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engineering
mechanical engineering
Fundamentals of Thermodynamics 6th edition Richard E. Sonntag, Claus Borgnakke, Gordon J. Van Wylen - Solutions
A 2 m tall cylinder has a small hole in the bottom. It is filled with liquid water 1 m high, on top of which is 1 m high air column at atmospheric pressure of 100 kPa. As the liquid water near the hole has a higher P than 100 kPa it runs out. Assume a slow process with constant T. Will the flow
A 2-m3 insulated vessel, shown in Fig. P6.121 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
A 750-L rigid tank, shown in Fig P6.122 initially contains water at 250°C, 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 A valve at the bottom of the tank is opened, and liquid is slowly withdrawn.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
Consider the previous problem but let the line and valve be located in the top of the tank. Now saturated vapor is slowly withdrawn while heat transfer keeps the temperature inside constant. Find the heat transfer required to reach a state where half the original mass is withdrawn.
Two kg of water at 500 kPa, 20oC is heated in a constant pressure process to 1700oC. Find the best estimate for the heat transfer.
In a glass factory a 2 m wide sheet of glass at 1500 K comes out of the final rollers that fix the thickness at 5 mm with a speed of 0.5 m/s. Cooling air in the amount of 20 kg/s comes in at 17oC from a slot 2 m wide and flows parallel with the glass. Suppose this setup is very long so the glass
Assume a setup similar to the previous problem but the air flows in the opposite direction of the glass; it comes in where the glass goes out. How much air flow at 17oC is required to cool the glass to 450 K assuming the air must be at least 120 K cooler than the glass at any location?
Three air flows all at 200 kPa are connected to the same exit duct and mix without external heat transfer. Flow one has 1 kg/s at 400 K, flow two has 3 kg/s at 290 K and flow three has 2 kg/s at 700 K. Neglect kinetic energies and find the volume flow rate in the exit flow.
Consider the power plant as described in Problem 6.102. 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 6.102. 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 is, there a heat transfer not shown?
A 500-L insulated tank contains air at 40°C, 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. P6.131. 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
An insulated spring-loaded piston/cylinder, shown in Fig P6.132 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 + CV
A mass-loaded piston/cylinder, shown in Fig P6.133, containing air is at 300 kPa, 17°C 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 = 350 K. Find
A 2-m3 storage tank contains 95% liquid and 5% vapor by volume of liquefied natural gas (LNG) at 160 K, as shown in Fig. P6.65. 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
Liquid water at 80oC flows with 0.2 kg/s inside a square duct, side 2 cm insulated with a 1 cm thick layer of foam k = 0.1 W/m K. If the outside foam surface is at 25oC how much has the water temperature dropped for 10 m length of duct? Neglect the duct material and any corner effects (A = 4sL).
A counter-flowing heat exchanger conserves energy by heating cold outside fresh air at 10oC with the outgoing combustion gas (air) at 100oC. Assume both flows are 1 kg/s and the temperature difference between the flows at any point is 50oC. What is the incoming fresh air temperature after the heat
Saturated liquid water at 1000 kPa flows at 2 kg/s inside a 10 cm outer diameter steel pipe and outside of the pipe is a flow of hot gases at 1000 K with a convection coefficient of h = 150 W/m2 K. Neglect any ΔT in the steel and any inside convection h and find the length of pipe needed to
A flow of 1000 K, 100 kPa air with 0.5 kg/s in a furnace flows over a steel plate of surface temperature 400 K. The flow is such that the convective heat transfer coefficient is h = 125 W/m2 K. How much of a surface area does the air have to flow over to exit with a temperature of 800 K? How about
Liquid water at 60 F flows out of a nozzle straight up 40 ft. What is nozzle Vexit?
R-134a at 90 F, 125 psia is throttled so it becomes cold at 10 F. What is exit P?
In a boiler you vaporize some liquid water at 103 psia flowing at 3 ft/s. What is the velocity of the saturated vapor at 103 psia if the pipe size is the same? Can the flow then be constant P?
Air at 60 ft/s, 480 R, 11 psia with 10 lbm/s flows into a jet engine and it flows out at 1500 ft/s, 1440 R, 11 psia. What is the change (power) in flow of kinetic energy?
An initially empty cylinder is filled with air from 70 F, 15 psia until it is full. Assuming no heat transfer is the final temperature larger, equal to or smaller than 70 F? Does the final T depend on the size of the cylinder?
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?
A hot air home heating system takes 500 ft3/min (cfm) air at 14.7 psia, 65 F into a furnace and heats it to 130 F and delivers the flow to a square duct 0.5 ft by 0.5 ft at 15 psia. What is the velocity in the duct?
Saturated vapor R-134a leaves the evaporator in a heat pump at 50 F, with a steady mass flow rate of 0.2 lbm/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 40 F liquid water from a river at 14 lbf/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
In a jet engine a flow of air at 1800 R, 30 psia and 90 ft/s enters a nozzle where the air exits at 1500 R, 13 psia, as shown in Fig. P.6.33. What is the exit velocity assuming no heat loss?
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 P6.36 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/in2; 70 F to a pressure of 15 lbf/in2; 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/in2, what is the temperature as it leaves the valve assuming no changes in kinetic energy and no heat transfer?
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, as shown in Fig. P6.51. 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 expander (a turbine with heat transfer) has 0.1 lbm/s helium entering at 160 psia, 1000 R and it leaves at 40 psia, 540 R. The power output on the shaft is measured to 55 Btu/s. Find the rate of heat transfer neglecting kinetic energies.
An exhaust fan in a building should be able to move 5 lbm/s air at 14.4 psia, 68 F through a 1.25 ft diameter vent hole. How high a velocity must it generate and how much power is required to do that?
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.
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. P6.63 here changes in kinetic and potential energies are negligible. Calculate the required heat transfer per lbm of carbon dioxide flowing through the heater.
A flow of liquid glycerine flows around an engine, cooling it as it absorbs energy. The glycerine enters the engine at 140 F and receives 13 hp of heat transfer. What is the required mass flow rate if the glycerine should come out at a maximum 200 F?
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 10 lbm/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
A steam turbine receives water at 2000 lbf/in.2, 1200 F at a rate of 200 lbm/s as shown in Fig P6.78 In the middle section 40 lbm/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
A condenser, as the heat exchanger shown in Fig P6.84 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.
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. P6.86. If the water leaves as saturated vapor find the ratio of the flow rates m.H2O/m.air.
An automotive radiator has glycerine at 200 F enter and return at 130 F as shown in Fig. P6.88. Air flows in at 68 F and leaves at 77 F. If the radiator should transfer 33 hp what is the mass flow rate of the glycerine and what is the volume flow rate of air in at 15 psia?
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
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. P6.99. State 6 has x6 = 0.92, and velocity of 600 ft/s. The rate of steam flow is 200 000 lbm/h, with 400 hp input to the pump. Piping diameters are 8 in. from steam generator to the turbine and 3 in. from the condenser to the
For the same steam power plant as shown in Fig P6.99 and Problem 6.167E 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
A proposal is made to use a geothermal supply of hot water to operate a steam turbine, as shown in Fig. P6.105. 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/in.2. The liquid is discarded
A 1-ft3 tank, shown in Fig P6.111 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
Helium in a steel tank is at 40 psia, 540 R with a volume of 4 ft3. It is used to fill a balloon. When the tank pressure drops to 24 psia the flow of helium stops by itself, if all the helium still is at 540 R how big a balloon did I get? Assume the pressure in the balloon varies linearly with
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.
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 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, as shown in Fig. P6.119. 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,
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, as shown in Fig. P6.133. The valve is then opened until a final inside pressure of 60 lbf/in.2 is reached, at which
Electrical appliances (TV, stereo) use electric power as input. What happens to the power? Are those heat engines? What does the second law say about those devices?
A gasoline engine produces 20 hp using 35 kW of heat transfer from burning fuel. What is its thermal efficiency and how much power is rejected to the ambient?
A refrigerator removes 1.5 kJ from the cold space using 1 kJ work input. How much energy goes into the kitchen and what is its coefficient of performance?
Assume we have a refrigerator operating at steady state using 500 W of electric power with a COP of 2.5. What is the net effect on the kitchen air?
A window air-conditioner unit is placed on a laboratory bench and tested in cooling mode using 750 W of electric power with a COP of 1.75. What is the cooling power capacity and what is the net effect on the laboratory?
Geothermal underground hot water or steam can be used to generate electric power. Does that violate the second law?
A car engine takes atmospheric air in at 20oC, no fuel, and exhausts the air at –20oC producing work in the process. What do the first and the second laws say about that?
A windmill produces power on a shaft taking kinetic energy out of the wind. Is it a heat engine? Is it a perpetual machine? Explain.
Ice cubes in a glass of liquid water will eventually melt and all the water approach room temperature. Is this a reversible process? Why?
A room is heated with a 1500 W electric heater. How much power can be saved if a heat pump with a COP of 2.0 is used instead?
If the efficiency of a power plant goes up as the low temperature drops why do they not just reject energy at say –40oC?
If the efficiency of a power plant goes up as the low temperature drops why not let the heat rejection go to a refrigerator at say –10oC instead of ambient 20oC?
A coal-fired power plant operates with a high T of 600oC whereas a jet engine has about 1400 K. Does that mean we should replace all power plants with jet engines?
A heat transfer requires a temperature difference, see chapter 4, to push the Q. What implications do that have for a real heat engine? A refrigerator?
A large stationary diesel engine produces 15 MW with a thermal efficiency of 40%. The exhaust gas, which we assume is air, flows out at 800 K and the intake is 290 K. How large a mass flow rate is that if that accounts for half the Q.L? Can the exhaust flow energy be used?
Hot combustion gases (air) at 1500 K is, used as heat source in a heat engine where the gas is cooled to 750 K and the ambient is at 300 K. This is not a constant T source. How does that affect the efficiency?
A remote location without electricity operates a refrigerator with a bottle of propane feeding a burner to create hot gases. Sketch the setup in terms of cyclic devices and give a relation for the ratio of Q.L in the refrigerator to Q.fuel in the burner in terms of the various reservoir
Calculate the thermal efficiency of the steam power plant cycle described in Example 6.9.
Calculate the coefficient of performance of the R-134a refrigerator given in Example 6.10.
Calculate the thermal efficiency of the steam power plant cycle described in Problem 6.99.
Calculate the coefficient of performance of the R-12 heat pump cycle described in Problem 6.106.
A farmer runs a heat pump with a 2 kW motor. It should keep a chicken hatchery at 30oC, which loses energy at a rate of 10 kW to the colder ambient Tamb. What is the minimum coefficient of performance that will be acceptable for the heat pump?
A power plant generates 150 MW of electrical power. It uses a supply of 1000 MW from a geothermal source and rejects energy to the atmosphere. Find the power to the air and how much air should be flowed to the cooling tower (kg/s) if its temperature cannot be increased more than 10oC
A car engine delivers 25 hp to the driveshaft with a thermal efficiency of 30%. The fuel has a heating value of 40 000 kJ/kg. Find the rate of fuel consumption and the combined power rejected through the radiator and exhaust.
For each of the cases below determine if the heat engine satisfies the first law (energy equation) and if it violates the second law. a. Q.H = 6 kW, Q.L = 4 kW, W. = 2 kW b. Q.H = 6 kW, Q.L = 0 kW, W. = 6 kW c. Q.H = 6 kW, Q.L = 2 kW, W. = 5 kW d. Q.H = 6 kW, Q.L = 6 kW, W. = 0 kW
In a steam power plant 1 MW is added in the boiler, 0.58 MW is taken out in the condenser and the pump work is 0.02 MW. Find the plant thermal efficiency. If everything could be reversed find the coefficient of performance as a refrigerator.
Electric solar cells can produce power with 15% efficiency. Compare that to a heat engine driving an electric generator with 80% efficiency. What should the heat engine efficiency be to have the same overall efficiency as the solar cells?
For each of the cases in problem 7.25 determine if a heat pump satisfies the first law (energy equation) and if it violates the second law? a. Q.H = 6 kW, Q.L = 4 kW, W. = 2 kW b. Q.H = 6 kW, Q.L = 0 kW, W. = 6 kW c. Q.H = 6 kW, Q.L = 2 kW, W. = 5 kW d. Q.H = 6 kW, Q.L = 6 kW, W. = 0 kW
An air-conditioner discards 5.1 kW to the ambient with a power input of 1.5 kW. Find the rate of cooling and the coefficient of performance.
Calculate the amount of work input a refrigerator needs to make ice cubes out of a tray of 0.25 kg liquid water at 10oC. Assume the refrigerator has β = 3.5 and a motor-compressor of 750 W. How much time does it take if this is the only cooling load?
A house should be heated by a heat pump, β′ = 2.2, and maintained at 20oC at all times. It is estimated that it looses 0.8 kW per degree the ambient is lower than the inside. Assume an outside temperature of –10oC and find the needed power to drive the heat pump?
Refrigerant-12 at 95°C, x = 0.1 flowing at 2 kg/s is brought to saturated vapor in a constant-pressure heat exchanger. The energy is supplied by a heat pump with a coefficient of performance of β′ = 2.5. Find the required power to drive the heat pump.
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 6.99 an irreversible cycle.
Assume a cyclic machine that exchanges 6 kW with a 250oC reservoir and has a. Q.L = 0 kW, W. = 6 kW b. Q.L = 6 kW, W. = 0 kW and Q.L is exchanged with a 30oC ambient. What can you say about the processes in the two cases a and b if the machine is a heat engine? Repeat the question for the case
Discuss the factors that would make the heat pump described in Problem 6.106 an irreversible cycle.
The water in a shallow pond heats up during the day and cools down during the night. Heat transfer by radiation, conduction and convection with the ambient thus cycles the water temperature. Is such a cyclic process reversible or irreversible?
Consider a heat engine and heat pump connected as shown in figure P.7.38. Assume TH1 = TH2 > Tamb and determine for each of the three cases if the setup satisfy the first law and/or violates the 2nd law. Q.H1 Q.L1 W.1 Q.H2 Q.L2 W.2 A 6 4 2 3 2 1 B 6 4 2 5 4 1 C 3 2 1 4 3 1
Consider the four cases of a heat engine in problem 7.25 and determine if any of those are perpetual machines of the first or second kind.
Calculate the thermal efficiency of a Carnot cycle heat engine operating between reservoirs at 300oC and 45oC. Compare the result to that of Problem 7.18.
At a few places where the air is very cold in the winter, like –30oC it is possible to find a temperature of 13oC down below ground. What efficiency will a heat engine have operating between these two thermal reservoirs? Discuss.
Calculate the coefficient of performance of a Carnot-cycle heat pump operating between reservoirs at 0°C and 45°C. Compare the result with that of Problem 7.21.
Find the power output and the low T heat rejection rate for a Carnot cycle heat engine that receives 6 kW at 250oC and rejects heat at 30oC as in Problem 7.35.
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?
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