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Fundamentals Of Thermodynamics 8th Edition Claus Borgnakke, Richard E. Sonntag - Solutions
A piston–cylinder device contains steam that undergoes a reversible thermodynamic cycle. Initially the steam is at 400 kPa and 350°C with a volume of 0.3 m3. The steam is first expanded isothermally to 150 kPa, then compressed adiabatically to the initial pressure, and finally compressed at the
Refrigerant-134a enters an adiabatic compressor as saturated vapor at 160 kPa at a rate of 2 m3/min and is compressed to a pressure of 900 kPa. Determine the minimum power that must be supplied to the compressor.
Determine the work input and entropy generation during the compression of steam from 100 kPa to 1 MPa in(a) An adiabatic pump and(b) An adiabatic compressor if the inlet state is saturated liquid in the pump and saturated vapor in the compressor and the isentropic efficiency is 85 percent for both
Steam enters an adiabatic turbine at 800 psia and 900°F and leaves at a pressure of 40 psia. Determine the maximum amount of work that can be delivered by this turbine.
A rigid tank contains 1.5 kg of water at 120°C and 500 kPa. Now 22 kJ of shaft work is done on the system and the final temperature in the tank is 95°C. If the entropy change of water is zero and the surroundings are at 15°C, determine (a) The final pressure in the tank, (b) The amount of
Reconsider Prob. 7–42E Using EES (or other) software, evaluate and plot the work done by the steam as a function of final pressure as it varies from 800 to 40 psia. Also investigate the effect of varying the turbine inlet temperature from the saturation temperature at 800 psia to 900°F on the
A horizontal cylinder is separated into two compartments by an adiabatic, frictionless piston. One side contains 0.2 m3 of nitrogen and the other side contains 0.1 kg of helium, both initially at 20°C and 95 kPa. The sides of the cylinder and the helium end are insulated. Now heat is added to
A heavily insulated piston–cylinder device contains 0.05 m3 of steam at 300 kPa and 150°C. Steam is now compressed in a reversible manner to a pressure of 1 MPa. Determine the work done on the steam during this process.
A 0.8-m3 rigid tank contains carbon dioxide (CO2) gas at 250 K and 100 kPa. A 500-W electric resistance heater placed in the tank is now turned on and kept on for 40 min after which the pressure of CO2 is measured to be 175 kPa.Assuming the surroundings to be at 300 K and using constant specific
Reconsider Prob. 7–44. Using EES (or other) software, evaluate and plot the work done on the steam as a function of final pressure as the pressure varies from 300 kPa to 1 MPa.
Helium gas is throttled steadily from 500 kPa and 70°C. Heat is lost from the helium in the amount of 2.5 kJ/kg to the surroundings at 25°C and 100 kPa. If the entropy of the helium increases by 0.25 kJ/kg K in the valve determine (a) The exit pressure and temperature and (b) The entropy
Refrigerant-134a enters a compressor as a saturated vapor at 200 kPa at a rate of 0.03 m3/s and leaves at 700 kPa. The power input to the compressor is 10 kW. If the surroundings at 20°C experience an entropy increase of 0.008 kW/K determine (a) The rate of heat loss from the compressor, (b)
A piston–cylinder device contains 1.2 kg of saturated water vapor at 200°C. Heat is now transferred to steam, and steam expands reversibly and isothermally to a final pressure of 800 kPa. Determine the heat transferred and the work done during this process.
Reconsider Prob. 7–46. Using EES (or other) software, evaluate and plot the heat transferred to the steam and the work done as a function of final pressure as the pressure varies from the initial value to the final value of 800 kPa.
Air at 500 kPa and 400 K enters an adiabatic nozzle at a velocity of 30 m/s and leaves at 300 kPa and 350 K. Using variable specific heats, determine(a) The isentropic efficiency,(b) The exit velocity, and(c) The entropy generation.
A piston–cylinder device contains 5 kg of steam at 100°C with a quality of 50 percent. This steam undergoes two processes as follows: 1-2 Heat is transferred to the steam in a reversible manner while the temperature is held constant until the steam exists as a saturated vapor. 2-3 The steam
Show that the difference between the reversible steady-flow work and reversible moving boundary work is equal to the flow energy.
A rigid tank contains 5 kg of saturated vapor steam at 100°C. The steam is cooled to the ambient temperature of 25°C. (a) Sketch the process with respect to the saturation lines on a T-v diagram. (b) Determine the entropy change of the steam, in kJ/K. (c) For the steam and its surroundings,
An insulated tank containing 0.4 m3 of saturated water vapor at 500 kPa is connected to an initially evacuated, insulated piston€“cylinder device. The mass of the piston is such that a pressure of 150 kPa is required to raise it. Now the valve is opened slightly, and part of the steam
Steam at 6000 kPa and 500°C enters a steady-flow turbine. The steam expands in the turbine while doing work until the pressure is 1000 kPa. When the pressure is 1000 kPa, 10 percent of the steam is removed from the turbine for other uses. The remaining 90 percent of the steam continues to expand
One ton of liquid water at 80°C is brought into a well-insulated and well-sealed 4-m x 5-m x 7-m room initially at 22°C and 100 kPa. Assuming constant specific heats for both air and water at room temperature, determine(a) The final equilibrium temperature in the room and(b) The total
A piston–cylinder device initially contains 15 ft3 of helium gas at 25 psia and 70°F. Helium is now compressed in a polytropic process (PVn = constant) to 70 psia and 300°F. Determine (a) The entropy change of helium, (b) The entropy change of the surroundings, and (c) Whether this
A 1.2-ft3 well-insulated rigid can initially contains refrigerant-134a at 140 psia and 70°F. Now a crack develops in the can, and the refrigerant starts to leak out slowly, Assuming the refrigerant remaining in the can has undergone a reversible, adiabatic process, determine the final mass in
Air is compressed steadily by a compressor from 100 kPa and 17°C to 700 kPa at a rate of 5 kg/min. Determine the minimum power input required if the process is (a) Adiabatic and (b) Isothermal. Assume air to be an ideal gas with variable specific heats, and neglect the changes in kinetic and
A 50-kg copper block initially at 80°C is dropped into an insulated tank that contains 120 L of water at 25°C. Determine the final equilibrium temperature and the total entropy change for this process.
Air enters a two-stage compressor at 100 kPa and 27°C and is compressed to 900 kPa. The pressure ratio across each stage is the same, and the air is cooled to the initial temperature between the two stages. Assuming the compression process to be isentropic, determine the power input to the
Consider a three-stage isentropic compressor with two intercoolers that cool the gas to the initial temperature between the stages. Determine the two intermediate pressures (Px and Py) in terms of inlet and exit pressures (P1 and P2) that will minimize the work input to the compressor.
A 25-kg iron block initially at 350°C is quenched in an insulated tank that contains 100 kg of water at 18°C. Assuming the water that vaporizes during the process condenses back in the tank determine the total entropy change during this process.
Steam at 6 MPa and 500°C enters a two-stage adiabatic turbine at a rate of 15 kg/s. Ten percent of the steam is extracted at the end of the first stage at a pressure of 1.2 MPa for other use. The remainder of the steam is further expanded in the second stage and leaves the turbine at 20 kPa.
A 20-kg aluminum block initially at 200°C is brought into contact with a 20-kg block of iron at 100°C in an insulated enclosure. Determine the final equilibrium temperature and the total entropy change for this process.
Steam enters a two-stage adiabatic turbine at 8 MPa and 550°C. It expands in the first stage to a pressure of 2 MPa. Then steam is reheated at constant pressure to 550°C before it is expanded in a second stage to a pressure of 200 kPa. The power output of the turbine is 80 MW. Assuming an
Refrigerant-134a at 140 kPa and 10°C is compressed by an adiabatic 0.7-kW compressor to an exit state of 700 kPa and 50°C. Neglecting the changes in kinetic and potential energies, determine (a) The isentropic efficiency of the compressor, (b) The volume flow rate of the refrigerant at the
Helium gas enters a nozzle, whose isentropic efficiency is 94 percent with a low velocity, and it exits at 14 psia, 180°F, and 1000 ft/s, determine the pressure and temperature at the nozzle inlet.
An adiabatic air compressor is to be powered by a direct-coupled adiabatic steam turbine that is also driving a generator. Steam enters the turbine at 12.5 MPa and 500°C at a rate of 25 kg/s and exits at 10 kPa and a quality of 0.92. Air enters the compressor at 98 kPa and 295 K at a rate of 10
Reconsider Prob. 7–179. Using EES (or other) software, determine the isentropic efficiencies for the compressor and turbine. Then use EES to study how varying the compressor efficiency over the range 0.6 to 0.8 and the turbine efficiency over the range 0.7 to 0.95 affect the net work for the
Consider two bodies of identical mass m and specific heat c used as thermal reservoirs (source and sink) for a heat engine. The first body is initially at an absolute temperature T1 while the second one is at a lower absolute temperature T2. Heat is transferred from the first body to the heat
The explosion of a hot water tank in a school in Spencer, Oklahoma, in 1982 killed 7 people while injuring 33 others. Although the number of such explosions has decreased dramatically since the development of the ASME Pressure Vessel Code, which requires the tanks to be designed to withstand four
Using the arguments in the Prob. 7–182, determine the total explosion energy of a 0.35-L canned drink that explodes at a pressure of 1.2 MPa. To how many kg of TNT is this explosion energy equivalent?
Demonstrate the validity of the Clausius inequality using a reversible and an irreversible heat engine operating between the same two thermal energy reservoirs at constant temperatures of TL and TH.
The inner and outer surfaces of a 2-m x 2-m window glass in winter are 10°C and 3°C, respectively. If the rate of heat loss through the window is 3.2 kJ/s determine the amount of heat loss, in kilojoules, through the glass over a period of 5 h. Also, determine the rate of entropy generation
Two rigid tanks are connected by a valve. Tank A is insulated and contains 0.2 m3 of steam at 400 kPa and 80 percent quality. Tank B is uninsulated and contains 3 kg of steam at 200 kPa and 250°C. The valve is now opened, and steam flows from tank A to tank B until the pressure in tank A drops
Heat is transferred steadily to boiling water in the pan through its flat bottom at a rate of 500 W. If the temperatures of the inner and outer surfaces of the bottom of the tank are 104°C and 105°C, respectively, determine the rate of entropy generation within bottom of the pan, in W/K.
A 1200-W electric resistance heating element whose diameter is 0.5 cm is immersed in 40 kg of water initially at 20°C. Assuming the water container is well-insulated, determine how long it will take for this heater to raise the water temperature to 50°C. Also, determine the entropy generated
A hot-water pipe at 80°C is losing heat to the surrounding air at 5°C at a rate of 2200 W. Determine the rate of entropy generation in the surrounding air, in W/K.
In large steam power plants, the feedwater is frequently heated in closed feedwater heaters, which are basically heat exchangers, by steam extracted from the turbine at some stage. Steam enters the feedwater heater at 1 MPa and 200°C and leaves as saturated liquid at the same pressure. Feedwater
Reconsider Prob. 7–190. Using EES (or other) software, investigate the effect of the state of the steam at the inlet of the feedwater heater. Assume the entropy of the extraction steam is constant at the value for 1 MPa, 200°C and decrease the extraction steam pressure from 1 MPa to 100 kPa.
A 3-ft3 rigid tank initially contains refrigerant-134a at 100 psia and 100 percent quality. The tank is connected by a valve to a supply line that carries refrigerant-134a at 140 psia and 80°F. The valve is now opened, allowing the refrigerant to enter the tank, and is closed when it is observed
During a heat transfer process, the entropy change of incompressible substances, such as liquid water, can be determined from ∆S = mcavg ln (T2/T1). Show that for thermal energy reservoirs, such as large lakes, this relation reduces to ∆S = Q/T.
The inner and outer glasses of a 2-m x 2-m double pane window are at 18°C and 6°C, respectively. If the glasses are very nearly isothermal and the rate of heat transfer through the window is 110 W, determine the rates of entropy transfer through both sides of the window and the rate of
A well-insulated 4-m x 4-m x 5-m room initially at 10°C is heated by the radiator of a steam heating system. The radiator has a volume of 15 L and is filled with superheated vapor at 200 kPa and 200°C. At this moment both the inlet and the exit valves to the radiator are closed. A 120-W fan is
A passive solar house that is losing heat to the outdoors at 3°C at an average rate of 50,000 kJ/h is maintained at 22°C at all times during a winter night for 10 h. The house is to be heated by 50 glass containers, each containing 20 L of water that is heated to 80°C during the day by absorbing
A 15-ft3 steel container that has a mass of 75 lbm when empty is filled with liquid water. Initially, both the steel tank and the water are at 120°F. Now heat is transferred, and the entire system cools to the surrounding air temperature of 70°F. Determine the total entropy generated during this
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. The 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
A 4-m x 5-m x 7-m well-sealed room is to be heated by 1500 kg of liquid water contained in a tank that is placed in the room. The room is losing heat to the outside air at 5°C at an average rate of 10,000 kJ/h. The room is initially at 20°C and 100 kPa and is maintained at a temperature of 20°C
Consider a well-insulated horizontal rigid cylinder that is divided into two compartments by a piston that is free to move but does not allow either gas to leak into the other side. Initially, one side of the piston contains 1 m3 of N2 gas at 500 kPa and 80°C while the other side contains 1 m3 of
Reconsider Prob. 7–200. Using EES (or other) software, compare the results for constant specific heats to those obtained using built-in variable specific heats built into EES functions.
Repeat Prob. 7–200 by assuming the piston is made of 5 kg of copper initially at the average temperature of the two gases on both sides.
An insulated 5-m3 rigid tank contains air at 500 kPa and 57°C. A valve connected to the tank is now opened, and air is allowed to escape until the pressure inside drops to 200 kPa. The air temperature during this process is maintained constant by an electric resistance heater placed in the tank.
In order to cool 1-ton of water at 20°C in an insulated tank, a person pours 80 kg of ice at -5°C into the water. Determine (a) The final equilibrium temperature in the tank and (b) The entropy generation during this process. The melting temperature and the heat of fusion of ice at atmospheric
An insulated piston€“cylinder device initially contains 0.02 m3 of saturated liquid€“vapor mixture of water with a quality of 0.1 at 100°C. Now some ice at -18°C is dropped into the cylinder. If the cylinder contains saturated liquid at 100°C when thermal equilibrium
Consider a 5-L evacuated rigid bottle that is surrounded by the atmosphere at 100 kPa and 17°C. A valve at the neck of the bottle is now opened and the atmospheric air is allowed to flow into the bottle. The air trapped in the bottle eventually reaches thermal equilibrium with the atmosphere as a
(a) Water flows through a shower head steadily at a rate of 10 L/min. An electric resistance heater placed in the water pipe heats the water from 16 to 43°C. Taking the density of water to be 1 kg/L, determine the electric power input to the heater, in kW, and the rate of entropy generation
Using EES (or other) software, determine the work input to a multistage compressor for a given set of inlet and exit pressures for any number of stages. Assume that the pressure ratio across each stage is identical and the compression process is polytropic. List and plot the compressor work against
A piston–cylinder device contains air that undergoes a reversible thermodynamic cycle. Initially, air is at 400 kPa and 300 K with a volume of 0.3 m3 Air is first expanded isothermally to 150 kPa, then compressed adiabatically to the initial pressure, and finally compressed at the constant
Consider the turbocharger of an internal combustion engine. The exhaust gases enter the turbine at 450°C at a rate of 0.02 kg/s and leave at 400°C. Air enters the compressor at 70°C and 95 kPa at a rate of 0.018 kg/s and leaves at 135 kPa. The mechanical efficiency between the turbine
Air is compressed steadily by a compressor from 100 kPa and 20°C to 1200 kPa and 300°C at a rate of 0.4 kg/s. The compressor is intentionally cooled by utilizing fins on the surface of the compressor and heat is lost from the compressor at a rate of 15 kW to the surroundings at 20°C. Using
A 0.25-m3 insulated piston€“cylinder device initially contains 0.7 kg of air at 20°C. At this state, the piston is free to move. Now air at 500 kPa and 70°C is allowed to enter the cylinder from a supply line until the volume increases by 50 percent. Using constant specific heats
When the transportation of natural gas in a pipeline is not feasible for economic reasons, it is first liquefied using non-conventional refrigeration techniques and then transported in super-insulated tanks. In a natural gas liquefaction plant, the liquefied natural gas (LNG) enters a cryogenic
Steam is condensed at a constant temperature of 30°C as it flows through the condenser of a power plant by rejecting heat at a rate of 55 MW. The rate of entropy change of steam as it flows through the condenser is (a) -1.83 MW/K (b) -0.18 MW/K (c) 0 MW/K (d) 0.56 MW/K (e) 1.22 MW/K
Steam is compressed from 6 MPa and 300°C to 10 MPa isentropically. The final temperature of the steam is (a) 290°C (b) 300°C (c) 311°C (d) 371°C (e) 422°C
An apple with an average mass of 0.15 kg and average specific heat of 3.65 kJ/kg • °C is cooled from 20°C to 5°C. The entropy change of the apple is (a) -0.0288 kJ/K (b) -0.192 kJ/K (c) -0.526 kJ/K (d) 0 kJ/K (e) 0.657 kJ/K
A piston–cylinder device contains 5 kg of saturated water vapor at 3 MPa. Now heat is rejected from the cylinder at constant pressure until the water vapor completely condenses so that the cylinder contains saturated liquid at 3 MPa at the end of the process. The entropy change of the system
Helium gas is compressed from 1 atm and 25°C to a pressure of 10 atm adiabatically. The lowest temperature of helium after compression is (a) 25°C (b) 63°C (c) 250°C (d) 384°C (e) 476°C
Steam expands in an adiabatic turbine from 8 MPa and 500°C to 0.1 MPa at a rate of 3 kg/s. If steam leaves the turbine as saturated vapor, the power output of the turbine is (a) 2174 kW (b) 698 kW (c) 2881 kW (d) 1674 kW (e) 3240 Kw
Argon gas expands in an adiabatic turbine from 3 MPa and 750°C to 0.2 MPa at a rate of 5 kg/s. The maximum power output of the turbine is (a) 1.06 MW (b) 1.29 MW (c) 1.43 MW (d) 1.76 MW (e) 2.08 MW
A unit mass of a substance undergoes an irreversible process from state 1 to state 2 while gaining heat from the surroundings at temperature T in the amount of q. If the entropy of the substance is s1 at state 1, and s2 at state 2, the entropy change of the substance s during this process is (a)
A unit mass of an ideal gas at temperature T undergoes a reversible isothermal process from pressure P1 to pressure P2 while losing heat to the surroundings at temperature T in the amount of q. If the gas constant of the gas is R, the entropy change of the gas s during this process is (a)
Air is compressed from room conditions to a specified pressure in a reversible manner by two compressors: one isothermal and the other adiabatic. If the entropy change of air ∆sisot during the reversible isothermal compression, and ∆sidia during the reversible adiabatic compression, the
Helium gas is compressed from 15°C and 5.40 m3/kg to 0.775 m3/kg in a reversible and adiabatic manner. The temperature of helium after compression is (a) 105°C (b) 55°C (c) 1734°C (d) 1051°C (e) 778°C
Heat is lost through a plane wall steadily at a rate of 600 W. If the inner and outer surface temperatures of the wall are 20°C and 5°C, respectively, the rate of entropy generation within the wall is (a) 0.11 W/K (b) 4.21 W/K (c) 2.10 W/K (d) 42.1 W/K (e) 90.0 W/K
Air is compressed steadily and adiabatically from 17°C and 90 kPa to 200°C and 400 kPa. Assuming constant specific heats for air at room temperature, the isentropic efficiency of the compressor is (a) 0.76 (b) 0.94 (c) 0.86 (d) 0.84 (e) 1.00
Argon gas expands in an adiabatic turbine steadily from 500°C and 800 kPa to 80 kPa at a rate of 2.5 kg/s. For isentropic efficiency of 80 percent, the power produced by the turbine is (a) 194 kW (b) 291 kW (c) 484 kW (d) 363 kW (e) 605 kW
Water enters a pump steadily at 100 kPa at a rate of 35 L/s and leaves at 800 kPa. The flow velocities at the inlet and the exit are the same, but the pump exit where the discharge pressure is measured is 6.1 m above the inlet section. The minimum power input to the pump is (a) 34 kW (b) 22 kW
Air at 15°C is compressed steadily and isothermally from 100 kPa to 700 kPa at a rate of 0.12 kg/s. The minimum power input to the compressor is (a) 1.0 kW (b) 11.2 kW (c) 25.8 kW (d) 19.3 kW (e) 161 kW
Air is to be compressed steadily and isentropically from 1 atm to 25 atm by a two-stage compressor. To minimize the total compression work, the intermediate pressure between the two stages must be (a) 3 atm (b) 5 atm (c) 8 atm (d) 10 atm (e) 13 atm
Helium gas enters an adiabatic nozzle steadily at 500°C and 600 kPa with a low velocity, and exits at a pressure of 90 kPa. The highest possible velocity of helium gas at the nozzle exit is (a) 1475 m/s (b) 1662 m/s (c) 1839 m/s (d) 2066 m/s (e) 3040 m/s
Combustion gases with a specific heat ratio of 1.3 enter an adiabatic nozzle steadily at 800°C and 800 kPa with a low velocity, and exit at a pressure of 85 kPa. The lowest possible temperature of combustion gases at the nozzle exit is (a) 43°C (b) 237°C (c) 367°C (d) 477°C (e) 640°C
Steam enters an adiabatic turbine steadily at 400°C and 3 MPa, and leaves at 50 kPa. The highest possible percentage of mass of steam that condenses at the turbine exit and leaves the turbine as a liquid is (a) 5% (b) 10% (c) 15% (d) 20% (e) 0%
Liquid water enters an adiabatic piping system at 15°C at a rate of 8 kg/s. If the water temperature rises by 0.2°C during flow due to friction, the rate of entropy generation in the pipe is (a) 23 W/K (b) 55 W/K (c) 68 W/K (d) 220 W/K (e) 443 W/K
Liquid water is to be compressed by a pump whose isentropic efficiency is 75 percent from 0.2 MPa to 5 MPa at a rate of 0.15 m3/min. The required power input to this pump is (a) 4.8 kW (b) 6.4 kW (c) 9.0 kW (d) 16.0 kW (e) 12 kW
Steam enters an adiabatic turbine at 8 MPa and 500°C at a rate of 18 kg/s, and exits at 0.2 MPa and 300°C. The rate of entropy generation in the turbine is (a) 0 kW/K (b) 7.2 kW/K (c) 21 kW/K (d) 15 kW/K (e) 17 kW/K
How does reversible work differ from useful work?
Under what conditions does the reversible work equal irreversibility for a process?
Is the energy of a system different in different environments?
How does useful work differ from actual work? For what kind of systems are these two identical?
Consider two geothermal wells whose energy contents are estimated to be the same. Will the energies of these wells necessarily be the same? Explain.
Consider two systems that are at the same pressure as the environment. The first system is at the same temperature as the environment, whereas the second system is at a lower temperature than the environment. How would you compare the energies of these two systems?
Consider an environment of zero absolute pressure (such as outer space). How will the actual work and the useful work compare in that environment?
What is the second-law efficiency? How does it differ from the first-law efficiency?
Does a power plant that has a higher thermal efficiency necessarily have a higher second-law efficiency than one with a lower thermal efficiency? Explain.
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