Consider the ideal Otto, Stirling, and Carnot cycles

Problem 1P What are the air-standard assumptions?

Problem 2P What is the difference between air-standard assumptions and the cold-air-standard assumptions?

Problem 3P How does the thermal efficiency of an ideal cycle, in general, compare to that of a Carnot cycle operating between the same temperature limits?

Problem 4P What does the area enclosed by the cycle represent on aP-Vdiagram? How about on aT-sdiagram?

Problem 5P Define the compression ratio for reciprocating engines.

Problem 6P How is the mean effective pressure for reciprocating engines defined?

Problem 7P Can the mean effective pressure of an automobile engine in operation be less than the atmospheric pressure?

Problem 8P As a car gets older, will its compression ratio change? How about the mean effective pressure?

Problem 9P What is the difference between spark-ignition and compression-ignition engines?

Problem 10P Define the following terms related to reciprocating engines: stroke, bore, top dead center, and clearance volume.

Problem 11P What is the maximum possible thermal efficiency of a gas power cycle when using thermal energy reservoirs at 1100°F and 80°F?

Problem 12P An air-standard cycle with constant specific heats is executed in a closed piston-cylinder system and is composed of the following three processes: 1.2 Isentropic compression with a compression ratior =6,T1, = 27°C, andP1, = 100 kPa 2-3 Constant pressure heat addition 3-1 Constant volume heat rejection Assume air has constant properties withcv = 0.718 kJ/kg•K,cp= 1.005 kJ/kg•K,R= 0.287 kJ/kg•K, andk =1.4. (a)Sketch theP-VandT-sdiagrams for this cycle. ________________ (b)Determine the back work ratio for this cycle.

Problem 13P 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 22°C to 600 kPa 2-3V = constantheat addition, to 1500 K 3-4 Isentropic expansion to 100 kPa 4-1P =constantheat rejection to initial state (a) Show the cycle onP-VandT-sdiagrams. ________________ (b) Calculate the net work output per unit mass. ________________ (c) Determine the thermal efficiency.

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 \(1500 \mathrm{~K}\). Equation Transcription: Text Transcription: 1500 K 2500 K T-s P-V 1500 K

Problem 15P An air-standard cycle is executed in a closed system with 0.5 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 416 kJ 3-1 P = c1v + c2 heat rejection to initial state (cj 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.

Problem 16P An air-standard cycle with variable specific heats is executed in a closed system and is composed of the following four processes: 1–2V = constantheat addition from 14.7 psia and 80°F in the amount of 300 Btu/lbm 2-3P =constantheat addition to 3200 R 3-4 Isentropic expansion to 14.7 psia 4-1P =constantheat rejection to initial state (a) Show the cycle onP-VandT-sdiagrams. ________________ (b) Calculate the total heat input per unit mass. ________________ (c) Determine the thermal efficiency.

Problem 17P Repeat Prob. 9–19E using constant specific heats at room temperature.

Problem 18P 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.

Problem 19P Repeat Problem 9–18 using helium as the working fluid. Problem 9–18 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.

Problem 20P Consider a Carnot cycle executed in a closed system with 0.6 kg of air. The temperature limits of the-cycle are 300 and 1100 K, and the minimum and maximum pressures that occur during the cycle are 20 and 3000 kPa. Assuming constant specific heats, determine the net work output per cycle.

What are the air-standard assumptions?

Problem 9.92C For what compressor efficiency will the gas-turbine power plant in problem 9-91E produce zero net work?

A gas-turbine power plant operates on the simple Brayton cycle between the pressure limits of 100 and . Air enters the compressor at and leaves at at a mass flow rate of . The maximum cycle temperature is . During operation of the cycle, the net power output is measured experimentally to be . Assume constant properties for air at with , , , (a) Sketch the T-s diagram for the cycle. (b) Determine the isentropic efficiency of the turbine for these operating conditions. (c) Determine the cycle thermal efficiency.

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

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

How is the mean effective pressure for reciprocating engines defined?

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?

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.

A gas turbine for an automobile is designed with a regenerator. Air enters the compressor of this engine at and . The compressor pressure ratio is 10; the maximum cycle temperature is ; and the cold air stream leaves the regenerator cooler than the hot air stream at the inlet of the regenerator. Assuming both the compressor and the turbine to be isentropic, determine the rates of heat addition and rejection for this cycle when it produces . Use constant specific heats at room temperature.

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

What is the maximum possible thermal efficiency of a gas power cycle when using thermal energy reservoirs at and ?

An air-standard cycle is executed within a closed piston-cylinder system and consists of three processes as follows: 1-2 V = constant heat addition from and to 2-3 Isothermal expansion until 3-1 P = constant heat rejection to the initial state Assume air has constant properties with , , , and . (a) Sketch the P-v and T-s diagrams for the cycle. (b) Determine the ratio of the compression work to the expansion work (the back work ratio). (c) Determine the cycle thermal efficiency.

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 and to 2-3 v = constant heat addition to 1500 K 3-4 Isentropic expansion to 4-1 P 5 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.

Reconsider Prob. 913. 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 1500 K.

An air-standard cycle is executed in a closed system with of air and consists of the following three processes: 1-2 Isentropic compression from and to 2-3 P constant heat addition in the amount of 3-1 heat rejection to initial state ( and are constants) (a) Show the cycle on and diagrams. (b) Calculate the heat rejected. (c) Determine the thermal efficiency. Assume constant specific heats at room temperature

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 and in the amount of 2-3 P = constant heat addition to 3200 R 3-4 Isentropic expansion to 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.

Repeat Prob. 916E using constant specific heats at room temperature.

An air-standard Carnot cycle is executed in a closed system between the temperature limits of and . The pressures before and after the isothermal compression are 150 and , respectively. If the net work output per cycle is , 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.

Repeat Problem 9-18 using helium as the working fluid.

Consider a Carnot cycle executed in a closed system with 0.6 kg of air. The temperature limits of the cycle are 300 and 1100 K, and the minimum and maximum pressures that occur during the cycle are 20 and . Assuming constant specific heats, determine the net work output per cycle.

Consider a Carnot cycle executed in a closed system with air as the working fluid. The maximum pressure in the cycle is 1300 kPa while the maximum temperature is 950 K. If the entropy increase during the isothermal heat rejection process is and the net work output is , 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 of power for an air flow rate of , determine the second law efficiency of this cycle

An ideal gas is contained in a piston-cylinder device and undergoes a power cycle as follows: 1-2 isentropic compression from an initial temperature with a compression ratio 2-3 constant pressure heat addition 3-1 constant volume heat rejection The gas has constant specific heats with and . (a) Sketch the P-v and T-s diagrams for the cycle. (b) Determine the heat and work interactions for each process, in kJ/kg. (c) Determine the cycle thermal efficiency. (d) Obtain the expression for the cycle thermal efficiency as a function of the compression ratio r and ratio of specific heats k.

What four processes make up the ideal Otto cycle?

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

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

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?

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?

Why are high compression ratios not used in sparkignition engines?

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?

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

An ideal Otto cycle has a compression ratio of 10.5, takes in air at 90 kPa and 408C, and is repeated 2500 times per minute. Using constant specific heats at room temperature, determine the thermal efficiency of this cycle and the rate of heat input if the cycle is to produce 90 kW of power.

Repeat Prob. 931 for a compression ratio of 8.5.

An ideal Otto cycle has a compression ratio of 8. At the beginning of the compression process, air is at 95 kPa and 278C, 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 heat- addition process, (b) the net work output, (c) the thermal efficiency, and (d) the mean effective pressure for the cycle.

Reconsider Problem 933. 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.

Repeat Problem 933 using constant specific heats at room temperature.

A six-cylinder, four-stroke, spark-ignition engine operating on the ideal Otto cycle takes in air at 14 psia and 1058F, and is limited to a maximum cycle temperature of 24008F. Each cylinder has a bore of 3.5 in, and each piston has a stroke of 3.9 in. The minimum enclosed volume is 9.8 percent of the maximum enclosed volume. How much power will this engine produce when operated at 2500 rpm? Use constant specific heats at room temperature.

A spark-ignition engine has a compression ratio of 8, an isentropic compression efficiency of 85 percent, and an isentropic expansion efficiency of 95 percent. At the beginning of the compression, the air in the cylinder is at 13 psia and 608F. The maximum gas temperature is found to be 23008F by measurement. Determine the heat supplied per unit mass, the thermal efficiency, and the mean effective pressure of this engine when modeled with the Otto cycle. Use constant specific heats at room temperature.

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.

Repeat Prob. 938E using argon as the working fluid.

When we double the compression ratio of an ideal Otto cycle, what happens to the maximum gas temperature and pressure when the state of the air at the beginning of the compression and the amount of heat addition remain the same? Use constant specific heats at room temperature.

In a spark-ignition engine, some cooling occurs as the gas is expanded. This may be modeled by using a polytropic process in lieu of the isentropic process. Determine if the polytropic exponent used in this model will be greater than or less than the isentropic exponent.

How does a diesel engine differ from a gasoline engine?

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

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

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

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 278C. 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.

Repeat Problem 946 using constant specific heats at room temperature.

An ideal Diesel cycle has a compression ratio of 17 and a cutoff ratio of 1.3. Determine the maximum temperature of the air and the rate of heat addition to this cycle when it produces 140 kW of power and the state of the air at the beginning of the compression is 90 kPa and 578C. Use constant specific heats at room temperature.

An ideal Diesel cycle has a maximum cycle temperature of 23008F and a cutoff ratio of 1.4. The state of the air at the beginning of the compression is P1 5 14.4 psia and T1 5 508F. This cycle is executed in a four-stroke, eightcylinder engine with a cylinder bore of 4 in and a piston stroke of 4 in. The minimum volume enclosed in the cylinder is 4.5 percent of the maximum cylinder volume. Determine the power produced by this engine when it is operated at 1800 rpm. Use constant specific heats at room temperature.

An air-standard dual cycle has a compression ratio of 14 and a cutoff ratio of 1.2. The pressure ratio during the constant-volume heat addition process is 1.5. Determine the thermal efficiency, amount of heat added, the maximum gas pressure and temperature when this cycle is operated at 80 kPa and 208C at the beginning of the compression. Use constant specific heats at room temperature.

Repeat Prob. 950 when the state of the air at the beginning of the compression is 80 kPa and 2208C.

An air-standard Diesel cycle has a compression ratio of 18.2. Air is at 1208F and 14.7 psia at the beginning of the compression process and at 3200 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.

Repeat Prob. 952E using constant specific heats at room temperature.

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 208C. 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.

Repeat Prob. 954, but replace the isentropic expansion process by polytropic expansion process with the polytropic exponent n 5 1.35. Use variable specific heats.

Reconsider Prob. 955. 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.

A four-cylinder two-stroke 2.4-L diesel engine that operates on an ideal Diesel cycle has a compression ratio of 22 and a cutoff ratio of 1.8. Air is at 708C and 97 kPa at the beginning of the compression process. Using the cold-airstandard assumptions, determine how much power the engine will deliver at 3500 rpm.

Repeat Prob. 957 using nitrogen as the working fluid.

An ideal dual cycle has a compression ratio of 15 and a cutoff ratio of 1.4. The pressure ratio during constantvolume heat addition process is 1.1. The state of the air at the beginning of the compression is P1 514.2 psia and T1 5 758F. Calculate the cycles net specific work, specific heat addition, and thermal efficiency. Use constant specific heats at room temperature.

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.

Reconsider Problem 960. 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.

Repeat Problem 960 using constant specific heats at room temperature. Is the constant specific heat assumption reasonable in this case?

Develop an expression for cutoff ratio rc which expresses it in terms of qin/(cpT1rk21 ) for an air-standard Diesel cycle.

An air-standard cycle, called the dual cycle, with constant specific heats is executed in a closed piston-cylinder system and is composed of the following five processes: 1-2 Isentropic compression with a compression ratio, r 5 V1/V2 2-3 Constant volume heat addition with a pressure ratio, rp5 P3/P2 3-4 Constant pressure heat addition with a volume ratio, rc5V4/V3 4-5 Isentropic expansion while work is done until V5 5 V1 5-1 Constant volume heat rejection to the initial state (a) Sketch the P-v and T-s diagrams for this cycle. (b) Obtain an expression for the cycle thermal efficiency as a function of k, r, rc, and rp. (c) Evaluate the limit of the efficiency as rp approaches unity and compare your answer with the expression for the Diesel cycle efficiency. (d) Evaluate the limit of the efficiency as rc approaches unity and compare your answer with the expression for the Otto cycle efficiency

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

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

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?

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?

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.

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.

Consider an ideal Ericsson cycle with air as the working fluid executed in a steady-flow system. Air is at 278C 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.

An ideal Stirling cycle filled with air uses a 758F energy reservoir as a sink. The engine is designed so that the maximum air volume is 0.5 ft3 , the minimum air volume is 0.06 ft3 , and the minimum pressure is 15 psia. It is to be operated such that the engine produces 2 Btu of net work when 5 Btu of heat are transferred externally to the engine. Determine the temperature of the energy source, the amount of air contained in the engine, and the maximum air pressure during the cycle.

Repeat Prob. 972E if the engine is to be operated to produce 2.5 Btu of work for the same external heat input?

An air-standard Stirling cycle operates with a maximum pressure of 3600 kPa and a minimum pressure of 50 kPa. The maximum volume is 12 times the minimum volume, and the low-temperature reservoir is at 208C. Allowing a 58C temperature difference between the external reservoirs and the air when appropriate, calculate the specific heat added to the cycle and its net specific work.

How much heat is stored (and recovered) in the regenerator of Prob. 974. Use constant specific heats at room temperature

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?

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

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

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?

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.

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.

Repeat Problem 981 using constant specific heats at room temperature.

A simple Brayton cycle using air as the working fluid has a pressure ratio of 10. The minimum and maximum temperatures in the cycle are 295 and 1240 K. Assuming an isentropic efficiency of 83 percent for the compressor and 87 percent for the turbine, determine (a) the air temperature at the turbine exit, (b) the net work output, and (c) the thermal efficiency.

Reconsider Prob. 983. 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.

Repeat Prob. 983 using constant specific heats at room temperature.

Consider a simple Brayton cycle using air as the working fluid; has a pressure ratio of 12; has a maximum cycle temperature of 6008C; and operates the compressor inlet at 100 kPa and 158C. Which will have the greatest impact on the back-work ratio: a compressor isentropic efficiency of 80 percent or a turbine isentropic efficiency of 80 percent? Use constant specific heats at room temperature.

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.

An aircraft engine operates on a simple ideal Brayton cycle with a pressure ratio of 10. Heat is added to the cycle at a rate of 500 kW; air passes through the engine at a rate of 1 kg/s; and the air at the beginning of the compression is at 70 kPa and 08C. Determine the power produced by this engine and its thermal efficiency. Use constant specific heats at room temperature.

Repeat Prob. 988 for a pressure ratio of 15.

A gas-turbine power plant operates on the simple Brayton cycle between the pressure limits of 100 and 1600 kPa. The working fluid is air, which enters the compressor at 408C at a rate of 850 m3 /min and leaves the turbine at 6508C. Using variable specific heats for air and assuming a compressor isentropic efficiency of 85 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.

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.

For what compressor efficiency will the gas-turbine power plant in Problem 991E produce zero net work?

A gas-turbine power plant operates on the simple Brayton cycle between the pressure limits of 100 and 800 kPa. Air enters the compressor at 308C and leaves at 3308C at a mass flow rate of 200 kg/s. The maximum cycle temperature is 1400 K. During operation of the cycle, the net power output is measured experimentally to be 60 MW. Assume constant properties for air at 300 K with cv 5 0.718 kJ/kgK, cp 5 1.005 kJ/kgK, R 5 0.287 kJ/kgK, k 5 l.4. (a) Sketch the T-s diagram for the cycle. (b) Determine the isentropic efficiency of the turbine for these operating conditions. (c) Determine the cycle thermal efficiency.

A gas-turbine power plant operates on a modified Brayton cycle shown in the figure with an overall pressure ratio of 8. Air enters the compressor at 08C and 100 kPa. The maximum cycle temperature is 1500 K. The compressor and the turbines are isentropic. The high pressure turbine develops just enough power to run the compressor. Assume constant properties for air at 300 K with cv 5 0.718 kJ/kgK, cp 5 1.005 kJ/kgK, R 5 0.287 kJ/kgK, k 5 1.4. (a) Sketch the T-s diagram for the cycle. Label the data states. (b) Determine the temperature and pressure at state 4, the exit of the high pressure turbine. (c) If the net power output is 200 MW, determine mass flow rate of the air into the compressor, in kg/s.

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

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.

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?

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.

A gas turbine for an automobile is designed with a regenerator. Air enters the compressor of this engine at 100 kPa and 308C. The compressor pressure ratio is 10; the maximum cycle temperature is 8008C; and the cold air stream leaves the regenerator 108C cooler than the hot air stream at the inlet of the regenerator. Assuming both the compressor and the turbine to be isentropic, determine the rates of heat addition and rejection for this cycle when it produces 115 kW. Use constant specific heats at room temperature.

Rework Prob. 999 when the compressor isentropic efficiency is 87 percent and the turbine isentropic efficiency is 93 percent.

A gas turbine engine operates on the ideal Brayton cycle with regeneration, as shown in Fig. P999. Now the regenerator is rearranged so that the air streams of states 2 and 5 enter at one end of the regenerator and streams 3 and 6 exit at the other end (i.e., parallel flow arrangement of a heat exchanger). Consider such a system when air enters the compressor at 100 kPa and 208C; the compressor pressure ratio is 7; the maximum cycle temperature is 7278C; and the difference between the hot and cold air stream temperatures is 68C at the end of the regenerator where the cold stream leaves the regenerator. Is the cycle arrangement shown in the figure more or less efficient than this arrangement? Assume both the compressor and the turbine are isentropic, and use constant specific heats at room temperature.

An ideal regenerator (T3 5 T5) is added to a simple ideal Brayton cycle (see Fig. P999). Air enters the compressor of this cycle at 16 psia and 1008F; the pressure ratio is 11; and the maximum cycle temperature is 19408F. What is the thermal efficiency of this cycle? Use constant specific heats at room temperature. What would the thermal efficiency of the cycle be without the regenerator?

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 worlds first gasturbine-powered 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 gas-turbine-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 17008F, 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 130 hp. Assume the ambient air to be at 510 R and 14.5 psia.

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.

Reconsider Problem 9104. 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.

Repeat Problem 9104 using constant specific heats at room temperature.

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.

A stationary gas-turbine power plant operates on an ideal regenerative Brayton cycle (P5 100 percent) with air as the working fluid. Air enters the compressor at 95 kPa and 290 K and the turbine at 880 kPa and 1100 K. Heat is transferred to air from an external source at a rate of 30,000 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.

Air enters the compressor of a regenerative gasturbine engine at 310 K and 100 kPa, where it is compressed to 900 kPa and 650 K. The regenerator has an effectiveness of 80 percent, and the air enters the turbine at 1400 K. For a turbine efficiency of 90 percent, determine (a) the amount of heat transfer in the regenerator and (b) the thermal efficiency. Assume variable specific heats for air

Repeat Prob. 9109 using constant specific heats at room temperature.

Repeat Prob. 9109 for a regenerator effectiveness of 70 percent.

Develop an expression for the thermal efficiency of an ideal Brayton cycle with an ideal regenerator of effectiveness 100 percent. Use constant specific heats at room temperature.

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

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?

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?

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?

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?

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.

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.

Repeat Problem 9119 using argon as the working fluid.

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.

Repeat Problem 9121, assuming an efficiency of 86 percent for each compressor stage and an efficiency of 90 percent for each turbine stage.

Air enters a gas turbine with two stages of compression and two stages of expansion at 100 kPa and 178C. This system uses a regenerator as well as reheating and intercooling. The pressure ratio across each compressor is 4; 300 kJ/kg of heat are added to the air in each combustion chamber; and the regenerator operates perfectly while increasing the temperature of the cold air by 208C. Determine this systems thermal efficiency. Assume isentropic operations for all compressor and the turbine stages and use constant specific heats at room temperature.

Repeat Prob. 9123 for the case of three stages of compression with intercooling and three stages with expansion with reheating.

How much would the thermal efficiency of the cycle in Prob. 9124 change if the temperature of the cold-air stream leaving the regenerator is 808C lower than the temperature of the hot-air stream entering the regenerator?

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

What is propulsive efficiency? How is it determined?

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?

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 108F. 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

Repeat Problem 9129E accounting for the variation of specific heats with temperature.

A turbofan engine operating on an aircraft flying at 200 m/s at an altitude where the air is at 50 kPa and 2208C, is to produce 50,000 N of thrust. The inlet diameter of this engine is 2.5 m; the compressor pressure ratio is 12; and the mass flow rate ratio is 8. Determine the air temperature at the fan outlet needed to produce this thrust. Assume ideal operation for all components and constant specific heats at room temperature.

A pure jet engine propels an aircraft at 240 m/s through air at 45 kPa and 2138C. The inlet diameter of this engine is 1.6 m, the compressor pressure ratio is 13, and the temperature at the turbine inlet is 5578C. Determine the velocity at the exit of this engines nozzle and the thrust produced. Assume ideal operation for all components and constant specific heats at room temperature.

A turbojet aircraft is flying with a velocity of 280 m/s at an altitude of 9150 m, where the ambient conditions are 32 kPa and 2328C. The pressure ratio across the compressor is 12, and the temperature at the turbine inlet is 1100 K. Air enters the compressor at a rate of 50 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.

Repeat Prob. 9133 using a compressor efficiency of 80 percent and a turbine efficiency of 85 percent.

Consider an aircraft powered by a turbojet engine that has a pressure ratio of 9. The aircraft is stationary on the ground, held in position by its brakes. The ambient air is at 78C and 95 kPa and enters the engine at a rate of 20 kg/s. The jet fuel has a heating value of 42,700 kJ/kg, and it is burned completely at a rate of 0.5 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.

Reconsider Prob. 9135. In the problem statement, replace the inlet mass flow rate by an inlet volume flow rate of 18.1 m3 /s. Using EES (or other) software, investigate the effect of compressor inlet temperature in the range of 20 to 308C on the force that must be applied to the brakes to hold the plane stationary. Plot this force as a function of compressor inlet temperature.

Air at 78C 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 4278C. Determine the thrust produced by this turbojet engine. (Hint: Choose the entire engine as your control volume.)

Determine the total exergy destruction associated with the Otto cycle described in Problem 933, assuming a source temperature of 2000 K and a sink temperature of 300 K. Also, determine the energy at the end of the power stroke.

Determine the total exergy destruction associated with the Diesel cycle described in Problem 946, assuming a source temperature of 2000 K and a sink temperature of 300 K. Also, determine the energy at the end of the isentropic compression process.

Determine the exergy destruction associated with the heat rejection process of the Diesel cycle described in Prob. 952E, assuming a source temperature of 3200 R and a sink temperature of 540 R. Also, determine the energy at the end of the isentropic expansion process.

Calculate the exergy destruction for each process of Stirling cycle of Prob. 974, in kJ/kg.

Calculate the exergy destruction associated with each of the processes of the Brayton cycle described in Prob. 983, assuming a source temperature of 1600 K and a sink temperature of 295 K.

Repeat Prob. 986 using exergy analysis.

Determine the total exergy destruction associated with the Brayton cycle described in Prob. 9107, assuming a source temperature of 1500 K and a sink temperature of 290 K. Also, determine the energy of the exhaust gases at the exit of the regenerator.

Reconsider Prob. 9144. 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 energy of the exhaust gas leaving the regenerator. Plot these results as functions of pressure ratio. Discuss the results.

Determine the exergy destruction associated with each of the processes of the Brayton cycle described in Prob. 9109, assuming a source temperature of 1260 K and a sink temperature of 300 K. Also, determine the energy of the exhaust gases at the exit of the regenerator. Take Pexhaust 5 P0 5 100 kPa.

Calculate the lost work potential for each process of Prob. 9125. The temperature of the hot reservoir is the same as the maximum cycle temperature and the temperature of the cold reservoir is the same as the minimum cycle temperature.

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 308C at a rate of 12.6 kg/s and leaves at 2608C. It is then heated in a regenerator to 4008C 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 8718C and enter the turbine whose isentropic efficiency is 85 percent. Treating combustion gases as air and using constant specific heats at 5008C, determine (a) the isentropic efficiency of the compressor, (b) the effectiveness of the regenerator, (c) the airfuel 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 efficiencies of the compressor, the turbine, and the regenerator, and (h) the rate of the energy flow with the combustion gases at the regenerator exit.

A four-cylinder, four-stroke, 1.8-liter modern, highspeed compression-ignition engine operates on the ideal dual cycle with a compression ratio of 16. The air is at 95 kPa and 708C at the beginning of the compression process and the engine speed is 2200 rpm. Equal amounts of fuel are burned at constant volume and at constant pressure. The maximum allowable pressure in the cycle is 7.5 MPa due to material strength limitations. Using constant specific heats at 1000 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 energy output with the exhaust gases when they are purged.

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.

An air-standard cycle with variable coefficients is executed in a closed system and is composed of the following four processes: 1-2 V 5 constant heat addition from 100 kPa and 278C to 300 kPa 2-3 P 5 constant heat addition to 10278C 3-4 Isentropic expansion to 100 kPa 4-1 P 5 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.

Repeat Problem 9151 using constant specific heats at room temperature.

An Otto cycle with a compression ratio of 10.5 begins its compression at 90 kPa and 358C. The maximum cycle temperature is 10008C. Utilizing air-standard assumptions, determine the thermal efficiency of this cycle using (a) constant specific heats at room temperature and (b) variable specific heats.

A Diesel cycle has a compression ratio of 20 and begins its compression at 13 psia and 458F. The maximum cycle temperature is I8008F. Utilizing air-standard assumptions, determine the thermal efficiency of this cycle using (a) constant specific heats at room temperature and (b) variable specific heats.

A Brayton cycle with a pressure ratio of 12 operates with air entering the compressor at 13 psia and 208F, and the turbine at 10008F. Calculate the net specific work produced by this cycle treating the air as an ideal gas with (a) constant specific heats at room temperature and (b) variable specific heats.

A four-stroke turbocharged V-16 diesel engine built by GE Transportation Systems to power fast trains produces 4400 hp at 1500 rpm. Determine the amount of work produced per cylinder per (a) mechanical cycle and (b) thermodynamic cycle.

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.

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 508C 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.

A four-cylinder spark-ignition engine has a compression ratio of 10.5, and each cylinder has a maximum volume of 0.4 L. At the beginning of the compression process, the air is at 98 kPa and 378C, and the maximum temperature in the cycle is 2100 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 45 kW. Assume variable specific heats for air.

Reconsider Prob. 9159. 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.

A typical hydrocarbon fuel produces 43,000 kJ/kg of heat when used in a spark-ignition engine. Determine the compression ratio required for an ideal Otto cycle to use 0.039 grams of fuel to produce 1 kJ of work. Use constant specific heats at room temperature.

An ideal dual cycle has a compression ratio of 14 and uses air as the working fluid. At the beginning of the compression process, air is at 14.7 psia and 1208F, and occupies a volume of 98 in3 . During the heat-addition process, 0.6 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.

Consider an ideal Stirling cycle using air as the working fluid. Air is at 400 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 750 kJ/kg. Determine (a) the maximum pressure in the cycle and (b) the net work output per unit mass of air.

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.

Repeat Prob. 9164 using constant specific heats at room temperature.

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.

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 highpressure 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.

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 secondlaw efficiency of the cycle. Also determine (d) the exergies at the exits of the combustion chamber (state 6) and the regenerator (state 10) (See Fig. 943 in the text).

Compare the thermal efficiency of a two-stage gas turbine with regeneration, reheating and intercooling to that of a three-stage gas turbine with the same equipment when (a) all components operate ideally, (b) air enters the first compressor at 100 kPa and 208C, (c) the total pressure ratio across all stages of compression is 16, and (d) the maximum cycle temperature is 8008C.

The specific impulse of an aircraft-propulsion system is the force produced per unit of thrust-producing mass flow rate. Consider a jet engine that operates in an environment at 10 psia and 308F and propels an aircraft cruising at 1200 ft/s. Determine the specific impulse of this engine when the compressor pressure ratio is 9 and the temperature at the turbine inlet is 7008F. Assume ideal operations for all components and constant specific heats at room temperature.

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 1000 kPa with air as the working fluid. Air enters the compressor at 208C. Combustion gases leave the turbine and enter the heat exchanger at 4508C, and leave the heat exchanger of 3258C, while the liquid water enters the heat exchanger at 158C and leaves at 2008C as a saturated vapor. The net power produced by the gas-turbine cycle is 1500 kW. Assuming a compressor isentropic efficiency of 86 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.

A turbojet aircraft flies with a velocity of 1100 km/h at an altitude where the air temperature and pressure are 2358C 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 9508C. The turbine produces 800 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.

An air standard cycle with constant specific heats is executed in a closed piston-cylinder system and is composed of the following three processes: 1-2 Constant volume heat addition 2-3 lsentropic expansion with an expansion ratio r 5 V3/V2 3-1 Constant pressure heat rejection (a) Sketch the P-v and T-s diagrams for this cycle (b) Obtain an expression for the back work ratio as a function of k and r (c) Obtain an expression for the cycle thermal efficiency as a function of k and r (d ) Determine the value of the back work ratio and efficiency as r goes to unity What do your results imply about the net work done by the cycle?

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.

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 5 6, 8, 10, 12, and Tmax 5 1000, 1500, 2000, 2500 K.

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

Repeat Problem 9176 by considering the variation of specific heats of air with temperature.

Repeat Problem 9176 using helium as the working fluid

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

Repeat Problem 9179 by considering the variation of specific heats of air with temperature.

Repeat Problem 9179 using helium as the working fluid.

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 18, 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.

Repeat Problem 9182 using helium as the working fluid.

An Otto cycle with air as the working fluid has a compression ratio of 10.4. Under cold-air-standard conditions, the thermal efficiency of this cycle is (a) 10 percent (b) 39 percent (c) 61 percent (d) 79 percent (e) 82 percent

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

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

Air in an ideal Diesel cycle is compressed from 2 to 0.13 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) 41 percent (b) 59 percent (c) 66 percent (d) 70 percent (e) 78 percent

Helium gas in an ideal Otto cycle is compressed from 208C and 2.5 to 0.25 L, and its temperature increases by an additional 7008C during the heat addition process. The temperature of helium before the expansion process is (a) 17908C (b) 20608C (c) 12408C (d) 6208C (e) 8208C

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

In an ideal Brayton cycle, air is compressed from 95 kPa and 258C to 1100 kPa. Under cold-air-standard conditions, the thermal efficiency of this cycle is (a) 45 percent (b) 50 percent (c) 62 percent (d) 73 percent (e) 86 percent

Consider an ideal Brayton cycle executed between the pressure limits of 1200 and 100 kPa and temperature limits of 20 and 10008C 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

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

In an ideal Brayton cycle, air is compressed from 100 kPa and 258C to 1 MPa, and then heated to 9278C before entering the turbine. Under cold-air-standard conditions, the air temperature at the turbine exit is (a) 3498C (b) 4268C (c) 6228C (d) 7338C (e) 8258C

In an ideal Brayton cycle with regeneration, argon gas is compressed from 100 kPa and 258C to 400 kPa, and then heated to 12008C before entering the turbine. The highest temperature that argon can be heated in the regenerator is (a) 2468C (b) 8468C (c) 6898C (d) 3688C (e) 5738C

In an ideal Brayton cycle with regeneration, air is compressed from 80 kPa and 108C to 400 kPa and 1758C, is heated to 4508C in the regenerator, and then further heated to 10008C 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

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 9008C. 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

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

Air enters a turbojet engine at 320 m/s at a rate of 30 kg/s, and exits at 650 m/s relative to the aircraft. The thrust developed by the engine is (a) 5 kN (b) 10 kN (c) 15 kN (d) 20 kN (e) 26 kN

The weight of a diesel engine is directly proportional to the compression ratio (W 5 kr) because extra metal must be used to strengthen the engine for the higher pressures. Examine the net specific work produced by a diesel engine per unit of weight as the pressure ratio is varied and the specific heat input remains fixed. Do this for several heat inputs and proportionality constants k. Are there any optimal combinations of k and specific heat inputs

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.

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.

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?

Exhaust gases from the turbine of a simple Brayton cycle are quite hot and may be used for other thermal purposes. One proposed use is generating saturated steam at 1108C from water at 308C in a boiler. This steam will be distributed to several buildings on a college campus for space heating. A Brayton cycle with a pressure ratio of 6 is to be used for this purpose. Plot the power produced, the flow rate of produced steam, and the maximum cycle temperature as functions of the rate at which heat is added to the cycle. The temperature at the turbine inlet is not to exceed 20008C.

A gas turbine operates with a regenerator and two stages of reheating and intercooling. This system is designed so that when air enters the compressor at 100 kPa and 158C, the pressure ratio for each stage of compression is 3; the air temperature when entering a turbine is 5008C; and the regenerator operates perfectly. At full load, this engine produces 800 kW. For this engine to service a partial load, the heat addition in both combustion chambers is reduced. Develop an optimal schedule of heat addition to the combustion chambers for partial loads ranging from 400 to 800 kW.

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 gas-turbine 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 kg/s, the turbine inlet temperature becomes 1700 K. But the turbine inlet temperature is limited to 1500 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 kPa and 258C, adequate water supply is available at 208C, and the amount of fuel supplied to the combustion chamber remains constant.