Thermodynamics: An Engineering Approach w/ Student Resources DVD

Yunus A. Cengel, Michael A. Boles

Chapter 9

GAS POWER CYCLES - all with Video Answers

Educators

Chapter Questions

Problem 1

Why is the Carnot cycle not suitable as an ideal cycle for all power-producing cyclic devices?

Saman Zulfiqar

Saman Zulfiqar

Numerade Educator

Problem 2

How does the thermal efficiency of an ideal cycle, in general, compare to that of a Carnot cycle operating between the same temperature limits?

Nathan Silvano

Numerade Educator

Problem 3

What does the area enclosed by the cycle represent on a $P$ - $v$ diagram? How about on a $T-s$ diagram?

Nathan Silvano

Numerade Educator

Problem 4

What is the difference between air-standard assumptions and the cold-air-standard assumptions?

Nathan Silvano

Numerade Educator

Problem 5

How are the combustion and exhaust processes modeled under the air-standard assumptions?

Saman Zulfiqar

Numerade Educator

Problem 6

What are the air-standard assumptions?

Narayan Hari

Numerade Educator

Problem 7

What is the difference between the clearance volume and the displacement volume of reciprocating engines?

Saman Zulfiqar

Numerade Educator

Problem 8

Define the compression ratio for reciprocating engines.

Nathan Silvano

Numerade Educator

Problem 9

How is the mean effective pressure for reciprocating engines defined?

Nathan Silvano

Numerade Educator

Problem 10

Can the mean effective pressure of an automobile engine in operation be less than the atmospheric pressure?

Nathan Silvano

Numerade Educator

Problem 11

As a car gets older, will its compression ratio change? How about the mean effective pressure?

Nathan Silvano

Numerade Educator

Problem 12

What is the difference between spark-ignition and compression-ignition engines?

Nathan Silvano

Numerade Educator

Problem 13

Define the following terms related to reciprocating engines: stroke, bore, top dead center, and clearance volume.

Nathan Silvano

Numerade Educator

Problem 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 $100 \mathrm{kPa}$ and $27^{\circ} \mathrm{C}$ to $800 \mathrm{kPa}$
2-3 $\quad V=$ constant heat addition to $1800 \mathrm{~K}$
3-4 Isentropic expansion to $100 \mathrm{kPa}$
4-1 $\quad P=$ 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.

Nathan Silvano

Numerade Educator

Problem 15

Reconsider Problem 9-14. Using EES (or other)
software, study the effect of varying the temperature after the constant-volume heat addition from $1500 \mathrm{~K}$ to $2500 \mathrm{~K}$. 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 $1800 \mathrm{~K}$.

Mark Scythian

Numerade Educator

Problem 16

An air-standard cycle is executed in a closed system and is composed of the following four processes:
1-2 Isentropic compression from $100 \mathrm{kPa}$ and $27^{\circ} \mathrm{C}$ to $1 \mathrm{MPa}$
2-3 $\quad P=$ constant heat addition in amount of 2800 $\mathrm{kJ} / \mathrm{kg}$
3-4 $\quad V=$ constant heat rejection to $100 \mathrm{kPa}$
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.

Nathan Silvano

Numerade Educator

Problem 17

An air-standard cycle with variable specific heats is executed in a closed system and is composed of the following four processes:
1-2 $\quad v=$ constant heat addition from 14.7 psia and $80^{\circ} \mathrm{F}$ in the amount of $300 \mathrm{Btu} / \mathrm{lbm}$
2-3 $\quad P=$ constant heat addition to $3200 \mathrm{R}$
3-4 Isentropic expansion to $14.7 \mathrm{psia}$
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.

Nathan Silvano

Numerade Educator

Problem 18

Repeat Problem 9-17E using constant specific heats at room temperature.

Ryan Pollard

Numerade Educator

Problem 19

An air-standard cycle is executed in a closed system with $0.004 \mathrm{~kg}$ of air and consists of the following three processes:
1-2 Isentropic compression from $100 \mathrm{kPa}$ and $27^{\circ} \mathrm{C}$ to $1 \mathrm{MPa}$
2-3 $\quad P=$ constant heat addition in the amount of $2.76 \mathrm{~kJ}$
3-1 $P=c_1 \vee+c_2$ heat rejection to initial state $\left(c_1\right.$ and $c_2$ 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.

Nathan Silvano

Numerade Educator

Problem 20

An air-standard cycle with variable specific heats is executed in a closed system with $0.003 \mathrm{~kg}$ of air and consists of the following three processes:
1-2 $v=$ constant heat addition from $95 \mathrm{kPa}$ and $17^{\circ} \mathrm{C}$ to $380 \mathrm{kPa}$
2-3 Iscntropic cxpansion to $95 \mathrm{kPa}$
3-1 $\quad P=$ 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.

Saman Zulfiqar

Numerade Educator

Problem 21

Repeat Problem 9-20 using constant specific heats at room temperature.

Nathan Silvano

Numerade Educator

Problem 22

Consider a Carnot cycle executed in a closed system with $0.003 \mathrm{~kg}$ of air. The temperature limits of the cycle are 300 and $900 \mathrm{~K}$, and the minimum and maximum pressures that occur during the cycle are 20 and $2000 \mathrm{kPa}$. Assuming constant specific heats, determine the net work output per cycle.

Nathan Silvano

Numerade Educator

Problem 23

An air-standard Carnot cycle is executed in a closed system between the temperature limits of 350 and $1200 \mathrm{~K}$. The pressures before and after the isothermal compression are 150 and $300 \mathrm{kPa}$, respectively. If the net work output per cycle is $0.5 \mathrm{~kJ}$, 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. Answers: (a) $30,013 \mathrm{kPa}$, (b) $0.706 \mathrm{~kJ}$, (c) $0.00296 \mathrm{~kg}$

Nathan Silvano

Numerade Educator

Problem 24

Repeat Problem 9-23 using helium as the working fluid.

Nathan Silvano

Numerade Educator

Problem 25

Consider a Carnot cycle executed in a closed system with air as the working fluid. The maximum pressure in the cycle is $800 \mathrm{kPa}$ while the maximum temperature is $750 \mathrm{~K}$. If the entropy increase during the isothermal heat rejection process is $0.25 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}$ and the net work output is 100 $\mathrm{kJ} / \mathrm{kg}$, 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 $5200 \mathrm{~kW}$ of power for an air flow rate of $90 \mathrm{~kg} / \mathrm{s}$, determine the second law efficiency of this cycle.

Nathan Silvano

Numerade Educator

Problem 26

What four processes make up the ideal Otto cycle?

Nathan Silvano

Numerade Educator

Problem 27

How do the efficiencies of the ideal Otto cycle and the Carnot cycle compare for the same temperature limits? Explain.

Nathan Silvano

Numerade Educator

Problem 28

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?

Nathan Silvano

Numerade Educator

Problem 29

Are the processes that make up the Otto cycle analyzed as closed-system or steady-flow processes? Why?

Nathan Silvano

Numerade Educator

Problem 30

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?

Nathan Silvano

Numerade Educator

Problem 31

Why are high compression ratios not used in sparkignition engines?

Nathan Silvano

Numerade Educator

Problem 32

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?

Nathan Silvano

Numerade Educator

Problem 33

What is the difference between fuel-injected gasoline engines and diesel engines?

Nathan Silvano

Numerade Educator

Problem 34

An ideal Otto cycle has a compression ratio of 8. At the beginning of the compression process, air is at $95 \mathrm{kPa}$ and $27^{\circ} \mathrm{C}$, and $750 \mathrm{~kJ} / \mathrm{kg}$ 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.

Saman Zulfiqar

Numerade Educator

Problem 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 $P-\vee$ diagrams for the cycle when the compression ratio is 8 .

Prem Bijarniya

Numerade Educator

Problem 36

Repeat Problem 9-34 using constant specific heats at room temperature.

Nathan Silvano

Numerade Educator

Problem 37

The compression ratio of an air-standard Otto cycle is 9.5. Prior to the isentropic compression process, the air is at $100 \mathrm{kPa}, 35^{\circ} \mathrm{C}$, and $600 \mathrm{~cm}^3$. The temperature at the end of the isentropic expansion process is $800 \mathrm{~K}$. 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 $\mathrm{kJ} ;(c)$ the thermal efficiency; and $(d)$ the mean effective pressure.

Gordon Ayadju

Numerade Educator

Problem 38

Repeat Problem 9-37, but replace the isentropic expansion process by a polytropic expansion process with the polytropic exponent $n=1.35$.

Saman Zulfiqar

Numerade Educator

Problem 39

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.

Narayan Hari

Numerade Educator

Problem 40

Repeat Problem 9-39E using argon as the working fluid.

Saman Zulfiqar

Numerade Educator

Problem 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 $100 \mathrm{kPa}$ and $60^{\circ} \mathrm{C}$ at the beginning of the compression process, and the maximum pressure in the cycle is $8 \mathrm{MPa}$. The compression and expansion processes may be modeled as polytropic with a polytropic constant of 1.3. Using constant specific heats at $850 \mathrm{~K}$, 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 $70 \mathrm{~kW}$, and $(e)$ the specific fuel consumption, in $\mathrm{g} / \mathrm{kWh}$, 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 .

Saman Zulfiqar

Numerade Educator

Problem 42

How does a diesel engine differ from a gasoline engine?

Nathan Silvano

Numerade Educator

Problem 43

How does the ideal Diesel cycle differ from the ideal Otto cycle?

Nathan Silvano

Numerade Educator

Problem 44

For a specified compression ratio, is a diesel or gasoline engine more efficient?

Nathan Silvano

Numerade Educator

Problem 45

Do diesel or gasoline engines operate at higher compression ratios? Why?

Nathan Silvano

Numerade Educator

Problem 46

What is the cutoff ratio? How does it affect the thermal efficiency of a Diesel cycle?

Saman Zulfiqar

Numerade Educator

Problem 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 $95 \mathrm{kPa}$ and $27^{\circ} \mathrm{C}$. 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.

Saman Zulfiqar

Numerade Educator

Problem 48

Repeat Problem 9-47 using constant specific heats at room temperature.

Narayan Hari

Numerade Educator

Problem 49

An air-standard Diesel cycle has a compression ratio of 18.2. Air is at $80^{\circ} \mathrm{F}$ and $14.7 \mathrm{psia}$ at the beginning of the compression process and at $3000 \mathrm{R}$ 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.

Dominador Tan

Numerade Educator

Problem 50

Repeat Problem 9-49E using constant specific heats at room temperature.

Nathan Silvano

Numerade Educator

Problem 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 $95 \mathrm{kPa}$ and $20^{\circ} \mathrm{C}$. If the maximum temperature in the cycle is not to exceed 2200 $\mathrm{K}$, determine $(a)$ the thermal efficiency and $(b)$ the mean effective pressure. Assume constant specific heats for air at room temperature.

Narayan Hari

Numerade Educator

Problem 52

Repeat Problem 9-51, but replace the isentropic expansion process by polytropic expansion process with the polytropic exponent $n=1.35$.

Saman Zulfiqar

Numerade Educator

Problem 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 .

Prem Bijarniya

Numerade Educator

Problem 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 $55^{\circ} \mathrm{C}$ and $97 \mathrm{kPa}$ at the beginning of the compression process. Using the cold-airstandard assumptions, determine how much power the engine will deliver at $1500 \mathrm{rpm}$.

Narayan Hari

Numerade Educator

Problem 55

Repeat Problem 9-54 using nitrogen as the working fluid.

Saman Zulfiqar

Numerade Educator

Problem 56

The compression ratio of an ideal dual cycle is 14. Air is at $100 \mathrm{kPa}$ and $300 \mathrm{~K}$ at the beginning of the compression process and at $2200 \mathrm{~K}$ 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 $1520.4 \mathrm{~kJ} / \mathrm{kg}$. Assuming variable specific heats for air, determine (a) the fraction of heat transferred at constant volume and $(b)$ the thermal efficiency of the cycle.

Saman Zulfiqar

Numerade Educator

Problem 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.

Prem Bijarniya

Numerade Educator

Problem 58

Repeat Problem 9-56 using constant specific heats at room temperature. Is the constant specific heat assumption reasonable in this case?

Nathan Silvano

Numerade Educator

Problem 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 $95 \mathrm{kPa}$ and $55^{\circ} \mathrm{C}$ at the beginning of the compression process and the engine speed is $2000 \mathrm{rpm}$. The engine uses light diesel fuel with a heating value of $42,500 \mathrm{~kJ} / \mathrm{kg}$, an air-fuel ratio of 24 , and a combustion efficiency of 98 percent. Using constant specific heats at $850 \mathrm{~K}$, 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 $\mathrm{g} / \mathrm{kWh}$, defined as the ratio of the mass of the fuel consumed to the net work produced.

Saman Zulfiqar

Numerade Educator

Problem 60

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?

Nathan Silvano

Numerade Educator

Problem 61

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?

Nathan Silvano

Numerade Educator

Problem 61

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 $1800 \mathrm{~K}$. Take the working fluid to be air that is at $100 \mathrm{kPa}$ and $300 \mathrm{~K}$ 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?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 62

What cycle is composed of two isothermal and two constant-volume processes?

Nathan Silvano

Numerade Educator

Problem 63

How does the ideal Ericsson cycle differ from the Carnot cycle?

Nathan Silvano

Numerade Educator

Problem 64

An ideal Ericsson engine using helium as the working fluid operates between temperature limits of 550 and $3000 \mathrm{R}$ and pressure limits of 25 and 200 psia. Assuming a mass flow rate of $14 \mathrm{lbm} / \mathrm{s}$, determine $(a)$ the thermal efficiency of the cycle, (b) the heat transfer rate in the regenerator, and $(c)$ the power delivered.

Narayan Hari

Numerade Educator

Problem 65

Consider an ideal Ericsson cycle with air as the working fluid executed in a steady-flow system. Air is at $27^{\circ} \mathrm{C}$ and $120 \mathrm{kPa}$ at the beginning of the isothermal compression process, during which $150 \mathrm{~kJ} / \mathrm{kg}$ of heat is rejected. Heat transfer to air occurs at $1200 \mathrm{~K}$. 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.

Narayan Hari

Numerade Educator

Problem 66

An ideal Stirling engine using helium as the working fluid operates between temperature limits of 300 and $2000 \mathrm{~K}$ and pressure limits of $150 \mathrm{kPa}$ and $3 \mathrm{MPa}$. Assuming the mass of the helium used in the cycle is $0.12 \mathrm{~kg}$, determine (a) the thermal efficiency of the cycle, $(b)$ the amount of heat transfer in the regenerator, and (c) the work output per cycle.

Narayan Hari

Numerade Educator

Problem 67

Why are the back work ratios relatively high in gasturbine engines?

Nathan Silvano

Numerade Educator

Problem 69

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?

Nathan Silvano

Numerade Educator

Problem 70

What is the back work ratio? What are typical back work ratio values for gas-turbine engines?

Nathan Silvano

Numerade Educator

Problem 71

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?

Nathan Silvano

Numerade Educator

Problem 72

A simple ideal Brayton cycle with air as the working fluid has a pressure ratio of 10 . The air enters the compressor at $520 \mathrm{R}$ and the turbine at $2000 \mathrm{R}$. 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.

Narayan Hari

Numerade Educator

Problem 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 $1160 \mathrm{~K}$. 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.

Vipender Yadav

Numerade Educator

Problem 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 $100 \mathrm{kPa}$. Develop a general solution for the problem by taking advantage of the diagram window method for supplying data to EES software.

Hariprasad Annamalai

Hariprasad Annamalai

Numerade Educator

Problem 75

Repeat Problem 9-73 using constant specific heats at room temperature.

Narayan Hari

Numerade Educator

Problem 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 $300 \mathrm{~K}$, and a turbine inlet temperature of $1000 \mathrm{~K}$. Determine the required mass flow rate of air for a net power output of $70 \mathrm{MW}$, 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.

Saman Zulfiqar

Numerade Educator

Problem 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 $95 \mathrm{kPa}$ and $290 \mathrm{~K}$ and the turbine at $760 \mathrm{kPa}$ and $1100 \mathrm{~K}$. Heat is transferred to air at a rate of $35,000 \mathrm{~kJ} / \mathrm{s}$. 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.

Saman Zulfiqar

Numerade Educator

Problem 78

Air enters the compressor of a gas-turbine engine at $300 \mathrm{~K}$ and $100 \mathrm{kPa}$, where it is compressed to $700 \mathrm{kPa}$ and $580 \mathrm{~K}$. Heat is transferred to air in the amount of $950 \mathrm{~kJ} / \mathrm{kg}$ 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.

Dominador Tan

Numerade Educator

Problem 79

Repeat Problem 9-78 using constant specific heats at room temperature.

Narayan Hari

Numerade Educator

Problem 80

A gas-turbine power plant operates on a simple Brayton cycle with air as the working fluid. The air enters the turbine at $120 \mathrm{psia}$ and $2000 \mathrm{R}$ and leaves at $15 \mathrm{psia}$ and $1200 \mathrm{R}$. Heat is rejected to the surroundings at a rate of 6400 $\mathrm{Btu} / \mathrm{s}$, and air flows through the cycle at a rate of $40 \mathrm{lbm} / \mathrm{s}$. 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.

Saman Zulfiqar

Numerade Educator

Problem 81

For what compressor efficiency will the gas-turbine power plant in Problem 9-80E produce zero net work?

Narayan Hari

Numerade Educator

Problem 82

A gas-turbine power plant operates on the simple Brayton cycle with air as the working fluid and delivers $32 \mathrm{MW}$ of power. The minimum and maximum temperatures in the cycle are 310 and $900 \mathrm{~K}$, 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.

Saman Zulfiqar

Numerade Educator

Problem 83

Repeat Problem 9-82 using constant specific heats at room temperature.

Nathan Silvano

Numerade Educator

Problem 84

A gas-turbine power plant operates on the simple Brayton cycle between the pressure limits of 100 and 1200 $\mathrm{kPa}$. The working fluid is air, which enters the compressor at $30^{\circ} \mathrm{C}$ at a rate of $150 \mathrm{~m}^3 / \mathrm{min}$ and leaves the turbine at $500^{\circ} \mathrm{C}$. 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.
FIGURE P9–84(Figure Cant Copy)

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 85

How does regeneration affect the efficiency of a Brayton cycle, and how does it accomplish it?

Nathan Silvano

Numerade Educator

Problem 86

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.

Nathan Silvano

Numerade Educator

Problem 87

Define the effectiveness of a regenerator used in gas-turbine cycles.

Saman Zulfiqar

Numerade Educator

Problem 88

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?

Nathan Silvano

Numerade Educator

Problem 89

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.

Nathan Silvano

Numerade Educator

Problem 93

An ideal Brayton cycle with regeneration has a pressure ratio of 10 . Air enters the compressor at $300 \mathrm{~K}$ and the turbine at $1200 \mathrm{~K}$. 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.

Hast Aggarwal

Numerade Educator

Problem 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.

Prem Bijarniya

Numerade Educator

Problem 95

Repeat Problem 9-93 using constant specific heats at room temperature.

Nathan Silvano

Numerade Educator

Problem 96

A stationary gas-turbine power plant operates on an ideal regenerative Brayton cycle ( $\epsilon=100$ percent) with air as the working fluid. Air enters the compressor at $95 \mathrm{kPa}$ and $290 \mathrm{~K}$ and the turbine at $760 \mathrm{kPa}$ and $1100 \mathrm{~K}$. Heat is transferred to air from an external source at a rate of $75,000 \mathrm{~kJ} / \mathrm{s}$. 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.

Dominador Tan

Numerade Educator

Problem 98

Air enters the compressor of a regenerative gas-turbine engine at $300 \mathrm{~K}$ and $100 \mathrm{kPa}$, where it is compressed to 800 $\mathrm{kPa}$ and $580 \mathrm{~K}$. The regenerator has an effectiveness of 72 percent, and the air enters the turbine at $1200 \mathrm{~K}$. 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. Answers: (a) 152.5 $\mathrm{kJ} / \mathrm{kg}$, (b) 36.0 percent

Dominador Tan

Numerade Educator

Problem 99

Repeat Problem 9-98 using constant specific heats at room temperature.

Narayan Hari

Numerade Educator

Problem 100

Repeat Problem 9-98 for a regenerator effectiveness of 70 percent.

Saman Zulfiqar

Numerade Educator

Problem 101

Under what modifications will the ideal simple gas-turbine cycle approach the Ericsson cycle?

Nathan Silvano

Numerade Educator

Problem 102

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?

Nathan Silvano

Numerade Educator

Problem 103

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?

Nathan Silvano

Numerade Educator

Problem 104

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?

Saman Zulfiqar

Numerade Educator

Problem 105

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?

Dominador Tan

Numerade Educator

Problem 106

For a specified pressure ratio, why does multistage compression with intercooling decrease the compressor work, and multistage expansion with reheating increase the turbine work?

Dominador Tan

Numerade Educator

Problem 107

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.

Narayan Hari

Numerade Educator

Problem 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 $300 \mathrm{~K}$ and each stage of the turbine at $1200 \mathrm{~K}$. 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.

Saman Zulfiqar

Numerade Educator

Problem 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.

Saman Zulfiqar

Numerade Educator

Problem 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 $300 \mathrm{~K}$ and each stage of the turbine at $1200 \mathrm{~K}$. 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 $110 \mathrm{MW}$.

Vipender Yadav

Numerade Educator

Problem 111

Repeat Problem 9-110 using argon as the working fluid.

Saman Zulfiqar

Numerade Educator

Problem 112

What is propulsive power? How is it related to thrust?

Vysakh M

Numerade Educator

Problem 113

What is propulsive efficiency? How is it determined?

Narayan Hari

Numerade Educator

Problem 114

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?

Narayan Hari

Numerade Educator

Problem 115

A turbojet is flying with a velocity of $900 \mathrm{ft} / \mathrm{s}$ at an altitude of $20,000 \mathrm{ft}$, where the ambient conditions are $7 \mathrm{psia}$ and $10^{\circ} \mathrm{F}$. The pressure ratio across the compressor is 13 , and the temperature at the turbine inlet is $2400 \mathrm{R}$. 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.

Dominador Tan

Numerade Educator

Problem 116

Repeat Problem 9-115E accounting for the variation of specific heats with temperature.

Saman Zulfiqar

Numerade Educator

Problem 117

A turbojet aircraft is flying with a velocity of $320 \mathrm{~m} / \mathrm{s}$ at an altitude of $9150 \mathrm{~m}$, where the ambient conditions are $32 \mathrm{kPa}$ and $-32^{\circ} \mathrm{C}$. The pressure ratio across the compressor is 12 , and the temperature at the turbine inlet is $1400 \mathrm{~K}$. Air enters the compressor at a rate of $60 \mathrm{~kg} / \mathrm{s}$, and the jet fuel has a heating value of $42,700 \mathrm{~kJ} / \mathrm{kg}$. 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.

Dominador Tan

Numerade Educator

Problem 118

Repeat Problem 9-117 using a compressor efficiency of 80 percent and a turbine efficiency of 85 percent.

Saman Zulfiqar

Numerade Educator

Problem 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 $27^{\circ} \mathrm{C}$ and $95 \mathrm{kPa}$ and enters the engine at a rate of $10 \mathrm{~kg} / \mathrm{s}$. The jet fuel has a heating value of $42,700 \mathrm{~kJ} / \mathrm{kg}$, and it is burned completely at a rate of $0.2 \mathrm{~kg} / \mathrm{s}$. 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.

Saman Zulfiqar

Numerade Educator

Problem 120

Reconsider Problem 9-119. In the problem statement, replace the inlet mass flow rate by an inlet volume flow rate of $9.063 \mathrm{~m}^3 / \mathrm{s}$. Using EES (or other) software, investigate the effect of compressor inlet temperature in the range of -20 to $30^{\circ} \mathrm{C}$ 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.

Prem Bijarniya

Numerade Educator

Problem 121

Air at $7^{\circ} \mathrm{C}$ enters a turbojet engine at a rate of $16 \mathrm{~kg} / \mathrm{s}$ and at a velocity of $300 \mathrm{~m} / \mathrm{s}$ (relative to the engine).
Air is heated in the combustion chamber at a rate $15,000 \mathrm{~kJ} / \mathrm{s}$ and it leaves the engine at $427^{\circ} \mathrm{C}$. Determine the thrust produced by this turbojet engine.

Narayan Hari

Numerade Educator

Problem 122

Determine the total exergy destruction associated with the Otto cycle described in Problem 9-34, assuming a source temperature of $2000 \mathrm{~K}$ and a sink temperature of 300 K. Also, determine the exergy at the end of the power stroke.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 123

Determine the total exergy destruction associated with the Diesel cycle described in Problem 9-47, assuming a source temperature of $2000 \mathrm{~K}$ and a sink temperature of 300 $\mathrm{K}$. Also, determine the exergy at the end of the isentropic compression process.

Saman Zulfiqar

Numerade Educator

Problem 124

Determine the exergy destruction associated with the heat rejection process of the Diesel cycle described in Problem 9-49E, assuming a source temperature of $3500 \mathrm{R}$ and a sink temperature of 540 R. Also, determine the exergy at the end of the isentropic expansion process.

Saman Zulfiqar

Numerade Educator

Problem 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 $1600 \mathrm{~K}$ and a sink temperature of $290 \mathrm{~K}$.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 126

Determine the total exergy destruction associated with the Brayton cycle described in Problem 9-93, assuming a source temperature of $1800 \mathrm{~K}$ and a sink temperature of $300 \mathrm{~K}$. Also, determine the exergy of the exhaust gases at the exit of the regenerator.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 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.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 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 $1260 \mathrm{~K}$ and a sink temperature of $300 \mathrm{~K}$. Also, determine the exergy of the exhaust gases at the exit of the regenerator. Take $P_{\text {exhaust }}=P_0=100 \mathrm{kPa}$.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 129

A gas-turbine power plant operates on the simple Brayton cycle between the pressure limits of 100 and 700 $\mathrm{kPa}$. Air enters the compressor at $30^{\circ} \mathrm{C}$ at a rate of $12.6 \mathrm{~kg} / \mathrm{s}$ and leaves at $260^{\circ} \mathrm{C}$. A diesel fuel with a heating value of $42,000 \mathrm{~kJ} / \mathrm{kg}$ 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 $500^{\circ} \mathrm{C}$, 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.
FIGURE P9–129(Figure Cant Copy)

Saman Zulfiqar

Numerade Educator

Problem 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 $95 \mathrm{kPa}$ and $55^{\circ} \mathrm{C}$ at the beginning of the compression process and the engine speed is $3500 \mathrm{rpm}$. Equal amounts of fuel are burned at constant volume and at constant pressure. The maximum allowable pressure in the cycle is $9 \mathrm{MPa}$ due to material strength limitations. Using constant specific heats at $850 \mathrm{~K}$, 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.

Saman Zulfiqar

Numerade Educator

Problem 131

A gas-turbine power plant operates on the regenerative Brayton cycle between the pressure limits of 100 and $700 \mathrm{kPa}$. Air enters the compressor at $30^{\circ} \mathrm{C}$ at a rate of 12.6 $\mathrm{kg} / \mathrm{s}$ and leaves at $260^{\circ} \mathrm{C}$. It is then heated in a regenerator to $400^{\circ} \mathrm{C}$ by the hot combustion gases leaving the turbine. A diesel fuel with a heating value of $42,000 \mathrm{~kJ} / \mathrm{kg}$ is burned in the combustion chamber with a combustion efficiency of 97 percent. The combustion gases leave the combustion chamber at $871^{\circ} \mathrm{C}$ and enter the turbine whose isentropic efficiency is 85 percent. Treating combustion gases as air and using constant specific heats at $500^{\circ} \mathrm{C}$, 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.
FIGURE P9–131(Figure Cant Copy)

Saman Zulfiqar

Numerade Educator

Problem 132

A four-stroke turbocharged V-16 diesel engine built by GE Transportation Systems to power fast trains produces $3500 \mathrm{hp}$ at $1200 \mathrm{rpm}$. Determine the amount of power produced per cylinder per (a) mechanical cycle and (b) thermodynamic cycle.

Narayan Hari

Numerade Educator

Problem 133

Consider a simple ideal Brayton cycle operating between the temperature limits of 300 and $1500 \mathrm{~K}$. Using constant specific heats at room temperature, determine the pressure ratio for which the compressor and the turbine exit temperatures of air are equal.

Narayan Hari

Numerade Educator

Problem 134

An air-standard cycle with variable coefficients is executed in a closed system and is composed of the following four processes:
1-2 $\quad v=$ constant heat addition from $100 \mathrm{kPa}$ and $27^{\circ} \mathrm{C}$ to $300 \mathrm{kPa}$
2-3 $\quad P=$ constant heat addition to $1027^{\circ} \mathrm{C}$
3-4 Isentropic expansion to $100 \mathrm{kPa}$
4-1 $\quad P=$ 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.

Nathan Silvano

Numerade Educator

Problem 135

Repeat Problem 9-134 using constant specific heats at room temperature.

Nathan Silvano

Numerade Educator

Problem 136

An air-standard cycle with variable specific heats is executed in a closed system with $0.003 \mathrm{~kg}$ of air, and it consists of the following three processes:
1-2 Isentropic compression from $100 \mathrm{kPa}$ and $27^{\circ} \mathrm{C}$ to $700 \mathrm{kPa}$
2-3 $\quad P=$ constant heat addition to initial specific volume
3-1 $\quad v=$ 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.

Saman Zulfiqar

Numerade Educator

Problem 137

Repeat Problem 9-136 using constant specific heats at room temperature.

Nathan Silvano

Numerade Educator

Problem 138

A Carnot cycle is executed in a closed system and uses $0.0025 \mathrm{~kg}$ of air as the working fluid. The cycle efficiency is 60 percent, and the lowest temperature in the cycle is $300 \mathrm{~K}$. The pressure at the beginning of the isentropic expansion is $700 \mathrm{kPa}$, and at the end of the isentropic compression it is $1 \mathrm{MPa}$. Determine the net work output per cycle.

Dominador Tan

Numerade Educator

Problem 139

A four-cylinder spark-ignition engine has a compression ratio of 8 , and each cylinder has a maximum volume of $0.6 \mathrm{~L}$. At the beginning of the compression process, the air is at $98 \mathrm{kPa}$ and $17^{\circ} \mathrm{C}$, and the maximum temperature in the cycle is $1800 \mathrm{~K}$. 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 $60 \mathrm{~kW}$. Assume variable specific heats for air.

Saman Zulfiqar

Numerade Educator

Problem 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.

Prem Bijarniya

Numerade Educator

Problem 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 $98 \mathrm{kPa}$ and $27^{\circ} \mathrm{C}$. 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.

Saman Zulfiqar

Numerade Educator

Problem 142

Repeat Problem 9-141 using constant specific heats at room temperature.

Narayan Hari

Numerade Educator

Problem 143

Consider an engine operating on the ideal Diesel cycle with air as the working fluid. The volume of the cylinder is $1200 \mathrm{~cm}^3$ at the beginning of the compression process, $75 \mathrm{~cm}^3$ at the end, and $150 \mathrm{~cm}^3$ after the heat-addition process. Air is at $17^{\circ} \mathrm{C}$ and $100 \mathrm{kPa}$ 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 $\mathrm{kJ}$, and $(c)$ the mean effective pressure.

Saman Zulfiqar

Numerade Educator

Problem 144

Repeat Problem 9-143 using argon as the working fluid.

Saman Zulfiqar

Numerade Educator

Problem 145

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 $14.7 \mathrm{psia}$ and $90^{\circ} \mathrm{F}$, and occupies a volume of $75 \mathrm{in}^3$. During the heat-addition process, $0.3 \mathrm{Btu}$ 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.

Narayan Hari

Numerade Educator

Problem 146

Consider an ideal Stirling cycle using air as the working fluid. Air is at $350 \mathrm{~K}$ and $200 \mathrm{kPa}$ at the beginning of the isothermal compression process, and heat is supplied to air from a source at $1800 \mathrm{~K}$ in the amount of $900 \mathrm{~kJ} / \mathrm{kg}$. Determine $(a)$ the maximum pressure in the cycle and $(b)$ the net work output per unit mass of air.

Saman Zulfiqar

Numerade Educator

Problem 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 $1300 \mathrm{~K}$, 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.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 148

Repeat Problem 9-147 using constant specific heats at room temperature.

Saman Zulfiqar

Numerade Educator

Problem 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 $300 \mathrm{~K}$, and the turbine inlet temperature is $1800 \mathrm{~K}$. 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 $60 \mathrm{MW}$, assuming both the compressor and the turbine have an isentropic efficiency of (a) 100 percent and (b) 80 percent.

Saman Zulfiqar

Numerade Educator

Problem 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 $300 \mathrm{~K}$ and each stage of the turbine at $1200 \mathrm{~K}$. 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.

Dominador Tan

Numerade Educator

Problem 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.

Prem Bijarniya

Numerade Educator

Problem 152

Repeat Problem 9-150 using helium as the working fluid.

Nathan Silvano

Numerade Educator

Problem 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.

Saman Zulfiqar

Numerade Educator

Problem 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.

Saman Zulfiqar

Numerade Educator

Problem 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 $90 \mathrm{kPa}$ and $50^{\circ} \mathrm{C}$ at the beginning of the compression process. The heat input is $1.5 \mathrm{~kJ}$ 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 $3000 \mathrm{rpm}$.

Saman Zulfiqar

Numerade Educator

Problem 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 $1200 \mathrm{kPa}$. The working fluid is air. The air enters the first and the second stages of the compressor at $300 \mathrm{~K}$ and $350 \mathrm{~K}$, respectively, and the first and the second stages of the turbine at $1400 \mathrm{~K}$ and $1300 \mathrm{~K}$, 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).

Saman Zulfiqar

Numerade Educator

Problem 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.
FIGURE P9–157(Figure Cant Copy)

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 158

A turbojet aircraft flies with a velocity of $900 \mathrm{~km} / \mathrm{h}$ at an altitude where the air temperature and pressure are $-35^{\circ} \mathrm{C}$ and $40 \mathrm{kPa}$. Air leaves the diffuser at $50 \mathrm{kPa}$ with a velocity of $15 \mathrm{~m} / \mathrm{s}$, and combustion gases enter the turbine at $450 \mathrm{kPa}$ and $950^{\circ} \mathrm{C}$. The turbine produces $500 \mathrm{~kW}$ 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.

Saman Zulfiqar

Numerade Educator

Problem 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 $\mathrm{kPa}$ and $300 \mathrm{~K}$. 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 $T_{\max }=1000$, $1500,2000,2500 \mathrm{~K}$.

Saman Zulfiqar

Numerade Educator

Problem 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 $2000 \mathrm{~K}$. Take the working fluid to be air that is at $100 \mathrm{kPa}$ and $300 \mathrm{~K}$ 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.

Manik Pulyani

Numerade Educator

Problem 162

Repeat Problem 9-161 assuming isentropic efficiencies of 85 percent for both the turbine and the compressor.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 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 $100 \mathrm{kPa}$ and $300 \mathrm{~K}$ 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.
$$
\begin{array}{ll}
\text { Pressure ratio: } & 5,8,14 \\
\text { Maximum cycle temperature: } & 800,1200,1600 \mathrm{~K} \\
\text { Compressor isentropic efficiency: } & 80,100 \text { percent } \\
\text { Turbine isentropic efficiency: } & 80,100 \text { percent }
\end{array}
$$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 164

Repeat Problem $9-163$ by considering the variation of specific heats of air with temperature.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 165

Repeat Problem 9-163 using helium as the working fluid.

Nathan Silvano

Numerade Educator

Problem 166

Using EES (or other) software, determine the effects of pressure ratio, maximum cycle tem-
perature, 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 $100 \mathrm{kPa}$ and $300 \mathrm{~K}$ 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.
$$
\begin{array}{ll}
\text { Pressure ratio: } & 6,10 \\
\text { Maximum cycle temperature: } & 1500,2000 \mathrm{~K} \\
\text { Compressor isentropic efficiency: } & 80,100 \text { percent } \\
\text { Turbine isentropic efficiency: } & 80,100 \text { percent } \\
\text { Regenerator effectiveness: } & 70,90 \text { percent }
\end{array}
$$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 167

Repeat Problem $9-166$ by considering the variation of specific heats of air with temperature.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 168

Repeat Problem 9-166 using helium as the working fluid.

Nathan Silvano

Numerade Educator

Problem 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 $300 \mathrm{~K}$ and each stage of the turbine at $1200 \mathrm{~K}$. 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.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 170

Repeat Problem 9-169 using helium as the working fluid.

Nathan Silvano

Numerade Educator

Problem 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

Narayan Hari

Numerade Educator

Problem 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

Narayan Hari

Numerade Educator

Problem 173

A Carnot cycle operates between the temperature limits of 300 and $2000 \mathrm{~K}$, and produces $600 \mathrm{~kW}$ of net power. The rate of entropy change of the working fluid during the heat addition process is
(a) 0
(b) $0.300 \mathrm{~kW} / \mathrm{K}$
(c) $0.353 \mathrm{~kW} / \mathrm{K}$
(d) $0.261 \mathrm{~kW} / \mathrm{K}$
(e) $2.0 \mathrm{~kW} / \mathrm{K}$

Narayan Hari

Numerade Educator

Problem 174

Air in an ideal Diesel cycle is compressed from 3 to $0.15 \mathrm{~L}$, and then it expands during the constant pressure heat addition process to $0.30 \mathrm{~L}$. 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

Saman Zulfiqar

Numerade Educator

Problem 175

Helium gas in an ideal Otto cycle is compressed from $20^{\circ} \mathrm{C}$ and 2.5 to $0.25 \mathrm{~L}$, and its temperature increases by an additional $700^{\circ} \mathrm{C}$ during the heat addition process. The temperature of helium before the expansion process is
(a) $1790^{\circ} \mathrm{C}$
(b) $2060^{\circ} \mathrm{C}$
(c) $1240^{\circ} \mathrm{C}$
(d) $620^{\circ} \mathrm{C}$
(e) $820^{\circ} \mathrm{C}$

Narayan Hari

Numerade Educator

Problem 176

In an ideal Otto cycle, air is compressed from 1.20 $\mathrm{kg} / \mathrm{m}^3$ and 2.2 to $0.26 \mathrm{~L}$, and the net work output of the cycle is $440 \mathrm{~kJ} / \mathrm{kg}$. The mean effective pressure (MEP) for this cycle is
(a) $612 \mathrm{kPa}$
(b) $599 \mathrm{kPa}$
(c) $528 \mathrm{kPa}$
(d) $416 \mathrm{kPa}$
(e) $367 \mathrm{kPa}$

Narayan Hari

Numerade Educator

Problem 177

In an ideal Brayton cycle, air is compressed from 95 $\mathrm{kPa}$ and $25^{\circ} \mathrm{C}$ to $800 \mathrm{kPa}$. 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

Saman Zulfiqar

Numerade Educator

Problem 178

Consider an ideal Brayton cycle executed between the pressure limits of 1200 and $100 \mathrm{kPa}$ and temperature limits of 20 and $1000^{\circ} \mathrm{C}$ with argon as the working fluid. The net work output of the cycle is
(a) $68 \mathrm{~kJ} / \mathrm{kg}$
(b) $93 \mathrm{~kJ} / \mathrm{kg}$
(d) $186 \mathrm{~kJ} / \mathrm{kg}$
(c) $158 \mathrm{~kJ} / \mathrm{kg}$
(e) $310 \mathrm{~kJ} / \mathrm{kg}$

Narayan Hari

Numerade Educator

Problem 179

An ideal Brayton cycle has a net work output of 150 $\mathrm{kJ} / \mathrm{kg}$ 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) $74 \mathrm{~kJ} / \mathrm{kg}$
(b) $95 \mathrm{~kJ} / \mathrm{kg}$
(c) $109 \mathrm{~kJ} / \mathrm{kg}$
(d) $128 \mathrm{~kJ} / \mathrm{kg}$
(e) $177 \mathrm{~kJ} / \mathrm{kg}$

Narayan Hari

Numerade Educator

Problem 180

In an ideal Brayton cycle, air is compressed from $100 \mathrm{kPa}$ and $25^{\circ} \mathrm{C}$ to $1 \mathrm{MPa}$, and then heated to $1200^{\circ} \mathrm{C}$ before entering the turbine. Under cold-air-standard conditions, the air temperature at the turbine exit is
(a) $490^{\circ} \mathrm{C}$
(b) $515^{\circ} \mathrm{C}$
(c) $622^{\circ} \mathrm{C}$
(d) $763^{\circ} \mathrm{C}$
(e) $895^{\circ} \mathrm{C}$

Narayan Hari

Numerade Educator

Problem 181

In an ideal Brayton cycle with regeneration, argon gas is compressed from $100 \mathrm{kPa}$ and $25^{\circ} \mathrm{C}$ to $400 \mathrm{kPa}$, and then heated to $1200^{\circ} \mathrm{C}$ before entering the turbine. The highest temperature that argon can be heated in the regenerator is
(a) $246^{\circ} \mathrm{C}$
(b) $846^{\circ} \mathrm{C}$
(c) $689^{\circ} \mathrm{C}$
(d) $368^{\circ} \mathrm{C}$
(e) $573^{\circ} \mathrm{C}$

Narayan Hari

Numerade Educator

Problem 182

In an ideal Brayton cycle with regeneration, air is compressed from $80 \mathrm{kPa}$ and $10^{\circ} \mathrm{C}$ to $400 \mathrm{kPa}$ and $175^{\circ} \mathrm{C}$, is heated to $450^{\circ} \mathrm{C}$ in the regenerator, and then further heated to $1000^{\circ} \mathrm{C}$ 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

Narayan Hari

Numerade Educator

Problem 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 $900^{\circ} \mathrm{C}$. 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

Narayan Hari

Numerade Educator

Problem 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 $290 \mathrm{~K}$, and every stage of turbine at $1200 \mathrm{~K}$. The thermal efficiency of this gas-turbine cycle is
(a) 36 percent
(b) 40 percent
(c) 52 percent
(d) 64 percent
(e) 76 percent

Narayan Hari

Numerade Educator

Problem 185

Air enters a turbojet engine at $260 \mathrm{~m} / \mathrm{s}$ at a rate of 30 $\mathrm{kg} / \mathrm{s}$, and exits at $800 \mathrm{~m} / \mathrm{s}$ relative to the aircraft. The thrust developed by the engine is
(a) $8 \mathrm{kN}$
(b) $16 \mathrm{kN}$
(c) $24 \mathrm{kN}$
(d) $20 \mathrm{kN}$
(e) $32 \mathrm{kN}$

Narayan Hari

Numerade Educator

Problem 186

Design a closed-system air-standard gas power cycle composed of three processes and having a minimum thermal efficiency of 20 percent. The processes may be isothermal, isobaric, isochoric, isentropic, polytropic, or pressure as a linear function of volume. Prepare an engineering report describing your design, showing the system, $P-V$ and $T-s$ diagrams, and sample calculations.

Saman Zulfiqar

Numerade Educator

Problem 187

Design a closed-system air-standard gas power cycle composed of three processes and having a minimum thermal efficiency of 20 percent. The processes may be isothermal, isobaric, isochoric, isentropic, polytropic, or pressure as a linear function of volume; however, the Otto, Diesel, Ericsson, and Stirling cycles may not be used. Prepare an engineering report describing your design, showing the system, $P-V$ and $T$-s diagrams, and sample calculations.

Saman Zulfiqar

Numerade Educator

Problem 188

Write an essay on the most recent developments on the two-stroke engines, and find out when we might be seeing cars powered by two-stroke engines in the market. Why do the major car manufacturers have a renewed interest in two-stroke engines?

Dominador Tan

Numerade Educator

Problem 189

In response to concerns about the environment, some major car manufacturers are currently marketing electric cars. Write an essay on the advantages and disadvantages of electric cars, and discuss when it is advisable to purchase an electric car instead of a traditional internal combustion car.

Prem Bijarniya

Numerade Educator

Problem 190

Intense research is underway to develop adiabatic engines that require no cooling of the engine block. Such engines are based on ceramic materials because of the ability of such materials to withstand high temperatures. Write an essay on the current status of adiabatic engine development. Also determine the highest possible efficiencies with these engines, and compare them to the highest possible efficiencies of current engines.

Prem Bijarniya

Numerade Educator

Problem 191

Since its introduction in 1903 by Aegidius Elling of Norway, steam injection between the combustion chamber and the turbine is used even in some modern gas turbines currently in operation to cool the combustion gases to a metallurgical-safe temperature while increasing the mass flow rate through the turbine. Currently there are several gasturbine power plants that use steam injection to augment power and improve thermal efficiency.
Consider a gas-turbine power plant whose pressure ratio is 8. The isentropic efficiencies of the compressor and the turbine are 80 percent, and there is a regenerator with an effectiveness of 70 percent. When the mass flow rate of air through the compressor is $40 \mathrm{~kg} / \mathrm{s}$, the turbine inlet temperature becomes 1700 $\mathrm{K}$. But the turbine inlet temperature is limited to $1500 \mathrm{~K}$, and thus steam injection into the combustion gases is being considered. However, to avoid the complexities associated with steam injection, it is proposed to use excess air (that is, to take in much more air than needed for complete combustion) to lower the combustion and thus turbine inlet temperature while increasing the mass flow rate and thus power output of the turbine. Evaluate this proposal, and compare the thermodynamic performance of "high air flow" to that of a "steam-injection" gas-turbine power plant under the following design conditions: the ambient air is at $100 \mathrm{kPa}$ and $25^{\circ} \mathrm{C}$, adequate water supply is available at $20^{\circ} \mathrm{C}$, and the amount of fuel supplied to the combustion chamber remains constant.

Prem Bijarniya

Numerade Educator