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mechanical engineering
Fundamentals of Thermodynamics 6th edition Richard E. Sonntag, Claus Borgnakke, Gordon J. Van Wylen - Solutions
An air-conditioner provides 1 kg/s of air at 15C cooled from outside atmospheric air at 35C. Estimate the amount of power needed to operate the air-conditioner. Clearly state all assumptions made.
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? Discuss.
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 kJ at 15C when the ambient is
We propose to heat a house in the winter with a heat pump. The house is to be maintained at 20C at all times. When the ambient temperature outside drops to 10C, the rate at which heat is lost from the house is estimated to be 25 kW. What is the minimum electrical power
Electric solar cells can produce power with 15% efficiency. Assume a heat engine with a low temperature heat rejection at 30C driving an electric generator with 80% efficiency. What should the effective high temperature in the heat engine be to have the same overall efficiency as the solar
A cyclic machine 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?
A household freezer operates in a room at 20C. Heat must be transferred from the cold space at a rate of 2 kW to maintain its temperature at 30C. What is the theoretically smallest (power) motor required to operate this freezer?
A heat pump has a coefficient of performance that is 50% of the theoretical maximum. It maintains a house at 20C, 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
A heat pump cools a house at 20C with a maximum of 1.2 kW power input. The house gains 0.6 kW 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
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 20C near the surface and 5C at some depth. What is the possible thermal
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
An inventor has developed a refrigeration unit that maintains the cold space at 10C, while operating in a 25C room. A coefficient of performance of 8.5 is claimed. How do you evaluate this?
A steel bottle V = 0.1 m3 contains R-134a at 20C, 200 kPa. It is placed in a deep freezer where it is cooled to -20C. The deep freezer sits in a room with ambient temperature of 20C and has an inside temperature of -20C. Find the amount of energy the freezer must
A certain solar-energy collector produces a maximum temperature of 100C. The energy is used in a cyclic heat engine that operates in a 10C environment. What is the maximum thermal efficiency? What is it, if the collector is redesigned to focus the incoming light to produce a maximum
Liquid sodium leaves a nuclear reactor at 800C and is used as the energy souce in a steam power plant. The condenser cooling water comes from a cooling tower at 15C. Determine the maximum thermal efficiency of the power plant. Is it misleading to use the temperatures given to
A 4L jug of milk at 25C is placed in your refrigerator where it is cooled down to 5C. The high temperature in the Carnot refrigeration cycle is 45C 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
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 Qloss = K (TH - TL). Determine the minimum electric power to drive the heat pump as a function of the two
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 20C instead of 24C. Assume that the house is losing energy to the
An air-conditioner with a power input of 1.2 kW is working as a refrigerator (= 3) or as a heat pump (’ = 4). It maintains an office at 20C year round which exchanges 0.5 kW per degree temperature difference with the atmosphere. Find the maximum and minimum outside
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 25C instead of 20C. Assume that the house is gaining energy from the
Helium has the lowest normal boiling point of any of the elements at 4.2 K. At this temperature the enthalpy of evaporation is 83.3kJ/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
We wish to produce refrigeration at 30C. A reservoir is available at 200C and the ambient temperature is 30C. Thus, work can be done by a cyclic heat engine operating between the 200C reservoir and the ambient. This work is used to drive the refrigerator.
A combination of a heat engine driving a heat pump (similar to Fig P7.33) takes waste energy at 50C as a source Qw1 to the heat engine rejecting heat at 30C. The remainder Qw2 goes into the heat pump that delivers a QH at 150C. If the total waste energy is 5 MW find the rate
A temperature of about 0.01 K can be achieved by magnetic cooling, (magnetic work was discussed in Problems 4.41 and 4.42). 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
The lowest temperature that has been achieved is about 1 106 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
A heat pump heats a house in the winter and then reverses to cool it in the summer. The interior temperature should be 20C in the winter and 25C in the summer. Heat transfer through the walls and ceilings is estimated to be 2400 kJ per hour per degree temperature difference between
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. The maximum steam temperature is 550C, and the pressure in the condensers will be 10 kPa. Estimate the temperature rise of the river downstream from the
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 2500 K delivering 52000 kJ/kg and costs $1.75 per kilogram. Fuel B burns at 1700 K, delivering 40000 kJ/kg and costs $1.50 per kilogram. Which fuel would
A refrigerator uses a power input of 2.5 kW to cool a 5C space with the high temperature in the cycle as 50C. The QH is pushed to the ambient air at 35C in a heat exchanger where the transfer coefficient is 50 W/m2K. Find the required minimum heat transfer area.
Refrigerant-12 at 95C, 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 low temperature of 10C. Find the required power input to the heat pump.
A furnace shown in Fig P7.42, 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 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 40 C. If the heat engine should deliver 2.5 kW what is the minimum size (area) solar collector?
In a cryogenic experiment you need to keep a container at 125C 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 20C?
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 16C. Find the rate of work into the heat pump.
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 7.22. 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 Carnot heat engine receives energy from a reservoir at Tres through a heat exchanger where the heat transferred is proportional to the temperature difference as QH = K (Tres - TH). It rejects heat at a given low temperature TL. To design the heat engine for maximum work output show that the high
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 25C between the air tank and the Carnot cycle high temperature is needed to transfer the heat. The heat engine runs until the air
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
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 250kJ/kg and the lowest pressure in the cycle is 75 kPa. Find the specific volume and pressure at
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 hydrogen.
Calculate the thermal efficiency of the steam power plant cycle described in Problem 6.91.
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 7.54.
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?
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
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.
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
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
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 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
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
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
We wish to produce refrigeration at 20 F. A reservoir is available at 400 F and the ambient temperature is 80 F. 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. Determine the ratio of the heat
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 30 lbf/in 2 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.
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
Consider the steam power plant in Problem 7.9 and the heat engine in Problem 7.17. Show that these cycles satisfy the inequality of Clausius.
Find the missing properties and give the phase of the substance a. H2O s 7.70 kJ/kg K, P 25 kPa h ? T ? x ? b. H2O u 3400 kJ/kg, P 10 MPa T ? x ? s
Consider a Carnot-cycle heat engine with water as the working fluid. The heat transfer to the water occurs at 300C, during which process the water changes from saturated liquid to saturated vapor. The heat is rejected from the water at 40C. Show the cycle on a T–s diagram and
In a Carnot engine with water as the working fluid, the high temperature is 250C and as QH is received, the water changes from saturated liquid to saturated vapor. The water pressure at the low temperature is 100 kPa. Find TL, the cycle thermal efficiency, the heat added per kilogram, and
Water is used as the working fluid in a Carnot cycle heat engine, where it changes from saturated liquid to saturated vapor at 200C as heat is added. Heat is rejected in a constant pressure process (also constant T) at 20 kPa. The heat engine powers a Carnot cycle refrigerator that operates
Consider a Carnot-cycle heat pump with R-22 as the working fluid. Heat is rejected from the R-22 at 40C, during which process the R-22 changes from saturated vapor to saturated liquid. The heat is transferred to the R-22 at 0C. a. Show the cycle on a T–s diagram. b. Find the
Do Problem 8.6 using refrigerant R-134a instead of R-22.
Water at 200 kPa, x = 1.0 is compressed in a piston/cylinder to 1 MPa, 250C in a reversible process. Find the sign for the work and the sign for the heat transfer.
One kilogram of ammonia in a piston/cylinder at 50C, 1000 kPa is expanded in a reversible isothermal process to 100 kPa. Find the work and heat transfer for this process.
One kilogram of ammonia in a piston/cylinder at 50C, 1000 kPa is expanded in a reversible isobaric process to 140C. Find the work and heat transfer for this process.
One kilogram of ammonia in a piston/cylinder at 50C, 1000 kPa is expanded in a reversible adiabatic process to 100 kPa. Find the work and heat transfer for this process.
A cylinder fitted with a piston contains ammonia at 50C, 20% quality with a volume of 1 L. The ammonia expands slowly, and during this process heat is transferred to maintain a constant temperature. The process continues until all the liquid is gone. Determine the work and heat transfer for
An insulated cylinder fitted with a piston contains 0.1 kg of water at 100C, 90% quality. The piston is moved, compressing the water until it reaches a pressure of 1.2 MPa. How much work is required in the process?
A cylinder fitted with a frictionless piston contains water. A constant hydraulic pressure on the back face of the piston maintains a cylinder pressure of 10 MPa. Initially, the water is at 700C, and the volume is 100 L. The water is now cooled and condensed to saturated liquid. The heat
One kilogram of water at 300C expands against a piston in a cylinder until it reaches ambient pressure, 100 kPa, at which point the water has a quality of 90%. It may be assumed that the expansion is reversible and adiabatic. What was the initial pressure in the cylinder and how much work
A piston/cylinder has 2 kg ammonia at 50C, 100 kPa which is compressed to 1000 kPa. The process happens so slowly that the temperature is constant. Find the heat transfer and work for the process assuming it to be reversible.
A heavily insulated cylinder/piston contains ammonia at 1200 kPa, 60C. The piston is moved, expanding the ammonia in a reversible process until the temperature is 20C. During the process 600 kJ of work is given out by the ammonia. What was the initial volume of the cylinder?
A closed tank, V 10L, containing 5 kg of water initially at 25C, is heated to 175C by a heat pump that is receiving heat from the surroundings at 25C. Assume that this process is reversible. Find the heat transfer to the water and the work input to the heat
A rigid, insulated vessel contains superheated vapor steam at 3 MPa, 400C. A valve on the vessel is opened, allowing steam to escape. The overall process is irreversible, but the steam remaining inside the vessel goes through a reversible adiabatic expansion. Determine the fraction of steam
A cylinder containing R-134a at 10C, 150 kPa has an initial volume of 20 L. A piston compresses the R-134a in a reversible, isothermal process until it reaches the saturated vapor state. Calculate the required work and heat transfer to accomplish this process.
An insulated cylinder fitted with a piston contains 0.1 kg of superheated vapor steam. The steam expands to ambient pressure, 100 kPa, at which point the steam inside the cylinder is at 150C. The steam does 50 kJ of work against the piston during the expansion. Verify that the initial
A heavily-insulated cylinder fitted with a frictionless piston contains ammonia at 6C, 90% quality, at which point the volume is 200 L. The external force on the piston is now increased slowly, compressing the ammonia until its temperature reaches 50C. How much work is done on the
A piston/cylinder with constant loading of piston contains 1L water at 400 kPa, quality 15%. It has some stops mounted so the maximum possible volume is 11L. A reversible heat pump extracting heat from the ambient at 300 K, 100 kPa heats the water to 300C. Find the total work and heat
A piston/cylinder contains 2 kg water at 200C, 10 MPa. The piston is slowly moved to expand the water in an isothermal process to a pressure of 200 kPa. Any heat transfer takes place with an ambient at 200C and the whole process may be assumed reversible. Sketch the process in a P-V
An insulated cylinder/piston has an initial volume of 0.15 m3 and contains steam at 400 kPa, 200C. The steam is expanded adiabatically, and the work output is measured very carefully to be 30 kJ. It is claimed that the final state of the water is in the two-phase (liquid and vapor) region.
An amount of energy, say 1000 kJ, comes from a furnace at 800C going into water vapor at 400C, from which it goes to a solid metal at 200C and then into some air at 70C. For each location calculate the flux of s through a surface as (Q/T). What makes the flux larger
An insulated cylinder/piston contains R-134a at 1 MPa, 50C, with a volume of 100 L. The R-134a expands, moving the piston until the pressure in the cylinder has dropped to 100 kPa. It is claimed that the R-134a does 190 kJ of work against the piston during the process. Is that possible?
A piece of hot metal should be cooled rapidly (quenched) to 25C, which requires removal of 1000 kJ from the metal. The cold space that absorbs the energy could be one of three possibilities: (1) Submerge the metal into a bath of liquid water and ice, thus melting the ice. (2) Let saturated
A mass and atmosphere loaded piston/cylinder contains 2 kg of water at 5 MPa, 100C. Heat is added from a reservoir at 700C to the water until it reaches 700C. Find the work, heat transfer, and total entropy production for the system and surroundings.
A cylinder fitted with a movable piston contains water at 3 MPa, 50% quality, at which point the volume is 20 L. The water now expands to 1.2 MPa as a result of receiving 600 kJ of heat from a large source at 300C. It is claimed that the water does 124 kJ of work during this process. Is
A 4 L jug of milk at 25C is placed in your refrigerator where it is cooled down to the refrigerators inside constant temperature of 5C. Assume the milk has the property of liquid water and find the entropy generated in the cooling process.
A piston/cylinder contains 1 kg water at 150 kPa, 20C. The piston is loaded so pressure is linear in volume. Heat is added from a 600C source until the water is at 1 MPa, 500C. Find the heat transfer and the total change in entropy.
Water in a piston/cylinder is at 1 MPa, 500C. There are two stops, a lower one at which Vmin 1 m3 and an upper one at Vmax 3 m3. The piston is loaded with a mass and outside atmosphere such that it floats when the pressure is 500 kPa. This setup is now cooled
Two tanks contain steam, and they are both connected to a piston/cylinder. Initially the piston is at the bottom and the mass of the piston is such that a pressure of 1.4 MPa below it will be able to lift it. Steam in A is 4 kg at 7 MPa, 700C and B has 2 kg at 3 MPa, 350C. The two
A cylinder/piston contains 3 kg of water at 500 kPa, 600C. The piston has a cross-sectional area of 0.1 m2 and is restrained by a linear spring with spring constant 10 kN/m. The setup is allowed to cool down to room temperature due to heat transfer to the room at 20C. Calculate the
A cylinder/piston contains water at 200 kPa, 200C with a volume of 20 L. The piston is moved slowly, compressing the water to a pressure of 800 kPa. The loading on the piston is such that the product PV is a constant. Assuming that the room temperature is 20C, show that this process
One kilogram of ammonia (NH3) is contained in a spring-loaded piston/cylinder as saturated liquid at 20C. Heat is added from a reservoir at 100C until a final condition of 800 kPa, 70C is reached. Find the work, heat transfer, and entropy generation, assuming the
A piston/cylinder has a piston loaded so pressure is linear with volume and it contains 2 kg water at 100C, quality 10%. Heat is added from a 700C energy reservoir so a final state of 500C, 1 MPa is reached. Find the specific work and heat transfer for the water and the
An insulated cylinder fitted with a frictionless piston contains saturated vapor R- 12 at ambient temperature, 20C. The initial volume is 10 L. The R-12 is now expanded to a temperature of -30C. The insulation is then removed from the cylinder, allowing it to warm at constant
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