Fundamentals Of Thermodynamics 8th Edition Claus Borgnakke, Richard E. Sonntag - Solutions

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Differences in surface water and deep water temperature can be utilized for power generation. It is proposed to construct a cyclic heat engine that will operate near Hawaii, where the ocean temperature is 20°C near the surface and 5°C at some depth. What is the possible thermal efficiency of such
Find the maximum coefficient of performance for the refrigerator in your kitchen, assuming it runs in a Carnot cycle.
An air-conditioner provides 1 kg/s of air at 15°C cooled from outside atmospheric air at 35°C. Estimate the amount of power needed to operate the air-conditioner. Clearly state all assumptions made.
We propose to heat a house in the winter with a heat pump. The house is to be maintained at 20°C at all times. When the ambient temperature outside drops to −10°C, the rate at which heat is lost from the house is estimated to be 25 kW. What is the minimum electrical power required to drive
A sales person selling refrigerators and deep freezers will guarantee a minimum coefficient of performance of 4.5 year round. How would you evaluate that? Are they all the same?
A cyclic machine, shown in Fig P7.50, receives 325 kJ from a 1000 K energy reservoir. It rejects 125 kJ to a 400 K energy reservoir and the cycle produces 200 kJ of work as output. Is this cycle reversible, irreversible, or impossible?
An inventor has developed a refrigeration unit that maintains the cold space at −10°C, while operating in a 25°C room. A coefficient of performance of 8.5 is claimed. How do you evaluate this?
A household freezer operates in a room at 20°C. Heat must be transferred from the cold space at a rate of 2 kW to maintain its temperature at −30°C. What is the theoretically smallest (power) motor required to operate this freezer?
In a cryogenic experiment you need to keep a container at −125°C although it gains 100 W due to heat transfer. What is the smallest motor you would need for a heat pump absorbing heat from the container and rejecting heat to the room at 20°C?
A temperature of about 0.01 K can be achieved by magnetic cooling. In this process a strong magnetic field is imposed on a paramagnetic salt, maintained at 1 K by transfer of energy to liquid helium boiling at low pressure. The salt is then thermally isolated from the helium, the magnetic field is
The lowest temperature that has been achieved is about 1 × 10−6 K. To achieve this an additional stage of cooling is required beyond that described in the previous problem, namely nuclear cooling. This process is similar to magnetic cooling, but it involves the magnetic moment associated
A certain solar-energy collector produces a maximum temperature of 100°C. The energy is used in a cyclic heat engine that operates in a 10°C environment. What is the maximum thermal efficiency? What is it, if the collector is redesigned to focus the incoming light to produce a maximum temperature
Helium has the lowest normal boiling point of any of the elements at 4.2 K. At this temperature the enthalpy of evaporation is 83.3 kJ/kmol. A Carnot refrigeration cycle is analyzed for the production of 1 kmol of liquid helium at 4.2 K from saturated vapor at the same temperature. What is the work
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 works in a Carnot cycle between –8oC and 35oC with a motor-compressor of 750 W. How much time does it take if this is the only cooling load?
A steel bottle V = 0.1 m3 contains R-134a at 20°C, 200 kPa. It is placed in a deep freezer where it is cooled to -20°C. The deep freezer sits in a room with ambient temperature of 20°C and has an inside temperature of -20°C. Find the amount of energy the freezer must remove from the R-134a and
Liquid sodium leaves a nuclear reactor at 800°C and is used as the energy souce in a steam power plant. The condenser cooling water comes from a cooling tower at 15°C. Determine the maximum thermal efficiency of the power plant. Is it misleading to use the temperatures given to calculate this
A thermal storage is made with a rock (granite) bed of 2 m3 which is heated to 400 K using solar energy. A heat engine receives a QH from the bed and rejects heat to the ambient at 290 K. The rock bed therefore cools down and as it reaches 290 K the process stops. Find the energy the rock bed can
A heat engine has a solar collector receiving 0.2 kW per square meter inside which a transfer media is heated to 450 K. The collected energy powers a heat engine which rejects heat at 40oC. If the heat engine should deliver 2.5 kW what is the minimum size (area) solar collector?
Sixty kilograms per hour of water runs through a heat exchanger, entering as saturated liquid at 200 kPa and leaving as saturated vapor. The heat is supplied by a Carnot heat pump operating from a low-temperature reservoir at 16°C. Find the rate of work into the heat pump.
A heat pump is driven by the work output of a heat engine as shown in figure P7.64. If we assume ideal devices find the ratio of the total power Q.L1 + Q.H2 that heats the house to the power from the hot energy source Q.H1 in terms of the temperatures.
It is proposed to build a 1000-MW electric power plant with steam as the working fluid. The condensers are to be cooled with river water (see Fig. P7.65). The maximum steam temperature is 550°C, and the pressure in the condensers will be 10 kPa. Estimate the temperature rise of the river
Two different fuels can be used in a heat engine operating between the fuel burning temperature and a low temperature of 350 K. Fuel A burns at 2200 K delivering 30 000 kJ/kg and costs $1.50/kg. Fuel B burns at 1200 K, delivering 40 000 kJ/kg and costs $1.30/kg. Which fuel will you buy and why?
A refrigerator keeping 5oC inside is located in a 30oC room. It must have a high temperature ΔT above room temperature and a low temperature ΔT below the refrigerated space in the cycle to actually transfer the heat. For a ΔT of 0, 5 and 10oC respectively calculate the COP assuming a
A refrigerator uses a power input of 2.5 kW to cool a 5°C space with the high temperature in the cycle as 50°C. The QH is pushed to the ambient air at 35°C in a heat exchanger where the transfer coefficient is 50 W/m2K. Find the required minimum heat transfer area.
A house is heated by a heat pump driven by an electric motor using the outside as the low-temperature reservoir. The house loses energy directly proportional to the temperature difference as Q.loss = K (TH - TL). Determine the minimum electric power to drive the heat pump as a function of the two
A farmer runs a heat pump with a motor of 2 kW. It should keep a chicken hatchery at 30oC which loses energy at a rate of 0.5 kW per degree difference to the colder ambient. The heat pump has a coefficient of performance that is 50% of a Carnot heat pump. What is the minimum ambient temperature for
Consider a Carnot cycle heat engine operating in outer space. Heat can be rejected from this engine only by thermal radiation, which is proportional to the radiator area and the fourth power of absolute temperature, Qrad ~ KAT4. Show that for a given engine work output and given TH, the radiator
A house is heated by an electric heat pump using the outside as the low-temperature reservoir. For several different winter outdoor temperatures, estimate the percent savings in electricity if the house is kept at 20°C instead of 24°C. Assume that the house is losing energy to the outside as in
A house is cooled by an electric heat pump using the outside as the high-temperature reservoir. For several different summer outdoor temperatures, estimate the percent savings in electricity if the house is kept at 25°C instead of 20°C. Assume that the house is gaining energy from the outside
A heat pump has a coefficient of performance that is 50% of the theoretical maximum. It maintains a house at 20°C, which leaks energy of 0.6 kW per degree temperature difference to the ambient. For a maximum of 1.0 kW power input find the minimum outside temperature for which the heat pump is a
An air conditioner cools a house at TL = 20°C with a maximum of 1.2 kW power input. The house gains 0.6 kW per degree temperature difference to the ambient and the refrigeration COP is β = 0.6 βCarnot. Find the maximum outside temperature, TH, for which the air conditioner provides
A Carnot heat engine, shown in Fig P7.76, receives energy from a reservoir at Tres through a heat exchanger where the heat transferred is proportional to the temperature difference as Q.H = K (Tres - TH). It rejects heat at a given low temperature TL. To design the heat engine for maximum work
Hydrogen gas is used in a Carnot cycle having an efficiency of 60% with a low temperature of 300 K. During the heat rejection the pressure changes from 90 kPa to 120 kPa. Find the high and low temperature heat transfer and the net cycle work per unit mass of hydrogen.
An ideal gas Carnot cycle with air in a piston cylinder has a high temperature of 1200 K and a heat rejection at 400 K. During the heat addition the volume triples. Find the two specific heat transfers (q) in the cycle and the overall cycle efficiency.
Air in a piston/cylinder goes through a Carnot cycle with the P-v diagram shown in Fig. 7.24. The high and low temperatures are 600 K and 300 K respectively. The heat added at the high temperature is 250 kJ/kg and the lowest pressure in the cycle is 75 kPa. Find the specific volume and pressure
A car engine operates with a thermal efficiency of 35%. Assume the air-conditioner has a coefficient of performance of β = 3 working as a refrigerator cooling the inside using engine shaft work to drive it. How much fuel energy should be spend extra to remove 1 kJ from the inside?
An air-conditioner with a power input of 1.2 kW is working as a refrigerator (β = 3) or as a heat pump (β′ = 4). It maintains an office at 20°C year round which exchanges 0.5 kW per degree temperature difference with the atmosphere. Find the maximum and minimum outside temperature
A rigid insulated container has two rooms separated by a membrane. Room A contains 1 kg air at 200oC and room B has 1.5 kg air at 20oC, both rooms at 100 kPa. Consider two different cases 1) Heat transfer between A and B creates a final uniform T. 2) The membrane breaks and the air comes to a
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 150°C. What is the maximum possible thermal efficiency of a cyclic heat engine using this source of energy with the ambient at
We wish to produce refrigeration at −30°C. A reservoir, shown in Fig P7.84, is available at 200°C and the ambient temperature is 30°C. Thus, work can be done by a cyclic heat engine operating between the 200°C reservoir and the ambient. This work is used to drive the refrigerator.
4L jug of milk at 25°C is placed in your refrigerator where it is cooled down to 5°C. The high temperature in the Carnot refrigeration cycle is 45°C and the properties of milk are the same as for liquid water. Find the amount of energy that must be removed from the milk and the additional work
A combination of a heat engine driving a heat pump (see Fig P7.86) takes waste energy at 50°C as a source Qw1 to the heat engine rejecting heat at 30°C. The remainder Qw2 goes into the heat pump that delivers a QH at 150°C. If the total waste energy is 5 MW find the rate of energy delivered at
Air in a rigid 1 m3 box is at 300 K, 200 kPa. It is heated to 600 K by heat transfer from a reversible heat pump that receives energy from the ambient at 300 K besides the work input. Use constant specific heat at 300 K. Since the coefficient of performance changes write dQ = mair Cv dT and find
Consider the rock bed thermal storage in Problem 7.61. Use the specific heat so you can write dQH in terms of dTrock and find the expression for dW out of the heat engine. Integrate this expression over temperature and find the total heat engine work output.
A heat pump heats a house in the winter and then reverses to cool it in the summer. The interior temperature should be 20°C in the winter and 25°C in the summer. Heat transfer through the walls and ceilings is estimated to be 2400 kJ per hour per degree temperature difference between the inside
A furnace, shown in Fig P7.90, can deliver heat, QH1 at TH1 and it is proposed to use this to drive a heat engine with a rejection at Tatm instead of direct room heating. The heat engine drives a heat pump that delivers QH2 at Troom using the atmosphere as the cold reservoir. Find the ratio QH2/QH1
A 10-m3 tank of air at 500 kPa, 600 K acts as the high-temperature reservoir for a Carnot heat engine that rejects heat at 300 K. A temperature difference of 25°C between the air tank and the Carnot cycle high temperature is needed to transfer the heat. The heat engine runs until the air
A gasoline engine produces 20 hp using 35 Btu/s 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 Btu from the cold space using 1 Btu work input. How much energy goes into the kitchen and what is its coefficient of performance?
A window air-conditioner unit is placed on a laboratory bench and tested in cooling mode using 0.75 Btu/s of electric power with a COP of 1.75. What is the cooling power capacity and what is the net effect on the laboratory?
A car engine takes atmospheric air in at 70 F, no fuel, and exhausts the air at 0 F producing work in the process. What do the first and the second laws say about that?
A large stationary diesel engine produces 20 000 hp with a thermal efficiency of 40%. The exhaust gas, which we assume is air, flows out at 1400 R and the intake is 520 R. How large a mass flow rate is that if that accounts for half the Q.L? Can the exhaust flow energy be used?
Calculate the thermal efficiency of the steam power plant cycle described in Problem 6.167.
A farmer runs a heat pump with a 2 kW motor. It should keep a chicken hatchery at 90 F, which loses energy at a rate of 10 Btu/s to the colder ambient Tamb. What is the minimum coefficient of performance that will be acceptable for the heat pump?
Calculate the amount of work input a refrigerator needs to make ice cubes out of a tray of 0.5 lbm liquid water at 50 F. 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?
In a steam power plant 1000 Btu/s is added at 1200 F in the boiler, 580 Btu/s is taken out at 100 F in the condenser and the pump work is 20 Btu/s. Find the plant thermal efficiency. Assume the same pump work and heat transfer to the boiler as given, how much turbine power could be produced if the
Calculate the thermal efficiency of a Carnot-cycle heat engine operating between reservoirs at 920 F and 110 F. Compare the result with that of Problem 7.97.
A car engine burns 10 lbm of fuel (equivalent to addition of QH) at 2600 R and rejects energy to the radiator and the exhaust at an average temperature of 1300 R. If the fuel provides 17 200 Btu/lbm what is the maximum amount of work the engine can provide?
An air-conditioner provides 1 lbm/s of air at 60 F cooled from outside atmospheric air at 95 F. Estimate the amount of power needed to operate the air-conditioner. Clearly state all assumptions made.
We propose to heat a house in the winter with a heat pump. The house is to be maintained at 68 F at all times. When the ambient temperature outside drops to 15 F, the rate at which heat is lost from the house is estimated to be 80000 Btu/h. What is the minimum electrical power required to drive the
An inventor has developed a refrigeration unit that maintains the cold space at 14 F, while operating in a 77 F room. A coefficient of performance of 8.5 is claimed. How do you evaluate this?
Liquid sodium leaves a nuclear reactor at 1500 F and is used as the energy source in a steam power plant. The condenser cooling water comes from a cooling tower at 60 F. Determine the maximum thermal efficiency of the power plant. Is it misleading to use the temperatures given to calculate this
A house is heated by an electric heat pump using the outside as the low-temperature reservoir. For several different winter outdoor temperatures, estimate the percent savings in electricity if the house is kept at 68 F instead of 75 F. Assume that the house is losing energy to the outside directly
Refrigerant-22 at 180 F, x = 0.1 flowing at 4 lbm/s is brought to saturated vapor in a constant-pressure heat exchanger. The energy is supplied by a heat pump with a low temperature of 50 F. Find the required power input to the heat pump.
A heat engine has a solar collector receiving 600 Btu/h per square foot inside which a transfer media is heated to 800 R. The collected energy powers a heat engine which rejects heat at 100 F. If the heat engine should deliver 8500 Btu/h what is the minimum size (area) solar collector?
Six-hundred pound-mass per hour of water runs through a heat exchanger, entering as saturated liquid at 250 F and leaving as saturated vapor, the heat is supplied by a Carnot heat pump operating from a low-temperature reservoir at 60 F. Find the rate of work into the heat pump.
A car engine operates with a thermal efficiency of 35%. Assume the air-conditioner has a coefficient of performance that is one third of the theoretical maximum and it is mechanically pulled by the engine. How much fuel energy should you spend extra to remove 1 Btu at 60 F when the ambient is at 95
A heat pump cools a house at 70 F with a maximum of 4000 Btu/h power input. The house gains 2000 Btu/h per degree temperature difference to the ambient and the heat pump coefficient of performance is 60% of the theoretical maximum. Find the maximum outside temperature for which the heat pump
A house is cooled by an electric heat pump using the outside as the high-temperature reservoir. For several different summer outdoor temperatures estimate the percent savings in electricity if the house is kept at 77 F instead of 68 F. Assume that the house is gaining energy from the outside
A thermal storage is made with a rock (granite) bed of 70 ft3 which is heated to 720 R using solar energy. A heat engine receives a QH from the bed and rejects heat to the ambient at 520 R. The rock bed therefore cools down and as it reaches 520 R the process stops. Find the energy the rock bed can
We wish to produce refrigeration at −20 F. A reservoir is available at 400 F and the ambient temperature is 80 F, as shown in Fig. P7.84. Thus, work can be done by a cyclic heat engine operating between the 400 F reservoir and the ambient. This work is used to drive the refrigerator.
Air in a rigid 40 ft3 box is at 540 R, 30 lbf/in.2. It is heated to 1100 R by heat transfer from a reversible heat pump that receives energy from the ambient at 540 R besides the work input. Use constant specific heat at 540 R. Since the coefficient of performance changes write dQ = mair Cv dT and
A 350-ft3 tank of air at 80 lbf/in.2, 1080 R acts as the high-temperature reservoir for a Carnot heat engine that rejects heat at 540 R. A temperature difference of 45 F between the air tank and the Carnot cycle high temperature is needed to transfer the heat. The heat engine runs until the air
Air in a piston/cylinder goes through a Carnot cycle with the P-v diagram shown in Fig. 7.24. The high and low temperatures are 1200 R and 600 R respectively. The heat added at the high temperature is 100 Btu/lbm and the lowest pressure in the cycle is 10 lbf/in.2 Find the specific volume and
Does Clausius say anything about the sign for ф dQ?
When a substance has completed a cycle v, u, h and s are unchanged. Did anything happen? Explain.
Assume a heat engine with a given QH. Can you say anything about QL if the engine is reversible? If it is irreversible?
How can you change s of a substance going through a reversible process?
Does the statement of Clausius require a constant T for the heat transfer as in a Carnot cycle?
A reversible process adds heat to a substance. If T is varying does that influence the change in s?
Water at 100 kPa, 150oC receives 75 kJ/kg in a reversible process by heat transfer? Which process changes s the most: constant T, constant v or constant P?
A substance has heat transfer out. Can you say anything about changes in s if the process is reversible? If it is irreversible?
A substance is compressed adiabatically so P and T go up. Does that change s?
Saturated water vapor at 200 kPa is compressed to 600 kPa in a reversible adiabatic process. Find the new v and T.
A computer chip dissipates 2 kJ of electric work over time and rejects that as heat transfer from its 50oC surface to 25oC air. How much entropy is generated in the chip? How much if any is generated outside the chip?
A car uses an average power of 25 hp for a one hour round trip. With a thermal efficiency of 35% how much fuel energy was used? What happened to all the energy? What change in entropy took place if we assume ambient at 20oC?
A liquid is compressed in a reversible adiabatic process. What is the change in T?
Two 5 kg blocks of steel, one at 250oC the other at 25oC, come in thermal contact. Find the final temperature and the total entropy generation in the process?
One kg of air at 300 K is mixed with one kg air at 400 K in a process at a constant 100 kPa and Q = 0. Find the final T and the entropy generation in the process.
One kg of air at 100 kPa is mixed with one kg air at 200 kPa, both at 300 K, in a rigid insulated tank. Find the final state (P, T) and the entropy generation in the process.
An ideal gas goes through a constant T reversible heat addition process. How do the properties (v, u, h, s, P) change (up, down or constant)?
Carbon dioxide is compressed to a smaller volume in a polytropic process with n = 1.2. How do the properties (u, h, s, P, T) change (up, down or constant)?
Hot combustion air at 1500 K expands in a polytropic process to a volume 6 times as large with n = 1.5. Find the specific boundary work and the specific heat transfer.
A window receives 200 W of heat transfer at the inside surface of 20oC and transmits the 200 W from its outside surface at 2oC continuing to ambient air at –5oC. Find the flux of entropy at all three surfaces and the window’s rate of entropy generation.
Consider the steam power plant in Example 6.9 and assume an average T in the line between 1 and 2. Show that this cycle satisfies the inequality of Clausius.
Assume the heat engine in Problem 7.25 has a high temperature of 1200 K and a low temperature of 400 K. What does the inequality of Clausius say about each of the four cases?
Let the steam power plant in Problem 7.26 have 700oC in the boiler and 40oC during the heat rejection in the condenser. Does that satisfy the inequality of Clausius? Repeat the question for the cycle operated in reverse as a refrigerator.
A heat engine receives 6 kW from a 250oC source and rejects heat at 30oC. Examine each of three cases with respect to the inequality of Clausius. a. W. = 6 kW b. W. = 0 kW c. Carnot cycle
Examine the heat engine given in Problem 7.50 to see if it satisfies the inequality of Clausius.
Find the entropy for the following water states and indicate each state on a T-s diagram relative to the two-phase region. a. 250oC, v = 0.02 m3/kg b. 250oC, 2000 kPa c. –2oC, 100 kPa d. 20oC, 100 kPa e. 20oC, 10 000 kPa

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Fundamentals Of Thermodynamics 8th Edition Claus Borgnakke, Richard E. Sonntag - Solutions

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