as air and using constant specific heats at 500°C, determine (a) the
isentropic efficiency of the compressor, (b) the net power output and
the back work ratio, (c) the thermal efficiency, and (d) the second-law
efficiency.
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9–130
A four-cylinder, four-stroke, 2.8-liter modern, highspeed
compression-ignition engine operates on the ideal dual cycle with a
compression ratio of 14. The air is at 95 kPa and 55°C at the beginning
of the compression process and the engine speed is 3500 rpm. Equal
amounts of fuel are burned at constant volume and at constant pressure.
The maximum allowable pressure in the cycle is 9 MPa due to material
strength limitations. Using constant specific heats at 850 K, determine
(a) the maximum temperature in the cycle, (b) the net work output and
the thermal efficiency, (c) the mean effective pressure, and (d) the net
power output. Also, determine (e) the second-law efficiency of the
cycle and the rate of exergy output with the exhaust gases when they are
purged.
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9–131
A gas-turbine power plant operates on the regenerative Brayton cycle
between the pressure limits of 100 and 700 kPa. Air enters the
compressor at 30°C at a rate of 12.6 kg/s and leaves at 260°C. It is
then heated in a regenerator to 400°C by the hot combustion gases
leaving the turbine. A diesel fuel with a heating value of 42,000 kJ/kg
is burned in the combustion chamber with a combustion efficiency of 97
percent. The combustion gases leave the combustion chamber at 871°C and
enter the turbine whose isentropic efficiency is 85 percent. Treating
combustion gases as air and using constant specific heats at 500°C,
determine (a) the isentropic efficiency of the compressor, (b) the
effectiveness of the regenerator, (c) the air–fuel ratio in the
combustion chamber, (d) the net power output and the back work ratio,
(e) the thermal efficiency, and (f) the second-law efficiency of the
plant. Also determine (g) the second-law (exergetic) efficiencies of the
compressor, the turbine, and the regenerator, and (h) the rate of the
exergy flow with the combustion gases at the regenerator exit.
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9–132
A four-stroke turbocharged V-16 diesel engine built by GE
Transportation Systems to power fast trains produces 3500 hp at 1200
rpm. Determine the amount of power produced per cylinder per (a)
mechanical cycle and (b) thermodynamic cycle.
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9–133
Consider a simple ideal Brayton cycle operating between the temperature
limits of 300 and 1500 K. Using constant specific heats at room
temperature, determine the pressure ratio for which the compressor and
the turbine exit temperatures of air are equal.
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9–134
An air-standard cycle with variable coefficients is executed in a
closed system and is composed of the following four processes: 1-2 v =
constant heat addition from 100 kPa and 27°C to 300 kPa 2-3 P = constant
heat addition to 1027°C 3-4 Isentropic expansion to 100 kPa 4-1 P =
constant heat rejection to initial state (a) Show the cycle on P-v and
T-s diagrams. (b) Calculate the net work output per unit mass. (c)
Determine the thermal efficiency.
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9–135 Repeat Problem 9–134 using constant specific heats at room temperature.
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9–136
An air-standard cycle with variable specific heats is executed in a
closed system with 0.003 kg of air, and it consists of the following
three processes: 1-2 Isentropic compression from 100 kPa and 27°C to 700
kPa 2-3 P = constant heat addition to initial specific volume 3-1 v =
constant heat rejection to initial state (a) Show the cycle on P-v and
T-s diagrams. (b) Calculate the maximum temperature in the cycle. (c)
Determine the thermal efficiency.
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9–137 Repeat Problem 9–136 using constant specific heats at room temperature.
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9–138
A Carnot cycle is executed in a closed system and uses 0.0025 kg of air
as the working fluid. The cycle efficiency is 60 percent, and the
lowest temperature in the cycle is 300 K. The pressure at the beginning
of the isentropic expansion is 700 kPa, and at the end of the isentropic
compression it is 1 MPa. Determine the net work output per cycle.
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9–139
A four-cylinder spark-ignition engine has a compression ratio of 8, and
each cylinder has a maximum volume of 0.6 L. At the beginning of the
compression process, the air is at 98 kPa and 17°C, and the maximum
temperature in the cycle is 1800 K. Assuming the engine to operate on
the ideal Otto cycle, determine (a) the amount of heat supplied per
cylinder, (b) the thermal efficiency, and (c) the number of revolutions
per minute required for a net power output of 60 kW. Assume variable
specific heats for air.
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9–140
Reconsider Problem 9–139. Using EES (or other) software, study the
effect of varying the compression ratio from 5 to 11 on the net work
done and the efficiency of the cycle. Plot the P-v and T-s diagrams for
the cycle, and discuss the results.
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9–141
An ideal Otto cycle has a compression ratio of 9.2 and uses air as the
working fluid. At the beginning of the compression process, air is at 98
kPa and 27°C. The pressure is doubled during the constant-volume
heat-addition process. Accounting for the variation of specific heats
with temperature, determine (a) the amount of heat transferred to the
air, (b) the net work output, (c) the thermal efficiency, and (d) the
mean effective pressure for the cycle.
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9–142 Repeat Problem 9–141 using constant specific heats at room temperature.
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9–143
Consider an engine operating on the ideal Diesel cycle with air as the
working fluid. The volume of the cylinder is 1200 cm3 at the beginning
of the compression process, 75 cm3 at the end, and 150 cm3 after the
heat-addition process. Air is at 17°C and 100 kPa at the beginning of
the compression process. Determine (a) the pressure at the beginning of
the heat-rejection process, (b) the net work per cycle, in kJ, and (c)
the mean effective pressure.
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9–144 Repeat Problem 9–143 using argon as the working fluid.
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9–145E
An ideal dual cycle has a compression ratio of 12 and uses air as the
working fluid. At the beginning of the compression process, air is at
14.7 psia and 90°F, and occupies a volume of 75 in3. During the
heat-addition process, 0.3 Btu of heat is transferred to air at constant
volume and 1.1 Btu at constant pressure. Using constant specific heats
evaluated at room temperature, determine the thermal efficiency of the
cycle.
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9–146
Consider an ideal Stirling cycle using air as the working fluid. Air is
at 350 K and 200 kPa at the beginning of the isothermal compression
process, and heat is supplied to air from a source at 1800 K in the
amount of 900 kJ/kg. Determine (a) the maximum pressure in the cycle and
(b) the net work output per unit mass of air.
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9–147
Consider a simple ideal Brayton cycle with air as the working fluid.
The pressure ratio of the cycle is 6, and the minimum and maximum
temperatures are 300 and 1300 K, respectively. Now the pressure ratio is
doubled without changing the minimum and maximum temperatures in the
cycle. Determine the change in (a) the net work output per unit mass and
(b) the thermal efficiency of the cycle as a result of this
modification. Assume variable specific heats for air.
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9–148 Repeat Problem 9–147 using constant specific heats at room temperature.
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9–149
Helium is used as the working fluid in a Brayton cycle with
regeneration. The pressure ratio of the cycle is 8, the compressor inlet
temperature is 300 K, and the turbine inlet temperature is 1800 K. The
effectiveness of the regenerator is 75 percent. Determine the thermal
efficiency and the required mass flow rate of helium for a net power
output of 60 MW, assuming both the compressor and the turbine have an
isentropic efficiency of (a) 100 percent and (b) 80 percent.
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9–150
A gas-turbine engine with regeneration operates with two stages of
compression and two stages of expansion. The pressure ratio across each
stage of the compressor and turbine is 3.5. The air enters each stage of
the compressor at 300 K and each stage of the turbine at 1200 K. The
compressor and turbine efficiencies are 78 and 86 percent, respectively,
and the effectiveness of the regenerator is 72 percent. Determine the
back work ratio and the thermal efficiency of the cycle, assuming
constant specific heats for air at room temperature. Answers: 53.2
percent, 39.2 percent
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9–151
Reconsider Problem 9–150. Using EES (or other) software, study the
effects of varying the isentropic efficiencies for the compressor and
turbine and regenerator effectiveness on net work done and the heat
supplied to the cycle for the variable specific heat case. Let the
isentropic efficiencies and the effectiveness vary from 70 percent to 90
percent. Plot the T-s diagram for the cycle.
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9–152 Repeat Problem 9–150 using helium as the working fluid.
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9–153
Consider the ideal regenerative Brayton cycle. Determine the pressure
ratio that maximizes the thermal efficiency of the cycle and compare
this value with the pressure ratio that maximizes the cycle net work.
For the same maximumto-minimum temperature ratios, explain why the
pressure ratio for maximum efficiency is less than the pressure ratio
for maximum work.
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9–154
Consider an ideal gas-turbine cycle with one stage of compression and
two stages of expansion and regeneration. The pressure ratio across each
turbine stage is the same. The high-pressure turbine exhaust gas enters
the regenerator and then enters the low-pressure turbine for expansion
to the compressor inlet pressure. Determine the thermal efficiency of
this cycle as a function of the compressor pressure ratio and the
high-pressure turbine to compressor inlet temperature ratio. Compare
your result with the efficiency of the standard regenerative cycle.
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9–155
A four-cylinder, four-stroke spark-ignition engine operates on the
ideal Otto cycle with a compression ratio of 11 and a total displacement
volume of 1.8 liter. The air is at 90 kPa and 50°C at the beginning of
the compression process. The heat input is 1.5 kJ per cycle per
cylinder. Accounting for the variation of specific heats of air with
temperature, determine (a) the maximum temperature and pressure that
occur during the cycle, (b) the net work per cycle per cyclinder and the
thermal efficiency of the cycle, (c) the mean effective pressure, and
(d) the power output for an engine speed of 3000 rpm.
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9–156
A gas-turbine plant operates on the regenerative Brayton cycle with two
stages of reheating and two-stages of intercooling between the pressure
limits of 100 and 1200 kPa. The working fluid is air. The air enters
the first and the second stages of the compressor at 300 K and 350 K,
respectively, and the first and the second stages of the turbine at 1400
K and 1300 K, respectively. Assuming both the compressor and the
turbine have an isentropic efficiency of 80 percent and the regenerator
has an effectiveness of 75 percent and using variable specific heats,
determine (a) the back work ratio and the net work output, (b) the
thermal efficiency, and (c) the second-law efficiency of the cycle. Also
determine (d) the exergies at the exits of the combustion chamber
(state 6) and the regenerator (state 10) (See Figure 9–43 in the text).
Answers: (a) 0.523, 317 kJ/kg, (b) 0.553, (c) 0.704, (d) 931 kJ/kg, 129
kJ/kg
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9–157
Electricity and process heat requirements of a manufacturing facility
are to be met by a cogeneration plant consisting of a gas turbine and a
heat exchanger for steam production The plant operates on the simple
Brayton cycle between the pressure limits of 100 and 1200 kPa with air
as the working fluid. Air enters the compressor at 30°C. Combustion
gases leave the turbine and enter the heat exchanger at 500°C, and leave
the heat exchanger of 350°C, while the liquid water enters the heat
exchanger at 25°C and leaves at 200°C as a saturated vapor. The net
power produced by the gas-turbine cycle is 800 kW. Assuming a compressor
isentropic efficiency of 82 percent and a turbine isentropic efficiency
of 88 percent and using variable specific heats, determine (a) the mass
flow rate of air, (b) the back work ratio and the thermal efficiency,
and (c) the rate at which steam is produced in the heat exchanger. Also
determine (d) the utilization efficiency of the cogeneration plant,
defined as the ratio of the total energy utilized to the energy supplied
to the plant.
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9–158
A turbojet aircraft flies with a velocity of 900 km/h at an altitude
where the air temperature and pressure are -35°C and 40 kPa. Air leaves
the diffuser at 50 kPa with a velocity of 15 m/s, and combustion gases
enter the turbine at 450 kPa and 950°C. The turbine produces 500 kW of
power, all of which is used to drive the compressor. Assuming an
isentropic efficiency of 83 percent for the compressor, turbine, and
nozzle, and using variable specific heats, determine (a) the pressure of
combustion gases at the turbine exit, (b) the mass flow rate of air
through the compressor, (c) the velocity of the gases at the nozzle
exit, and (d) the propulsive power and the propulsive efficiency for
this engine. Answers: (a) 147 kPa, (b) 1.76 kg/s, (c) 719 m/s, (d) 206
kW, 0.156
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9–159
Using EES (or other) software, study the effect of variable specific
heats on the thermal efficiency of the ideal Otto cycle using air as the
working fluid. At the beginning of the compression process, air is at
100 kPa and 300 K. Determine the percentage of error involved in using
constant specific heat values at room temperature for the following
combinations of compression ratios and maximum cycle temperatures: r =
6, 8, 10, 12, and Tmax = 1000, 1500, 2000, 2500 K.
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9–160
Using EES (or other) software, determine the effects of compression
ratio on the net work output and the thermal efficiency of the Otto
cycle for a maximum cycle temperature of 2000 K. Take the working fluid
to be air that is at 100 kPa and 300 K at the beginning of the
compression process, and assume variable specific heats. Vary the
compression ratio from 6 to 15 with an increment of 1. Tabulate and plot
your results against the compression ratio.
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9–161
Using EES (or other) software, determine the effects of pressure ratio
on the net work output and the thermal efficiency of a simple Brayton
cycle for a maximum cycle temperature of 1800 K. Take the working fluid
to be air that is at 100 kPa and 300 K at the beginning of the
compression process, and assume variable specific heats. Vary the
pressure ratio from 5 to 24 with an increment of 1. Tabulate and plot
your results against the pressure ratio. At what pressure ratio does the
net work output become a maximum? At what pressure ratio does the
thermal efficiency become a maximum?
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9–162 Repeat Problem 9–161 assuming isentropic efficiencies of 85 percent for both the turbine and the compressor.
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9–163
Using EES (or other) software, determine the effects of pressure ratio,
maximum cycle temperature, and compressor and turbine efficiencies on
the net work output per unit mass and the thermal efficiency of a simple
Brayton cycle with air as the working fluid. Air is at 100 kPa and 300 K
at the compressor inlet. Also, assume constant specific heats for air
at room temperature. Determine the net work output and the thermal
efficiency for all combinations of the following parameters, and draw
conclusions from the results. Pressure ratio: 5, 8, 14 Maximum cycle
temperature: 800, 1200, 1600 K Compressor isentropic efficiency: 80, 100
percent Turbine isentropic efficiency: 80, 100 percent
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9–164 Repeat Problem 9–163 by considering the variation of specific heats of air with temperature.
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9–165 Repeat Problem 9–163 using helium as the working fluid.
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9–166
Using EES (or other) software, determine the effects of pressure ratio,
maximum cycle temperature, regenerator effectiveness, and compressor
and turbine efficiencies on the net work output per unit mass and on the
thermal efficiency of a regenerative Brayton cycle with air as the
working fluid. Air is at 100 kPa and 300 K at the compressor inlet.
Also, assume constant specific heats for air at room temperature.
Determine the net work output and the thermal efficiency for all
combinations of the following parameters. Pressure ratio: 6, 10 Maximum
cycle temperature: 1500, 2000 K Compressor isentropic efficiency: 80,
100 percent Turbine isentropic efficiency: 80, 100 percent Regenerator
effectiveness: 70, 90 percent
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9–167 Repeat Problem 9–166 by considering the variation of specific heats of air with temperature.
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9–168 Repeat Problem 9–166 using helium as the working fluid.
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9–169
Using EES (or other) software, determine the effect of the number of
compression and expansion stages on the thermal efficiency of an ideal
regenerative Brayton cycle with multistage compression and expansion.
Assume that the overall pressure ratio of the cycle is 12, and the air
enters each stage of the compressor at 300 K and each stage of the
turbine at 1200 K. Using constant specific heats for air at room
temperature, determine the thermal efficiency of the cycle by varying
the number of stages from 1 to 22 in increments of 3. Plot the thermal
efficiency versus the number of stages. Compare your results to the
efficiency of an Ericsson cycle operating between the same temperature
limits.
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9–170 Repeat Problem 9–169 using helium as the working fluid
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9–171
An Otto cycle with air as the working fluid has a compression ratio of
8.2. Under cold-air-standard conditions, the thermal efficiency of this
cycle is (a) 24 percent (b) 43 percent (c) 52 percent (d) 57 percent (e)
75 percent
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9–172
For specified limits for the maximum and minimum temperatures, the
ideal cycle with the lowest thermal efficiency is (a) Carnot (b)
Stirling (c) Ericsson (d) Otto (e) All are the same
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9–173
A Carnot cycle operates between the temperature limits of 300 and 2000
K, and produces 600 kW of net power. The rate of entropy change of the
working fluid during the heat addition process is (a) 0 ( b) 0.300 kW/K
(c) 0.353 kW/K (d) 0.261 kW/K (e) 2.0 kW/K
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9–174
Air in an ideal Diesel cycle is compressed from 3 to 0.15 L, and then
it expands during the constant pressure heat addition process to 0.30 L.
Under cold air standard conditions, the thermal efficiency of this
cycle is (a) 35 percent (b) 44 percent (c) 65 percent (d) 70 percent (e)
82 percent
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9–175
Helium gas in an ideal Otto cycle is compressed from 20°C and 2.5 to
0.25 L, and its temperature increases by an additional 700°C during the
heat addition process. The temperature of helium before the expansion
process is (a) 1790°C (b) 2060°C (c) 1240°C (d) 620°C (e) 820°C
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9–176
In an ideal Otto cycle, air is compressed from 1.20 kg/m3 and 2.2 to
0.26 L, and the net work output of the cycle is 440 kJ/kg. The mean
effective pressure (MEP) for this cycle is (a) 612 kPa (b) 599 kPa (c)
528 kPa (d) 416 kPa (e) 367 kPa
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9–177
In an ideal Brayton cycle, air is compressed from 95 kPa and 25°C to
800 kPa. Under cold-air-standard conditions, the thermal efficiency of
this cycle is (a) 46 percent (b) 54 percent (c) 57 percent (d) 39
percent (e) 61 percent
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9–178
Consider an ideal Brayton cycle executed between the pressure limits of
1200 and 100 kPa and temperature limits of 20 and 1000°C with argon as
the working fluid. The net work output of the cycle is (a) 68 kJ/kg (b)
93 kJ/kg (c) 158 kJ/kg (d) 186 kJ/kg (e) 310 kJ/kg
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9–179
An ideal Brayton cycle has a net work output of 150 kJ/kg and a back
work ratio of 0.4. If both the turbine and the compressor had an
isentropic efficiency of 85 percent, the net work output of the cycle
would be (a) 74 kJ/kg (b) 95 kJ/kg (c) 109 kJ/kg (d) 128 kJ/kg (e) 177
kJ/kg
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9–180
In an ideal Brayton cycle, air is compressed from 100 kPa and 25°C to 1
MPa, and then heated to 1200°C before entering the turbine. Under
cold-air-standard conditions, the air temperature at the turbine exit is
(a) 490°C (b) 515°C (c) 622°C (d) 763°C (e) 895°C
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9–181
In an ideal Brayton cycle with regeneration, argon gas is compressed
from 100 kPa and 25°C to 400 kPa, and then heated to 1200°C before
entering the turbine. The highest temperature that argon can be heated
in the regenerator is (a) 246°C (b) 846°C (c) 689°C (d) 368°C (e) 573°C
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9–182
In an ideal Brayton cycle with regeneration, air is compressed from 80
kPa and 10°C to 400 kPa and 175°C, is heated to 450°C in the
regenerator, and then further heated to 1000°C before entering the
turbine. Under cold-air-standard conditions, the effectiveness of the
regenerator is (a) 33 percent (b) 44 percent (c) 62 percent (d) 77
percent (e) 89 percent
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9–183
Consider a gas turbine that has a pressure ratio of 6 and operates on
the Brayton cycle with regeneration between the temperature limits of 20
and 900°C. If the specific heat ratio of the working fluid is 1.3, the
highest thermal efficiency this gas turbine can have is (a) 38 percent
(b) 46 percent (c) 62 percent (d) 58 percent (e) 97 percent
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9–184
An ideal gas turbine cycle with many stages of compression and
expansion and a regenerator of 100 percent effectiveness has an overall
pressure ratio of 10. Air enters every stage of compressor at 290 K, and
every stage of turbine at 1200 K. The thermal efficiency of this
gas-turbine cycle is (a) 36 percent (b) 40 percent (c) 52 percent (d) 64
percent (e) 76 percent
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9–185
Air enters a turbojet engine at 260 m/s at a rate of 30 kg/s, and exits
at 800 m/s relative to the aircraft. The thrust developed by the engine
is (a) 8 kN (b) 16 kN (c) 24 kN (d) 20 kN (e) 32 kN
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