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engineering
mechanical engineering
Thermodynamics An Engineering Approach 8th edition Yunus A. Cengel, Michael A. Boles - Solutions
Does a refrigerator that has a higher COP necessarily have a higher second-law efficiency than one with a lower COP? Explain.
Can a process for which the reversible work is zero be reversible? Can it be irreversible? Explain.
The electric power needs of a community are to be met by windmills with 10-m-diameter rotors. The windmills are to be located where the wind is blowing steadily at an average velocity of 8 m/s. Determine the minimum number of windmills that need to be installed if the required power output is 600
One method of meeting the extra electric power demand at peak periods is to pump some water from a large body of water (such as a lake) to a water reservoir at a higher elevation at times of low demand and to generate electricity at times of high demand by letting this water run down and rotate a
Consider a thermal energy reservoir at 1500 K that can supply heat at a rate of 150,000 kJ/h. Determine the energy of this supplied energy, assuming an environmental temperature of 25°C.
A heat engine receives heat from a source at 1500 K at a rate of 700 kJ/s and it rejects the waste heat to a medium at 320 K. The measured power output of the heat engine is 320 kW, and the environment temperature is 25°C. Determine (a) The reversible power, (b) The rate of irreversibility,
Reconsider Prob. 8–18. Using EES (or other) software, study the effect of reducing the temperature at which the waste heat is rejected on the reversible power, the rate of irreversibility, and the second-law efficiency as the rejection temperature is varied from 500 to 298 K, and plot the results.
A heat engine that rejects waste heat to a sink at 530 R has a thermal efficiency of 36 percent and a second-law efficiency of 60 percent. Determine the temperature of the source that supplies heat to this engine.
How much of the 100 kJ of thermal energy at 800 K can be converted to useful work? Assume the environment to be at 25°C.
A heat engine that receives heat from a furnace at 1200°C and rejects waste heat to a river at 20°C has a thermal efficiency of 40 percent. Determine the second-law efficiency of this power plant.
A house that is losing heat at a rate of 80,000 kJ/h when the outside temperature drops to 15°C is to be heated by electric resistance heaters. If the house is to be maintained at 22°C at all times, determine the reversible work input for this process and the irreversibility.
A freezer is maintained at 20°F by removing heat from it at a rate of 75 Btu/min. The power input to the freezer is 0.70 hp, and the surrounding air is at 75°F. Determine (a) The reversible power, (b) The irreversibility, and (c) The second-law efficiency of this freezer.
Show that the power produced by a wind turbine is proportional to the cube of the wind velocity and to the square of the blade span diameter.
A geothermal power plant uses geothermal liquid water at 160°C at a rate of 440 kg/s as the heat source, and produces 14 MW of net power in an environment at 25°C. If 18.5 MW of energy entering the plant with the geothermal water is destructed within the plant, determine (a) The energy of the
Can a system have a higher second-law efficiency than the first-law efficiency during a process? Give examples.
A piston€“cylinder device initially contains 2 L of air at 100 kPa and 25°C. Air is now compressed to a final state of 600 kPa and 150°C. The useful work input is 1.2 kJ. Assuming the surroundings are at 100 kPa and 25°C, determine(a) The energy of the air at the initial and
A piston–cylinder device contains 5 kg of refrigerant- 134a at 0.7 MPa and 60°C. The refrigerant is now cooled at constant pressure until it exists as a liquid at 24°C. If the surroundings are at 100 kPa and 24°C, determine (a) The energy of the refrigerant at the initial and the final
The radiator of a steam heating system has a volume of 20 L and is filled with superheated water vapor at 200 kPa and 200°C. At this moment both the inlet and the exit valves to the radiator are closed. After a while it is observed that the temperature of the steam drops to 80°C as a result
Reconsider Prob. 8–31. Using EES (or other) software, investigate the effect of the final steam temperature in the radiator on the amount of actual heat transfer and the maximum amount of heat that can be transferred. Vary the final steam temperature from 80 to 21°C and plot the actual and
A well-insulated rigid tank contains 6 lbm of saturated liquid–vapor mixture of water at 35 psia. Initially, three-quarters of the mass is in the liquid phase. An electric resistance heater placed in the tank is turned on and kept on until all the liquid in the tank is vaporized. Assuming the
A rigid tank is divided into two equal parts by a partition. One part of the tank contains 1.5 kg of compressed liquid water at 300 kPa and 60°C and the other side is evacuated. Now the partition is removed, and the water expands to fill the entire tank. If the final pressure in the tank is 15
Reconsider Prob. 8–34. Using EES (or other) software, study the effect of final pressure in the tank on the energy destroyed during the process. Plot the energy destroyed as a function of the final pressure for final pressures between 25 and 15 kPa, and discuss the results.
An insulated piston€“cylinder device contains 2 L of saturated liquid water at a constant pressure of 150 kPa. An electric resistance heater inside the cylinder is turned on, and electrical work is done on the water in the amount of 2200 kJ. Assuming the surroundings to be at 25°C and
Reconsider Prob. 8–36. Using EES (or other) software, investigate the effect of the amount of electrical work supplied to the device on the minimum work and the energy destroyed as the electrical work is varied from 0 to 2200 kJ, and plot your results.
An insulated piston–cylinder device contains 0.05 m3 of saturated refrigerant-134a vapor at 0.8 MPa pressure. The refrigerant is now allowed to expand in a reversible manner until the pressure drops to 0.2 MPa. Determine the change in the energy of the refrigerant during this process and the
Oxygen gas is compressed in a piston–cylinder device from an initial state of 12 ft3/lbm and 75°F to a final state of 1.5 ft3/lbm and 525°F. Determine the reversible work input and the increase in the energy of the oxygen during this process. Assume the surroundings to be at 14.7 psia and 75°F.
A 1.2-m3 insulated rigid tank contains 2.13 kg of carbon dioxide at 100 kPa. Now paddle-wheel work is done on the system until the pressure in the tank rises to 120 kPa. Determine (a) the actual paddle-wheel work done during this process and(b) Te minimum paddle-wheel work with which this process
An insulated piston–cylinder device initially contains 30 L of air at 120 kPa and 27°C. Air is now heated for 5 min by a 50-W resistance heater placed inside the cylinder. The pressure of air is maintained constant during this process, and the surroundings are at 27°C and 100 kPa. Determine the
A mass of 8 kg of helium undergoes a process from an initial state of 3 m3/kg and 15°C to a final state of 0.5 m3/kg and 80°C. Assuming the surroundings to be at 25°C and 100 kPa, determine the increase in the useful work potential of the helium during this process.
An insulated rigid tank is divided into two equal parts by a partition. Initially, one part contains 3 kg of argon gas at 300 kPa and 70°C, and the other side is evacuated. The partition is now removed, and the gas fills the entire tank. Assuming the surroundings to be at 25°C, determine the
A 70-lbm copper block initially at 250°F is dropped into an insulated tank that contains 1.5 ft3 of water at 75°F. Determine (a) The final equilibrium temperature and (b) The work potential wasted during this process. Assume the surroundings to be at 75°F.
An iron block of unknown mass at 85°C is dropped into an insulated tank that contains 100 L of water at 20°C. At the same time, a paddle wheel driven by a 200-W motor is activated to stir the water. It is observed that thermal equilibrium is established after 20 min with a final temperature
A 50-kg iron block and a 20-kg copper block, both initially at 80°C, are dropped into a large lake at 15°C. Thermal equilibrium is established after a while as a result of heat transfer between the blocks and the lake water. Assuming the surroundings to be at 20°C, determine the amount of work
A 12-ft3 rigid tank contains refrigerant-134a at 40 psia and 55 percent quality. Heat is transferred now to the refrigerant from a source at 120°F until the pressure rises to 60 psia. Assuming the surroundings to be at 75°F, determine (a) The amount of heat transfer between the source and the
Chickens with an average mass of 2.2 kg and average specific heat of 3.54 kJ/kg • °C are to be cooled by chilled water that enters a continuous-flow-type immersion chiller at 0.5°C and leaves at 2.5°C. Chickens are dropped into the chiller at a uniform temperature of 15°C at a rate of 500
An ordinary egg can be approximated as a 5.5-cmdiameter sphere. The egg is initially at a uniform temperature of 8°C and is dropped into boiling water at 97°C. Taking the properties of egg to be r = 1020 kg/m3 and cp = 3.32 kJ/kg €¢ °C, determine how much heat is transferred
Reconsider Prob. 7–55. Using EES (or other) software, study the effect of the mass of the iron block on the final equilibrium temperature and the total entropy change for the process. Let the mass of the iron vary from 1 to 10 kg. Plot the equilibrium temperature and the total entropy change as a
Stainless steel ball bearings (r = 8085 kg/m3 and cp = 0.480 kJ/kg • °C) having a diameter of 1.2 cm are to be quenched in water at a rate of 1400 per minute. The balls leave the oven at a uniform temperature of 900°C and are exposed to air at 30°C for a while before they are dropped into the
Carbon steel balls (r = 7833 kg/m3 and cp = 0.465 kJ/kg €¢ °C) 8 mm in diameter are annealed by heating them first to 900°C in a furnace and then allowing them to cool slowly to 100°C in ambient air at 35°C. If 1200 balls are to be annealed per hour, determine(a) The rate
A 50-kg iron block and a 20-kg copper block, both initially at 80°C, are dropped into a large lake at 15°C. Thermal equilibrium is established after a while as a result of heat transfer between the blocks and the lake water. Determine the total entropy change for this process.
A 0.04-m3 tank initially contains air at ambient conditions of 100 kPa and 22°C. Now, a 15-liter tank containing liquid water at 85°C is placed into the tank without causing any air to escape. After some heat transfer from the water to the air and the surroundings, both the air and water
A piston–cylinder device initially contains 1.4 kg of refrigerant-134a at 140 kPa and 20°C. Heat is now transferred to the refrigerant, and the piston, which is resting on a set of stops, starts moving when the pressure inside reaches 180 kPa. Heat transfer continues until the temperature
Steam is throttled from 8 MPa and 450°C to 6 MPa. Determine the wasted work potential during this throttling process. Assume the surroundings to be at 25°C.
Air is compressed steadily by an 8-kW compressor from 100 kPa and 17°C to 600 kPa and 167°C at a rate of 2.1 kg/min, neglecting the changes in kinetic and potential energies, determine(a) The increase in the energy of the air and(b) The rate of energy destroyed during this process. Assume
An adiabatic pump is to be used to compress saturated liquid water at 10 kPa to a pressure to 15 MPa in a reversible manner. Determine the work input using(a) Entropy data from the compressed liquid table,(b) Inlet specific volume and pressure values,(c) Average specific volume and pressure values.
Reconsider Prob. 8–55. Using EES (or other) software, solve the problem and in addition determine the actual heat transfer, if any, and its direction, the minimum power input (the reversible power), and the compressor second-law efficiency. Then interpret the results when the outlet temperature
Prove that the two relations for entropy change of ideal gases under the constant-specific-heat assumption (Eqs. 7–33 and 7–34) are equivalent.
Refrigerant-134a at 1 MPa and 100°C is throttled to a pressure of 0.8 MPa. Determine the reversible work and energy destroyed during this throttling process. Assume the surroundings to be at 30°C.
Reconsider Prob. 8–57. Using EES (or other) software, investigate the effect of exit pressure on the reversible work and energy destruction. Vary the throttle exit pressure from 1 to 0.1 MPa and plot the reversible work and energy destroyed as functions of the exit pressure. Discuss the results.
Air enters a nozzle steadily at 300 kPa and 87°C with a velocity of 50 m/s and exits at 95 kPa and 300 m/s. The heat loss from the nozzle to the surrounding medium at 17°C is estimated to be 4 kJ/kg. Determine (a) The exit temperature and (b) The energy destroyed during this process.
Reconsider Prob. 8–59. Using EES (or other) software, study the effect of varying the nozzle exit velocity from 100 to 300 m/s on both the exit temperature and energy destroyed, and plot the results.
Steam enters a diffuser at 10 kPa and 50°C with a velocity of 300 m/s and exits as saturated vapor at 50°C and 70 m/s. The exit area of the diffuser is 3 m2. Determine (a) The mass flow rate of the steam and (b) The wasted work potential during this process. Assume the surroundings to be at
Air is compressed steadily by a compressor from 14.7 psia and 60°F to 100 psia and 480°F at a rate of 22 lbm/min, assuming the surroundings to be at 60°F determine the minimum power input to the compressor. Assume air to be an ideal gas with variable specific heats, and neglect the changes in
Steam enters an adiabatic turbine at 6 MPa, 600°C, and 80 m/s and leaves at 50 kPa, 100°C, and 140 m/s. If the power output of the turbine is 5 MW, determine(a) The reversible power output and(b) The second-law efficiency of the turbine. Assume the surroundings to be at 25°C.
Steam is throttled from 9 MPa and 500°C to a pressure of 7 MPa. Determine the decrease in energy of the steam during this process. Assume the surroundings to be at 25°C.
Combustion gases enter a gas turbine at 900°C, 800 kPa, and 100 m/s and leave at 650°C, 400 kPa, and 220 m/s. Taking cp = 1.15 kJ/kg • °C and k = 1.3 for the combustion gases, determine (a) The energy of the combustion gases at the turbine inlet and (b) The work output of the turbine under
Refrigerant-134a enters an adiabatic compressor as saturated vapor at 30 psia at a rate of 20 ft3/min and exits at 70 psia pressure. If the isentropic efficiency of the compressor is 80 percent, determine (a) The actual power input and (b) The second-law efficiency of the compressor. Assume the
Starting with the second T ds relation (Eq. 7–26), obtain Eq. 7–34 for the entropy change of ideal gases under the constant-specific-heat assumption.
Refrigerant-134a at 140 kPa and -10°C is compressed by an adiabatic 0.5-kW compressor to an exit state of 700 kPa and 60°C. Neglecting the changes in kinetic and potential energies and assuming the surroundings to be at 27°C, determine(a) The isentropic efficiency and(b) The second-law
Air is compressed by a compressor from 95 kPa and 27°C to 600 kPa and 277°C at a rate of 0.06 kg/s. Neglecting the changes in kinetic and potential energies and assuming the surroundings to be at 25°C, determine the reversible power input for this process.
Reconsider Prob. 8–68. Using EES (or other) software, investigate the effect of compressor exit pressure on reversible power. Vary the compressor exit pressure from 200 to 600 kPa while keeping the exit temperature at 277°C. Plot the reversible power input for this process as a function of the
Starting with Eq. 7–34, obtain Eq. 7–43.
Argon gas enters an adiabatic compressor at 120 kPa and 30°C with a velocity of 20 m/s and exits at 1.2 MPa, 530°C, and 80 m/s. The inlet area of the compressor is 130 cm2. Assuming the surroundings to be at 25°C, determine the reversible power input and energy destroyed.
What are Pr and vr called? Is their use limited to isentropic processes? Explain.
Steam expands in a turbine steadily at a rate of 15,000 kg/h, entering at 8 MPa and 450°C and leaving at 50 kPa as saturated vapor. Assuming the surroundings to be at 100 kPa and 25°C, determine (a) The power potential of the steam at the inlet conditions and (b) The power output of the
Can the entropy of an ideal gas change during an isothermal process?
An ideal gas undergoes a process between two specified temperatures, first at constant pressure and then at constant volume. For which case will the ideal gas experience a larger entropy change? Explain.
Oxygen gas is compressed in a piston–cylinder device from an initial state of 0.8 m3/kg and 25°C to a final state of 0.1 m3/kg and 287°C. Determine the entropy change of the oxygen during this process. Assume constant specific heats.
An insulated piston–cylinder device initially contains 300 L of air at 120 kPa and 17°C. Air is now heated for 15 min by a 200-W resistance heater placed inside the cylinder. The pressure of air is maintained constant during this process. Determine the entropy change of air, assuming (a)
A piston–cylinder device contains 1.2 kg of nitrogen gas at 120 kPa and 27°C. The gas is now compressed slowly in a polytropic process during which PV1.3 = constant. The process ends when the volume is reduced by one-half. Determine the entropy change of nitrogen during this process.
Reconsider Prob. 7–69. Using EES (or other) software, investigate the effect of varying the polytropic exponent from 1 to 1.4 on the entropy change of the nitrogen. Show the processes on a common P-v diagram.
A mass of 15 lbm of helium undergoes a process from an initial state of 50 ft3/lbm and 80°F to a final state of 10 ft3/lbm and 200°F. Determine the entropy change of helium during this process, assuming (a) The process is reversible and (b) The process is irreversible.
Air is compressed in a piston–cylinder device from 90 kPa and 20°C to 400 kPa in a reversible isothermal process. Determine (a) The entropy change of air and (b) The work done.
Air is compressed steadily by a 5-kW compressor from 100 kPa and 17°C to 600 kPa and 167°C at a rate of 1.6 kg/min. During this process, some heat transfer takes place between the compressor and the surrounding medium at 17°C. Determine the rate of entropy change of air during this
An insulated rigid tank is divided into two equal parts by a partition. Initially, one part contains 5 kmol of an ideal gas at 250 kPa and 40°C, and the other side is evacuated. The partition is now removed, and the gas fills the entire tank. Determine the total entropy change during this process.
Air enters a compressor at ambient conditions of 15 psia and 60°F with a low velocity and exits at 150 psia, 620°F, and 350 ft/s. The compressor is cooled by the ambient air at 60°F at a rate of 1500 Btu/min. The power input to the compressor is 400 hp. Determine (a) The mass flow rate of air
Hot combustion gases enter the nozzle of a turbojet engine at 260 kPa, 747°C, and 80 m/s and exit at 70 kPa and 500°C. Assuming the nozzle to be adiabatic and the surroundings to be at 20°C, determine(a) The exit velocity and(b) The decrease in the energy of the gases. Take k = 1.3 and
Steam is usually accelerated in the nozzle of a turbine before it strikes the turbine blades. Steam enters an adiabatic nozzle at 7 MPa and 500°C with a velocity of 70 m/s and exits at 5 MPa and 450°C. Assuming the surroundings to be at 25°C, determine (a) The exit velocity of the steam, (b)
Carbon dioxide enters a compressor at 100 kPa and 300 K at a rate of 0.2 kg/s and exits at 600 kPa and 450 K. Determine the power input to the compressor if the process involved no irreversibilities. Assume the surroundings to be at 25°C.
A hot-water stream at 160°F enters an adiabatic mixing chamber with a mass flow rate of 4 lbm/s where it is mixed with a stream of cold water at 70°F. If the mixture leaves the chamber at 110°F, determine (a) The mass flow rate of the cold water and (b) The energy destroyed during this
Liquid water at 200 kPa and 20°C is heated in a chamber by mixing it with superheated steam at 200 kPa and 300°C. Liquid water enters the mixing chamber at a rate of 2.5 kg/s, and the chamber is estimated to lose heat to the surrounding air at 25°C at a rate of 600 kJ/min. If the mixture leaves
Air is compressed in a piston–cylinder device from 100 kPa and 17°C to 800 kPa in a reversible, adiabatic process. Determine the final temperature and the work done during this process, assuming (a) Constant specific heats and (b) Variable specific heats for air.
Air enters the evaporator section of a window air conditioner at 100 kPa and 27°C with a volume flow rate of 6 m3/min. Refrigerant-134a at 120 kPa with a quality of 0.3 enters the evaporator at a rate of 2 kg/min and leaves as saturated vapor at the same pressure. Determine the exit temperature of
A 0.1-m3 rigid tank initially contains refrigerant-134a at 1.2 MPa and 100 percent quality. The tank is connected by a valve to a supply line that carries refrigerant-134a at 1.6 MPa and 30°C. The valve is now opened, allowing the refrigerant to enter the tank, and it is closed when the tank
A 0.6-m3 rigid tank is filled with saturated liquid water at 170°C. A valve at the bottom of the tank is now opened, and one-half of the total mass is withdrawn from the tank in liquid form. Heat is transferred to water from a source of 210°C so that the temperature in the tank remains constant.
An insulated 150-ft3 rigid tank contains air at 75 psia and 140°F. A valve connected to the tank is opened, and air is allowed to escape until the pressure inside drops to 30 psia. The air temperature during this process is maintained constant by an electric resistance heater placed in the tank.
A 0.1-m3 rigid tank contains saturated refrigerant- 134a at 800 kPa. Initially, 30 percent of the volume is occupied by liquid and the rest by vapor. A valve at the bottom of the tank is opened, and liquid is withdrawn from the tank. Heat is transferred to the refrigerant from a source at 60°C so
Reconsider Prob. 7–75. Using EES (or other) software, evaluate and plot the work done and final temperature during the compression process as functions of the final pressure for the two cases as the final pressure varies from 100 to 800 kPa.
A vertical piston€“cylinder device initially contains 0.1 m3 of helium at 20°C. The mass of the piston is such that it maintains a constant pressure of 300 kPa inside. A valve is now opened, and helium is allowed to escape until the volume inside the cylinder is decreased by one-half.
Helium gas is compressed from 90 kPa and 30°C to 450 kPa in a reversible, adiabatic process. Determine the final temperature and the work done, assuming the process takes place (a) In a piston–cylinder device and (b) In a steady-flow compressor.
A 0.2-m3 rigid tank initially contains saturated refrigerant- 134a vapor at 1 MPa. The tank is connected by a valve to a supply line that carries refrigerant-134a at 1.4 MPa and 60°C. The valve is now opened, and the refrigerant is allowed to enter the tank. The valve is closed when one-half of
An insulated vertical piston–cylinder device initially contains 15 kg of water, 9 kg of which is in the vapor phase. The mass of the piston is such that it maintains a constant pressure of 200 kPa inside the cylinder. Now steam at 1 MPa and 400°C is allowed to enter the cylinder from a supply
An insulated rigid tank contains 4 kg of argon gas at 450 kPa and 30°C. A valve is now opened, and argon is allowed to escape until the pressure inside drops to 200 kPa. Assuming the argon remaining inside the tank has undergone a reversible, adiabatic process; determine the final mass in the
Consider a family of four, with each person taking a 6-minute shower every morning. The average flow rate through the shower head is 10 L/min. City water at 15°C is heated to 55°C in an electric water heater and tempered to 42°C by cold water at the T-elbow of the shower before being routed to
Reconsider Prob. 7–78. Using EES (or other) software, investigate the effect of the final pressure on the final mass in the tank as the pressure varies from 450 to 150 kPa, and plot the results.
Ambient air at 100 kPa and 300 K is compressed isentropically in a steady-flow device to 1 MPa. Determine (a) The work input to the compressor, (b) The energy of the air at the compressor exit, and (c) The energy of compressed air after it is cooled to 300 K at 1 MPa pressure.
Air enters an adiabatic nozzle at 60 psia, 540°F, and 200 ft/s and exits at 12 psia. Assuming air to be an ideal gas with variable specific heats and disregarding any irreversibilities, determine the exit velocity of the air.
Cold water (cp = 4.18 kJ/kg €¢ °C) leading to a shower enters a well-insulated, thin-walled, double-pipe, counter-flow heat exchanger at 15°C at a rate of 0.25 kg/s and is heated to 45°C by hot water (cp = 4.19 kJ/kg €¢°C) that enters at 100°C at a rate of 3
Air enters a nozzle steadily at 280 kPa and 77°C with a velocity of 50 m/s and exits at 85 kPa and 320 m/s. The heat losses from the nozzle to the surrounding medium at 20°C are estimated to be 3.2 kJ/kg. Determine (a) the exit temperature and (b) the total entropy change for this process.
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