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engineering
mechanical engineering
Fundamentals of Thermodynamics 6th edition Richard E. Sonntag, Claus Borgnakke, Gordon J. Van Wylen - Solutions
A condenser (heat exchanger) brings 1 kg/s water flow at 10 kPa from 300C to saturated liquid at 10 kPa. The cooling is done by lake water at 20C that returns to the lake at 30C. For an insulated condenser, find the flow rate of cooling water.
Two kg of water at 500 kPa, 20C is heated in a constant pressure process (SSSF) to 1700C. Find the best estimate for the heat transfer.
A mixing chamber with heat transfer receives 2 kg/s of R-22 at 1 MPa, 40C in one line and 1 kg/s of R-22 at 30C, quality 50% in a line with a valve. The outgoing flow is at 1 MPa, 60C. Find the rate of heat transfer to the mixing chamber.
Compressed liquid R-22 at 1.5 MPa, 10C is mixed in a steady-state, steady-flow process with saturated vapor R-22 at 1.5 MPa. Both flow rates are 0.1 kg/s, and the exiting flow is at 1.2 MPa and a quality of 85%. Find the rate of heat transfer to the mixing chamber.
Nitrogen gas flows into a convergent nozzle at 200 kPa, 400 K and very low velocity. It flows out of the nozzle at 100 kPa, 330 K. If the nozzle is insulated find the exit velocity.
Superheated vapor ammonia enters an insulated nozzle at 20C, 800 kPa, with a low velocity and at the steady rate of 0.01 kg/s. The ammonia exits at 300 kPa with a velocity of 450 m/s. Determine the temperature (or quality, if saturated) and the exit area of the nozzle.
A diffuser has air entering at 100 kPa, 300 K, with a velocity of 200 m/s. The inlet cross-sectional area of the diffuser is 100 mm2. At the exit, the area is 860 mm2, and the exit velocity is 20 m/s. Determine the exit pressure and temperature of the air.
A diffuser receives an ideal gas flow at 100 kPa, 300 K with a velocity of 250 m/s and the exit velocity is 25 m/s. Determine the exit temperature if the gas is argon, helium or nitrogen.
The front of a jet engine acts as a diffuser receiving air at 900 km/h, -5C, 50 kPa, bringing it to 80 m/s relative to the engine before entering the compressor. If the flow area is reduced to 80% of the inlet area find the temperature and pressure in the compressor inlet.
Helium is throttled from 1.2 MPa, 20C, to a pressure of 100 kPa. The diameter of the exit pipe is so much larger than the inlet pipe that the inlet and exit velocities are equal. Find the exit temperature of the helium and the ratio of the pipe diameters.
Water flowing in a line at 400 kPa, saturated vapor, is taken out through a valve to 100 kPa. What is the temperature as it leaves the valve assuming no changes in kinetic energy and no heat transfer?
Methane at 3 MPa, 300 K, is throttled to 100 kPa. Calculate the exit temperature assuming no changes in the kinetic energy and ideal-gas behavior. Repeat the answer for real-gas behavior.
Water at 1.5 MPa, 150C, is throttled adiabatically through a valve to 200 kPa. The inlet velocity is 5 m/s, and the inlet and exit pipe diameters are the same. Determine the state and the velocity of the water at the exit.
An insulated mixing chamber receives 2 kg/s R-134a at 1 MPa, 100C in a line with low velocity. Another line with R-134a as saturated liquid 60C flows through a valve to the mixing chamber at 1MPa after the valve. The exit flow is saturated vapor at 1 MPa flowing at 20 m/s. Find the
A mixing chamber receives 2 kg/s R-134a at 1 MPa, 100C in a line with low velocity and 1 kg/s from a line with R-134a as saturated liquid 60C flows through a valve to the mixing chamber at 1 MPa after the valve. There is heat transfer so the exit flow is saturated vapor at 1 MPa
A steam turbine receives water at 15 MPa, 600C at a rate of 100 kg/s, shown in Fig. P6.29. In the middle section 20 kg/s is withdrawn at 2 MPa, 350C, and the rest exits the turbine at 75 kPa, and 95% quality. Assuming no heat transfer and no changes in kinetic energy, find the total
A small, high-speed turbine operating on compressed air produces a power output of 100 W. The inlet state is 400 kPa, 50C, and the exit state is 150 kPa, 30C. Assuming the velocities to be low and the process to be adiabatic, find the required mass flow rate of air through
A steam turbine receives steam from two boilers. One flow is 5 kg/s at 3 MPa, 700C and the other flow is 15 kg/s at 800 kPa, 500C. The exit state is 10 kPa, with a quality of 96%. Find the total power out of the adiabatic turbine.
A small turbine, shown in Fig P6.32, is operated at part load by throttling a 0.25 kg/s steam supply at 1.4 MPa, 250C down to 1.1 MPa before it enters the turbine and the exhaust is at 10 kPa. If the turbine produces 110 kW, find the exhaust temperature (and quality if saturated).
Hoover Dam across the Colorado River dams up Lake Mead 200 m higher than the river downstream. The electric generators driven by water-powered turbines deliver 1300 MW of power. If the water is 17.5C, find the minimum amount of water running through the turbines.
A large SSSF expansion engine has two low velocity flows of water entering. High pressure steam enters at point 1 with 2.0 kg/s at 2 MPa, 500C and 0.5 kg/s cooling water at 120 kPa, 30C enters at point 2. A single flow exits at point 3 with 150 kPa, 80% quality, through a 0.15 m
A small water pump is used in an irrigation system. The pump takes water in from a river at 10C, 100 kPa at a rate of 5 kg/s. The exit line enters a pipe that goes up to an elevation 20 m above the pump and river, where the water runs into an open channel. Assume the process is adiabatic
The compressor of a large gas turbine receives air from the ambient at 95 kPa, 20C, with a low velocity. At the compressor discharge, air exits at 1.52 MPa, 430C, with velocity of 90 m/s. The power input to the compressor is 5000 kW. Determine the mass flow rate of air through the
Two steady flow of air enters a control volume, shown in Fig. P6.37. One is 0.025 kg/s flow at 350 kPa, 150C, state 1, and the other enters at 350 kPa, 15C, both flows with low velocity. A single flow of air exits at 100 kPa, 40C through a 25-mm diameter pipe, state
An air compressor takes in air at 100 kPa, 17C and delivers it at 1 MPa, 600 K to a constant-pressure cooler, which it exits at 300 K. Find the specific compressor work and the specific heat transfer.
The following data are for a simple steam power plant as shown in Fig. P6.39 State 1 2 3 4 5 6 7 P MPa 6.2 6.1 5.9 5.7 5.5 0.01 0.009 T C 45 175 500 490 40
For the same steam power plant and Problem 6.39, determine the rate of heat transfer in the economizer which is a low temperature heat exchanger and the steam generator. Determine also the flow rate of cooling water through the condenser, if the cooling water increases from 15to
Cogeneration is often used where a steam supply is needed for industrial process energy. Assume a supply of 5 kg/s steam at 0.5 MPa is needed. Rather than generating this from a pump and boiler, the setup in Fig. P6.41 is used so the supply is extracted from the high-pressure turbine. Find the
A somewhat simplified flow diagram for a nuclear power plant shown in Fig. 1.4 is given in Fig. P6.42. Mass flow rates and the various states in the cycle are shown in the accompanying table. The cycle includes a number of heaters in which heat is transferred from steam, taken out of the turbine at
Consider the power plant as described in the previous problem.a. Determine the quality of the steam leaving the reactor.b. What is the power to the pump that feeds water to the reactor?
Consider the power plant as described in Problem 6.42.a. Determine the temperature of the water leaving the intermediate pressure heater, T13, assuming no heat transfer to the surroundings.b. Determine the pump work, between states 13 and 16.
Consider the power plant as described in Problem 6.42.a. Find the power removed in the condenser by the cooling water (not shown).b. Find the power to the condensate pump.c. Do the energy terms balance for the low pressure heater or are there a heat transfer not shown?
A proposal is made to use a geothermal supply of hot water to operate a steam turbine, as shown in Fig. P6.46. The high-pressure water at 1.5 MPa, 180C, is throttled into a flash evaporator chamber, which forms liquid and vapor at a lower pressure of 400 kPa. The liquid is discarded while
A R-12 heat pump cycle shown in Fig P6.47 has a R-12 flow rate of 0.05 kg/s with 4 kW into the compressor. The following data are givenCalculate the heat transfer from the compressor, the heat transfer from the R-12 in the condenser and the heat transfer to the R-12 in the evaporator.
A rigid 100-L tank contains air at 1 MPa, 200C. A valve on the tank is now opened and air flows out until the pressure drops to 100 kPa. During this process, heat is transferred from a heat source at 200C, such that when the valve is closed, the temperature inside the tank is
A 25-L tank that is initially evacuated is connected by a valve to an air supply line flowing air at 20C, 800 kPa. The valve is opened, and air flows into the tank until the pressure reaches 600 kPa. Determine the final temperature and mass inside the tank, assuming the process is
A 100-L rigid tank contains carbon dioxide gas at 1 MPa, 300 K. A valve is cracked open, and carbon dioxide escapes slowly until the tank pressure has dropped to 500 kPa. At this point the valve is closed. The gas remaining inside the tank may be assumed to have undergone a polytropic expansion,
A 1-m3 tank contains ammonia at 150 kPa, 25C. The tank is attached to a line flowing ammonia at 1200 kPa, 60C. The valve is opened, and mass flows in until the tank is half full of liquid, by volume at 25C. Calculate the heat transferred from the tank during this process.
A nitrogen line, 300 K and 0.5 MPa, is connected to a turbine that exhausts to a closed initially empty tank of 50 m3. The turbine operates to a tank pressure of 0.5 MPa, at which point the temperature is 250 K, assuming the entire process is adiabatic, determine the turbine work.
An evacuated 150-L tank is connected to a line flowing air at room temperature, 25C, and 8 MPa pressure. The valve is opened allowing air to flow into the tank until the pressure inside is 6 MPa. At this point the valve is closed. This filling process occurs rapidly and is essentially
A 0.5-m diameter balloon containing air at 200 kPa, 300 K, is attached by a valve to an air line flowing air at 400 kPa, 400 K. The valve is now opened, allowing air to flow into the balloon until the pressure inside reaches 300 kPa, at which point the valve is closed. The final temperature inside
A 500-L insulated tank contains air at 40C, 2 MPa. A valve on the tank is opened, and air escapes until half the original mass is gone, at which point the valve is closed. What is the pressure inside then?
A steam engine based on a turbine is shown in Fig. P6.56. The boiler tank has a volume of 100 L and initially contains saturated liquid with a very small amount of vapor at 100 kPa. Heat is now added by the burner, and the pressure regulator does not open before the boiler pressure reaches 700 kPa,
A 2-m3 insulated vessel contains saturated vapor steam at 4 MPa. A valve on the top of the tank is opened, and steam is allowed to escape. During the process any liquid formed collects at the bottom of the vessel, so that only saturated vapor exits. Calculate the total mass that has escaped when
A 1-m3 insulated, 40-kg rigid steel tank contains air at 500 kPa, and both tank and air are at 20C. The tank is connected to a line flowing air at 2 MPa, 20C. The valve is opened, allowing air to flow into the tank until the pressure reaches 1.5 MPa and is then closed. Assume the
A 750-L rigid tank initially contains water at 250C, 50% liquid and 50% vapor, by volume. A valve at the bottom of the tank is opened, and liquid is slowly withdrawn. Heat transfer takes place such that the temperature remains constant. Find the amount of heat transfer required to the state
An initially empty bottle, V 0.25 m3, is filled with water from a line at 0.8 MPa, 350C. Assume no heat transfer and that the bottle is closed when the pressure reaches line pressure. Find the final temperature and mass in the bottle.
A supply line of ammonia at 0C, 450 kPa is used to fill a 0.05-m3 container initially storing ammonia at 20C, 100 kPa. The supply line valve is closed when the pressure inside reaches 290.9 kPa. Find the final mass and temperature in the container.
An insulated spring-loaded piston/cylinder is connected to an air line flowing air at 600 kPa, 700 K by a valve. Initially the cylinder is empty and the spring force is zero. The valve is then opened until the cylinder pressure reaches 300 kPa. By noting that u2 uline
A mass-loaded piston/cylinder containing air is at 300 kPa, 17C with a volume of 0.25 m3, while at the stops V 1 m3. An air line, 500 kPa, 600 K, is connected by a valve that is then opened until a final inside pressure of 400 kPa is reached, at which point T
An elastic balloon behaves such that pressure is proportional to diameter and the balloon contains 0.5 kg air at 200 kPa, 30C. The balloon is momentarily connected to an air line at 400 kPa, 100C. Air is let in until the volume doubles, during which process there is a heat transfer
A 2-m3 storage tank contains 95% liquid and 5% vapor by volume of liquefied natural gas (LNG) at 160 K. It may be assumed that LNG has the same properties as pure methane. Heat is transferred to the tank and saturated vapor at 160 K flows into the a steady flow heater which it leaves at 300 K. The
A spherical balloon is constructed of a material such that the pressure inside is proportional to the balloon diameter to the power 1.5. The balloon contains argon gas at 1200 kPa, 700C, at a diameter of 2.0 m. A valve is now opened, allowing gas to flow out until the diameter reaches 1.8
A rigid tank initially contains 100 L of saturated-liquid R-12 and 100 L of saturated-vapor R-12 at 0C. A valve on the bottom of the tank is connected to a line flowing R-12 at 10C, 900 kPa. A pressure-relief valve on the top of the tank is set at 745 kPa (when tank pressure reaches
A cylinder with a constant load on the piston contains water at 500 kPa, 20 C and volume of 1 L. The bottom of the cylinder is connected with a line and valve to a steam supply line carrying steam at 1 MPa, 200 C. The valve is now opened for a short time to let steam in to a final
A 2-m3 insulated tank containing ammonia at 20C, 80% quality, is connected by a valve to line flowing ammonia at 2 MPa, 60C. The valve is opened, allowing ammonia to flow into the tank. At what pressure should the valve be closed if the manufacturer wishes to have 15 kg of
Air is contained in the insulated cylinder shown in Fig. P6.70. At this point the air is at 140 kPa, 25C, and the cylinder volume is 15 L. The piston cross-sectional area is 0.045 m2, and the spring is linear with spring constant 35 kN/m. The valve is opened, and air from the line at 700
An inflatable bag, initially flat and empty, is connected to a supply line of saturated vapor R-22 at ambient temperature of 10C. The valve is opened, and the bag slowly inflates at constant temperature to a final diameter of 2 m. The bag is inflated at constant pressure, Po
A cylinder fitted with a piston restrained by a linear spring contains 1 kg of R-12 at 100C, 800 kPa. The spring constant is 50kN/m, and the piston cross-sectional area is 0.05 m2. A valve on the cylinder is opened and R-12 flows out until half the initial mass is left. Heat is transferred
Air at 95 F, 16 lbf/in 2, flows in a 4 in 6 in. rectangular duct in a heating system. The volumetric flow rate is 30 cfm (ft3/min). What is the velocity of the air flowing in the duct?
Saturated vapor R-134a leaves the evaporator in a heat pump at 50 F, with a steady mass flow rate of 0.2lbm/s. What is the smallest diameter tubing that can be used at this location if the velocity of the refrigerant is not to exceed 20 ft/s?
A pump takes 40F liquid water from a river at 14lbf/in 2 and pumps it up to an irrigation canal 60 ft higher than the river surface. All pipes have diameter of 4 in. and the flow rate is 35 lbm/s. Assume the pump exit pressure is just enough to carry a water column of the 60 ft height with 15
Carbon dioxide gas enters a steady-state, steady-flow heater at 45 lbf/in.2 60 F and exits at 40 lbf/in 2, 1800 F. It is shown in Fig. P6.9, where changes in kinetic and potential energies are negligible, Calculate the required heat transfer per lbm of carbon dioxide flowing through the heater.
In a steam generator, compressed liquid water at 1500 lbf/in 2, 100 F, enters a 1-in. diameter tube at the rate of 5 ft3/min. Steam at 1250 lbf/in 2, 750 F exits the tube. Find the rate of heat transfer to the water.
A heat exchanger is used to cool an air flow from 1400 to 680 R, both states at 150 lbf/in 2. The coolant is a water flow at 60 F, 15 lbf/in 2 and it is shown in Fig. P6.13. If the water leaves as saturated vapor, find the ratio of the flow rates mH2O/mair.
A condenser, as the heat exchanger shown in Fig P6.14, brings 1 lbm/s water flow at 1 lbf/in 2 from 500 F to saturated liquid at 1 lbf/in 2. The cooling is done by lake water at 70 F that returns to the lake at 90 F. For an insulated condenser, find the flow rate of cooling water.
Four pound-mass of water at 80 lbf/in 2, 70 F is heated in a constant pressure process (SSSF) to 2600 F. Find the best estimate for the heat transfer.
Nitrogen gas flows into a convergent nozzle at 30 lbf/in 2, 600 R and very low velocity. It flows out of the nozzle at 15 lbf/in 2, 500 R. If the nozzle is insulated find the exit velocity.
A diffuser shown in Fig P6.20 has air entering at 14.7 lbf/in 2, 540 R, with a velocity of 600 ft/s. The inlet cross-sectional area of the diffuser is 0.2 in 2. At the exit, the area is 1.75 in 2, and the exit velocity is 60 ft/s. Determine the exit pressure and temperature of the air.
Helium is throttled from 175 lbf/in 2, 70 F, to a pressure of 15 lbf/in 2. The Diameter of the exit pipe is so much larger than the inlet pipe that the inlet and exit velocities are equal. Find the exit temperature of the helium and the ratio of the pipe diameters.
Water flowing in a line at 60 lbf/in 2, saturated vapor, is taken out through a valve to 14.7 lbf/in 2. What is the temperature as it leaves the valve assuming no changes in kinetic energy and no heat transfer?
An insulated mixing chamber receives 4 lbm/s R-134a at 150 lbf/in 2, 220 F in a line with low velocity. Another line with R-134a as saturated liquid 130 F flows through a valve to the mixing chamber at 150 lbf/in 2 after the valve. The exit flow is saturated vapor at 150 lbf/in 2 flowing at 60
A steam turbine receives water at 2000 lbf/in 2, 1200 F at a rate of 200lbm/s. In the middle section 40lbm/s is withdrawn at 300 lbf/in 2, 650 F and the rest exits the turbine at 10 lbf/in 2, 95% quality. Assuming no heat transfer and no changes in kinetic energy, find the total turbine work.
A small, high-speed turbine operating on compressed air produces a power output of 0.1 hp. The inlet state is 60 lbf/in 2, 120 F, and the exit state is 14.7 lbf/in 2, 20 F. Assuming the velocities to be low and the process to be adiabatic, find the required mass flow rate of air through the
Hoover Dam across the Colorado River dams up Lake Mead 600 ft higher than the river downstream. The electric generators driven by water-powered turbines deliver 1.2 106 Btu/s. If the water is 65 F, find the minimum amount of water running through the turbines.
A small water pump is used in an irrigation system. The pump takes water in from a river at 50 F, 1 atm at a rate of 10lbm/s. The exit line enters a pipe that goes up to an elevation 60 ft above the pump and river, where the water runs into an open channel. Assume the process is adiabatic and that
An air compressor takes in air at 14 lbf/in 2, 60 F and delivers it at 140 lbf/in 2, 1080 R to a constant-pressure cooler, which it exits at 560 R. Find the specific compressor work and the specific heat transfer.
The following data are for a simple steam power plant as shown in Fig. P6.39
For the same steam power plant determine the rate of heat transfer in the economizer which is a low temperature heat exchanger and the steam generator. Determine also the flow rate of cooling water through the condenser, if the cooling water increases from 55 to 75 F in the condenser.
A proposal is made to use a geothermal supply of hot water to operate a steam turbine. The high pressure water at 200 lbf/in 2, 350 F is throttled into a flash evaporator chamber, which forms liquid and vapor at a lower pressure of 60 lbf/in2. The liquid is discarded while the saturated vapor feeds
A 1-ft3 tank that is initially evacuated is connected by a valve to an air supply line flowing air at 70 F, 120 lbf/in 2. The valve is opened, and air flows into the tank until the pressure reaches 90 lbf/in 2. Determine the final temperature and mass inside the tank, assuming the process is
A 20-ft3 tank contains ammonia at 20 lbf/in 2, 80 F. The tank is attached to a line flowing ammonia at 180 lbf/in 2, 140 F. The valve is opened, and mass flows in until the tank is half full of liquid, by volume at 80 F. Calculate the heat transferred from the tank during this process.
A 18-ft3 insulated tank contains air at 100 F, 300 lbf/in 2. A valve on the tank is opened, and air escapes until half the original mass is gone, at which point the valve is closed. What is the pressure inside then?
Air is contained in the insulated cylinder shown in Fig. P6.70. At this point the air is at 20 lbf/in 2, 80 F, and the cylinder volume is 0.5 ft3. The piston cross-sectional area is 0.5 ft2, and the spring is linear with spring constant 200 lbf/in. The valve is opened, and air from the line at 100
A 35-ft3 insulated, 90-lbm rigid steel tank contains air at 75 lbf/in 2, and both tank and air are at 70 F. The tank is connected to a line flowing air at 300 lbf/in 2, 70 F. The valve is opened, allowing air to flow into the tank until the pressure reaches 250 lbf/in 2 and is then closed. Assume
A cylinder fitted with a piston restrained by a linear spring contains 2 lbm of R-22 at 220 F, 125 lbf/in 2. The system is shown in Fig. P6.72 where the spring constant is 285lbf/in, and the piston cross-sectional area is 75 in 2. A valve on the cylinder is opened and R-22 flows out until half the
An initially empty bottle, V 10 ft3, is filled with water from a line at 120 lbf/in 2, 500 F. Assume no heat transfer and that the bottle is closed when the pressure reaches line pressure. Find the final temperature and mass in the bottle.
A mass-loaded piston/cylinder containing air is at 45 lbf/in 2, 60 F with a volume of 9 ft3, while at the stops V 36 ft3. An air line, 75 lbf/in 2, 1100 R, is connected by a valve. The valve is then opened until a final inside pressure of 60 lbf/in.2 is reached, at which point T =
A nitrogen line, 540 R, and 75 lbf/in 2, is connected to a turbine that exhausts to a closed initially empty tank of 2000 ft3. The turbine operates to a tank pressure of 75 lbf/in 2, at which point the temperature is 450 R, assuming the entire process is adiabatic, determine the turbine work.
Calculate the thermal efficiency of the steam power plant cycle described in Problem 6.39.
Calculate the coefficient of performance of the R-12 heat pump cycle described in Problem 6.47.
Prove that a cyclic device that violates the Kelvin–Planck statement of the second law also violates the Clausius statement of the second law.
Discuss the factors that would make the power plant cycle described in Problem 6.39 an irreversible cycle.
Discuss the factors that would make the heat pump described in Problem 6.47 an irreversible cycle.
Calculate the thermal efficiency of a Carnot-cycle heat engine operating between reservoirs at 500C and 40C. Compare the result with that of Problem 7.1.
Calculate the coefficient of performance of a Carnot-cycle heat pump operating between reservoirs at 0C and 45C. Compare the result with that of Problem 7.2.
A car engine burns 5 kg fuel (equivalent to addition of QH) at 1500 K and rejects energy to the radiator and the exhaust at an average temperature of 750 K. If the fuel provides 40 000 kJ/kg what is the maximum amount of work the engine can provide?
In a steam power plant 1 MW is added at 700C in the boiler, 0.58 MW is taken out at 40C in the condenser and the pump work is 0.02 MW. Find the plant thermal efficiency. Assuming the same pump work and heat transfer to the boiler is given, how much turbine power could be produced if
At certain locations geothermal energy in underground water is available and used as the energy source for a power plant. Consider a supply of saturated liquid water at 150C. What is the maximum possible thermal efficiency of a cyclic heat engine using this source of energy with the ambient
Find the maximum coefficient of performance for the refrigerator in your kitchen, assuming it runs in a Carnot cycle.
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