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Fundamentals of Thermodynamics 6th edition Richard E. Sonntag, Claus Borgnakke, Gordon J. Van Wylen - Solutions
A foundry form box with 25 kg of 200C hot sand is dumped into a bucket with 50 L water at 15C. Assuming no heat transfer with the surroundings and no boiling away of liquid water, calculate the net entropy change for the process.
A large slab of concrete, 5 8 0.3 m, is used as a thermal storage mass in a solar-heated house. If the slab cools overnight from 23C to 18C in an 18C house, what is the net entropy change associated with this process?
Find the total work the heat engine can give out as it receives energy from the rock bed as described in Problem 7.22. Hint: write the entropy balance equation for the control volume that is the combination of the rock bed and the heat engine.
Liquid lead initially at 500C is poured into a form so that it holds 2 kg. It then cools at constant pressure down to room temperature of 20C as heat is transferred to the room. The melting point of lead is 327C and the enthalpy change between the phases, hif, is 24.6kJ/kg.
A hollow steel sphere with a 0.5-m inside diameter and a 2-mm thick wall contains water at 2 MPa, 250C. The system (steel plus water) cools to the ambient temperature, 30C, calculate the net entropy change of the system and surroundings for this process.
A mass of 1 kg of air contained in a cylinder at 1.5 MPa, 1000 K, expands in a reversible isothermal process to a volume 10 times larger. Calculate the heat transfer during the process and the change of entropy of the air.
A mass of 1 kg of air contained in a cylinder at 1.5 MPa, 1000 K, expands in a reversible adiabatic process to 100 kPa. Calculate the final temperature and the work done during the process, using a. Constant specific heat, value from Table A.5 b. The ideal gas tables, Table A.7
Consider a Carnot-cycle heat pump having 1 kg of nitrogen gas in a cylinder/piston arrangement. This heat pump operates between reservoirs at 300 K and 400 K. At the beginning of the low-temperature heat addition, the pressure is 1 MPa. During this processes the volume triples. Analyze each of the
A rigid tank contains 2 kg of air at 200 kPa and ambient temperature, 20C. An electric current now passes through a resistor inside the tank. After a total of 100 kJ of electrical work has crossed the boundary, the air temperature inside is 80C. Is this possible?
A handheld pump for a bicycle has a volume of 25 cm3 when fully extended. You now press the plunger (piston) in while holding your thumb over the exit hole, so that an air pressure of 300 kPa is obtained. The outside atmosphere is at P0, T0. Consider two cases: (1) it is done quickly (1 s),
An insulated cylinder/piston contains carbon dioxide gas at 120 kPa, 400 K. The gas is compressed to 2.5 MPa in a reversible adiabatic process. Calculate the final temperature and the work per unit mass, assuminga. Variable specific heat, Table A.8b. Constant specific heat, value from Table A.5c.
Consider a small air pistol with a cylinder volume of 1 cm3 at 250 kPa, 27C. The bullet acts as a piston initially held by a trigger. The bullet is released so the air expands in an adiabatic process. If the pressure should be 100 kPa as the bullet leaves the cylinder find the final volume
A rigid storage tank of 1.5 m3 contains 1 kg argon at 30C. Heat is then transferred to the argon from a furnace operating at 1300C until the specific entropy of the argon has increased by 0.343 kJ/kg K. Find the total heat transfer and the entropy generated in the process.
A piston/cylinder, contains air at 1380 K, 15 MPa, with V1 = 10 cm3, Acyl = 5 cm2. The piston is released, and just before the piston exits the end of the cylinder the pressure inside is 200 kPa. If the cylinder is insulated, what is its length? How much work is done by the air inside?
Two rigid tanks each contain 10 kg N2 gas at 1000 K, 500 kPa. They are now thermally connected to a reversible heat pump, which heats one and cools the other with no heat transfer to the surroundings. When one tank is heated to 1500 K the process stops. Find the final (P, T) in both tanks and the
Repeat the previous problem, but with variable heat capacities.
We wish to obtain a supply of cold helium gas by applying the following technique. Helium contained in a cylinder at ambient conditions, 100 kPa, 20C, is compressed in a reversible isothermal process to 600 kPa, after which the gas is expanded back to 100 kPa in a reversible adiabatic
A 1-m3 insulated, rigid tank contains air at 800 kPa, 25C. A valve on the tank is opened, and the pressure inside quickly drops to 150 kPa, at which point the valve is closed. Assuming that the air remaining inside has undergone a reversible adiabatic expansion, calculate the mass withdrawn
An uninsulated cylinder fitted with a piston contains air at 500 kPa, 200C, at which point the volume is 10 L. The external force on the piston is now varied in such a manner that the air expands to 150 kPa, 25 L volume. It is claimed that in this process the air produces 70% of the work
A rigid container with volume 200 L is divided into two equal volumes by a partition. Both sides contain nitrogen one side is at 2 MPa, 200C, and the other at 200 kPa, 100C. The partition ruptures, and the nitrogen comes to a uniform state at 70C. Assume the temperature of
Nitrogen at 600 kPa, 127C is in a 0.5 m3 insulated tank connected to a pipe with a valve to a second insulated initially empty tank of volume 0.5 m3. The valve is opened and the nitrogen fills both tanks. Find the final pressure and temperature and the entropy generation this process
Neon at 400 kPa, 20C is brought to 100C in a polytropic process with n 1.4. Give the sign for the heat transfer and work terms and explain.
A cylinder/piston contains carbon dioxide at 1 MPa, 300C with a volume of 200 L. The total external force acting on the piston is proportional to V 3. This system is allowed to cool to room temperature, 20C. What is the total entropy generation for the process?
A cylinder/piston contains 1 kg methane gas at 100 kPa, 20C. The gas is compressed reversibly to a pressure of 800 kPa. Calculate the work required if the process is a. Adiabatic b. Isothermal c. Polytropic, with exponent n 1.15
The power stroke in an internal combustion engine can be approximated with a polytropic expansion. Consider air in a cylinder volume of 0.2 L at 7 MPa, 1800 K. It now expands in a reversible polytropic process with exponent, n 1.5, through a volume ratio of 8; 1. Show this process
Helium in a piston/cylinder at 20C, 100 kPa is brought to 400 K in a reversible polytropic process with exponent n = 1.25. You may assume helium is an ideal gas with constant specific heat. Find the final pressure and both the specific heat transfer and specific work.
A cylinder/piston contains air at ambient conditions, 100 kPa and 20C with a volume of 0.3 m3. The air is compressed to 800 kPa in a reversible polytropic process with exponent, n 1.2, after which it is expanded back to 100 kPa in a reversible adiabatic process. a. Show the
An ideal gas having a constant specific heat undergoes a reversible polytropic expansion with exponent, n 1.4. If the gas is carbon dioxide will the heat transfer for this process be positive, negative, or zero?
A cylinder fitted with a piston contains 0.5 kg of R-134a at 60C, with a quality of 50 percent. The R-134a now expands in an internally reversible polytropic process to ambient temperature, 20C at which point the quality is 100 percent. Any heat transfer is with a
A cylinder/piston contains 100 L of air at 110 kPa, 25C. The air is compressed in a reversible polytropic process to a final state of 800 kPa, 200C. Assume the heat transfer is with the ambient at 25C and determines the polytropic exponent n and the final volume of the air.
A mass of 2 kg ethane gas at 500 kPa, 100C, undergoes a reversible polytropic expansion with exponent, n 1.3, to a final temperature of the ambient, 20C, calculate the total entropy generation for the process if the heat is exchanged with the ambient.
A cylinder/piston contains saturated vapor R-22 at 10C; the volume is 10 L. The R-22 is compressed to 2 MPa, 60C in a reversible (internally) polytropic process. If all the heat transfer during the process is with the ambient at 10C, calculate the net entropy change.
A closed, partly insulated cylinder divided by an insulated piston contains air in one side and water on the other, as shown in Fig. P8.59. There is no insulation on the end containing water. Each volume is initially 100 L, with the air at 40C and the water at 90C, quality 10%. Heat
A spring-loaded piston/cylinder contains water at 100 kPa with v 0.07237 m3/kg. The water is now heated to a pressure of 3 MPa by a reversible heat pump extracting Q from a reservoir at 300 K. It is known that the water will pass through saturated vapor at 1.5 MPa and that pressure
A cylinder with a linear spring-loaded piston contains carbon dioxide gas at 2 MPa with a volume of 50 L. The device is of aluminum and has a mass of 4 kg. Everything (Al and gas) is initially at 200C. By heat transfer the whole system cools to the ambient temperature of 25C, at
A cylinder fitted with a piston contains air at 400 K, 1.0 MPa, at which point the volume is 100 L. The air now expands to a final state at 300 K, 200 kPa, and during the process the cylinder receives heat transfer from a heat source at 400 K. The work done by the air is 70% of what the work would
An insulated cylinder with a frictionless piston contains water at ambient pressure, 100 kPa, a quality of 0.8 and the volume is 8 L. A force is now applied, slowly compressing the water until it reaches a set of stops, at which point the cylinder volume is 1 L. The insulation is then removed from
Consider the process. The insulated tank A has a volume of 600 L, and contains steam at 1.4 MPa, 300C. The uninsulated tank B has a volume of 300 L and contains steam at 200 kPa, 200C. A valve connecting the two tanks is opened, and steam flows from A to B until the temperature in A
A vertical cylinder/piston contains R–22 at 20C, 70% quality, and the volume is 50 L. This cylinder is brought into a 20C room, and an electric current of 10 A is passed through a resistor inside the cylinder. The voltage drop across the resistor is 12 V. It is claimed
Redo Problem 8.57, but calculate the mass withdrawn by a first-law, control volume analysis. Compare the result to that obtained in Problem 8.57. Show from a differential step of mass out that the first law leads to the same result. (Find the relation between dP and dT)
A vertical cylinder is fitted with a frictionless piston that is initially resting on stops. The cylinder contains carbon dioxide gas at 200 kPa, 300 K, and at this point the volume is 50 L. A cylinder pressure of 400 kPa is required to make the piston rise from the stops. Heat is now transferred
A piston/cylinder contains 2 kg water at 5 MPa, 800C. The piston is loaded so pressure is proportional to volume, P = CV. It is now cooled by an external reservoir at 0C to a final state of saturated vapor. Find the final pressure, work, heat transfer and the entropy generation for
A gas in a rigid vessel is at ambient temperature and at a pressure, P1, slightly higher than ambient pressure, P0. A valve on the vessel is opened, so gas escapes and the pressure drops quickly to ambient pressure. The valve is closed and after a long time the remaining gas returns to ambient
Consider the steam power plant in Problem 7.57 and show that this cycle satisfies the inequality of Clausius.
Find the missing properties and give the phase of the substance a. H2O s 1.75 Btu/lbm R, P 4 lbf/in 2 h ? T ? x ? b. H2O u 1350 Btu/lbm, P 1500 lbf/in 2 T ? x
In a Carnot engine with water as the working fluid, the high temperature is 450 F and as QL is received, the water changes from saturated liquid to saturated vapor. The water pressure at the low temperature is 14.7 lbf/in 2. Find TL, cycle thermal efficiency, heat added per pound-mass, and entropy,
Consider a Carnot-cycle heat pump with R-22 as the working fluid. Heat is rejected from the R-22 at 100 F, during which process the R-22 changes from saturated vapor to saturated liquid. The heat is transferred to the R-22 at 30 F.a. Show the cycle on a T–s diagram.b. Find the quality of the R-22
Do Problem 8.86 using refrigerant R-134a instead of R-22.
Water at 30 lbf/in 2, x = 1.0 is compressed in a piston/cylinder to 140 lbf/in 2, 600 F in a reversible process. Find the sign for the work and the sign for the heat transfer.
Two pound-mass of ammonia in a piston/cylinder at 120 F, 150 lbf/in 2 is expanded in a reversible adiabatic process to 15 lbf/in 2. Find the work and heat transfer for this process.
A cylinder fitted with a piston contains ammonia at 120 F, 20% quality with a volume of 60 in 3. 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
One pound-mass of water at 600 F expands against a piston in a cylinder until it reaches ambient pressure, 14.7 lbf/in 2, at which point the water has a quality of 90%. It may be assumed that the expansion is reversible and adiabatic.a. What was the initial pressure in the cylinder?b. How much work
A closed tank, V 0.35 ft3, containing 10 lbm of water initially at 77 F is heated to 350 F by a heat pump that is receiving heat from the surroundings at 77 F. Assume that this process is reversible. Find the heat transfer to the water and the work input to the heat pump.
A cylinder containing R-134a at 50 F, 20 lbf/in 2, has an initial volume of 1 ft3. 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.
A rigid, insulated vessel contains superheated vapor steam at 450 lbf/in 2, 700 F. A valve on the vessel is opened, allowing steam to escape. It may be assumed that the steam remaining inside the vessel goes through a reversible adiabatic expansion. Determine the fraction of steam that has escaped,
A cylinder/piston contains 5 lbm of water at 80 lbf/in 2, 1000 F. The piston has cross-sectional area of 1 ft2 and is restrained by a linear spring with spring constant 60 lbf/in. The setup is allowed to cool down to room temperature due to heat transfer to the room at 70 F. Calculate the total
An insulated cylinder/piston contains R-134a at 150 lbf/in 2, 120 F, with a volume of 3.5 ft3. The R-134a expands, moving the piston until the pressure in the cylinder has dropped to 15 lbf/in 2. It is claimed that the R-134a does 180 Btu of work against the piston during the process. Is that
A mass and atmosphere loaded piston/cylinder contains 4 lbm of water at 500 lbf/in 2, 200 F. Heat is added from a reservoir at 1200 F to the water until it reaches 1200 F. Find the work, heat transfer, and total entropy production for the system and surroundings.
A 1 gallon jug of milk at 75 F is placed in your refrigerator where it is cooled down to the refrigerators inside temperature of 40 F. Assume the milk has the properties of liquid water and find the entropy generated in the cooling process.
Water in a piston/cylinder is at 150 lbf/in 2, 900 F. There are two stops, a lower one at which Vmin 35 ft3 and an upper one at Vmax 105 ft3. The piston is loaded with a mass and outside atmosphere such that it floats when the pressure is 75 lbf/in 2. This setup is
A cylinder/piston contains water at 30 lbf/in 2, 400 F with a volume of 1 ft3. The piston is moved slowly, compressing the water to a pressure of 120 lbf/in 2. The loading on the piston is such that the product PV is a constant. Assuming that the room temperature is 70 F, show that this process
One pound mass of ammonia (NH3) is contained in a linear spring-loaded piston/cylinder as saturated liquid at 0 F. Heat is added from a reservoir at 225 F until a final condition of 125 lbf/in 2, 160 F is reached. Find the work, heat transfer, and entropy generation, assuming the process is
A foundry form box with 50 lbm of 400 F hot sand is dumped into a bucket with 2 ft3 water at 60 F. Assuming no heat transfer with the surroundings and no boiling away of liquid water, calculate the net entropy change for the process.
A hollow steel sphere with a 2-ft inside diameter and a 0.1-in. thick wall contains water at 300 lbf/in 2, 500 F. The system (steel plus water) cools to the ambient temperature, 90 F. Calculate the net entropy change of the system and surroundings for this process.
A handheld pump for a bicycle has a volume of 2 in 2 when fully extended. You now press the plunger (piston) in while holding your thumb over the exit hole so an air pressure of 45 lbf/in 2 is obtained. The outside atmosphere is at Po, To.
A piston/cylinder contains air at 2500 R, 2200 lbf/in 2, with V1 1 in 3, Acyl = 1 in 2. The piston is released and just before the piston exits the end of the cylinder the pressure inside is 30 lbf/in 2. If the cylinder is insulated, what is its length? How much work is done by the
A 25-ft3 insulated, rigid tank contains air at 110 lbf/in 2, 75 F. A valve on the tank is opened, and the pressure inside quickly drops to 15 lbf/in 2, at which point the valve is closed. Assuming that the air remaining inside has undergone a reversible adiabatic expansion, calculate the mass
A rigid container with volume 7 ft3 is divided into two equal volumes by a partition. Both sides contain nitrogen one side is at 300 lbf/in2, 400 F, and the other at 30 lbf/in2, 200 F. The partition ruptures, and the nitrogen comes to a uniform state at 160 F. Assume the temperature of the
Nitrogen at 90 lbf/in 2, 260 F is in a 20 ft3 insulated tank connected to a pipe with a valve to a second insulated initially empty tank of volume 20 ft3. The valve is opened and the nitrogen fills both tanks. Find the final pressure and temperature and the entropy generation this process causes.
A cylinder/piston contains carbon dioxide at 150 lbf/in 2, 600 F with a volume of 7 ft3. The total external force acting on the piston is proportional to V3. This system is allowed to cool to room temperature, 70 F. What is the total entropy generation for the process?
Helium in a piston/cylinder at 20C, 100 kPa is brought to 400 K in a reversible polytropic process with exponent n = 1.25. You may assume helium is an ideal gas with constant specific heat. Find the final pressure and both the specific heat transfer and specific work. Discuss.
A cylinder/piston contains air at ambient conditions, 14.7 lbf/in 2 and 70 F with a volume of 10 ft3. The air is compressed to 100 lbf/in 2 in a reversible polytropic process with exponent, n 1.2, after which it is expanded back to 14.7 lbf/in 2 in a reversible adiabatic
A cylinder/piston contains 4 ft3 of air at 16 lbf/in 2, 77 F. The air is compressed in a reversible polytropic process to a final state of 120 lbf/in 2, 400 F. Assume the heat transfer is with the ambient at 77 F and determine the polytropic exponent n and the final volume of the air. Find the work
A cylinder with a linear spring-loaded piston contains carbon dioxide gas at 300 lbf/in 2 with a volume of 2 ft3. The device is of aluminum and has a mass of 8 lbm. Everything (Al and gas) is initially at 400 F. By heat transfer the whole system cools to the ambient temperature of 77 F, at which
Steam enters a turbine at 3 MPa, 450C, expands in a reversible adiabatic process and exhausts at 10 kPa. Changes in kinetic and potential energies between the inlet and the exit of the turbine are small. The power output of the turbine is 800 kW. What is the mass flow rate of steam through
In a heat pump that uses R-134a as the working fluid, the R-134a enters the compressor at 150 kPa, 10C at a rate of 0.1 kg/s. In the compressor the R-134a is compressed in an adiabatic process to 1 MPa. Calculate the power input required to the compressor, assuming the process to be
Consider the design of a nozzle in which nitrogen gas flowing in a pipe at 500 kPa, 200C, and at a velocity of 10 m/s, is to be expanded to produce a velocity of 300 m/s. Determine the exit pressure and cross-sectional area of the nozzle if the mass flow rate is 0.15 kg/s, and the expansion
A compressor is surrounded by cold R-134a so it works as an isothermal compressor. The inlet state is 0C, 100 kPa and the exit state is saturated vapor. Find the specific heat transfer and specific work.
Air at 100 kPa, 17C is compressed to 400 kPa after which it is expanded through a nozzle back to the atmosphere. The compressor and the nozzle are both reversible and adiabatic and kinetic energy in/out of the compressor can be neglected. Find the compressor work and its exit temperature
A small turbine delivers 150 kW and is supplied with steam at 700C, 2 MPa. The exhaust passes through a heat exchanger where the pressure is 10 kPa and exits as saturated liquid. The turbine is reversible and adiabatic. Find the specific turbine work and the heat transfer in the heat
A counter flowing heat exchanger is used to cool air at 540 K, 400 kPa to 360 K by using a 0.05 kg/s supply of water at 20C, 200 kPa. The air flow is 0.5 kg/s in a 10-cm diameter pipe. Find the air inlet velocity, the water exit temperature, and total entropy generation in the process.
Analyse the steam turbine described in Problem 6.29. Is it possible?
A co-flowing heat exchanger has one line with 2 kg/s saturated water vapor at 100 kPa entering. The other line is 1 kg/s air at 200 kPa, 1200 K. The heat exchanger is very long so the two flows exit at the same temperature. Find the exit temperature by trial and error. Calculate the rate of entropy
Atmospheric air at -45C, 60 kPa enters the front diffuser of a jet engine with a velocity of 900 km/h and frontal area of 1 m2. After the adiabatic diffuser the velocity is 20 m/s. Find the diffuser exit temperature and the maximum pressure possible.
A Hilch tube has an air inlet flow at 20C, 200 kPa and two exit flows of 100 kPa, one at 0C and the other at 40C. The tube has no external heat transfer and no work and all the flows are SSSF and have negligible kinetic energy. Find the fraction of the inlet flow that comes
Two flow streams of water, one at 0.6 MPa, saturated vapor, and the other at 0.6 MPa, 600C, mix adiabatically in a SSSF process to produce a single flow out at 0.6 MPa, 400C. Find the total entropy generation for this process.
In a heat-driven refrigerator with ammonia as the working fluid, a turbine with inlet conditions of 2.0 MPa, 70C is used to drive a compressor with inlet saturated vapor at 20C. The exhausts, both at 1.2 MPa, are then mixed together. The ratio of the mass flow rate to the
A diffuser is a steady-state, steady-flow device in which a fluid flowing at high velocity is decelerated such that the pressure increases in the process. Air at 120 kPa, 30C enters a diffuser with velocity 200 m/s and exits with a velocity of 20m/s, assuming the process is reversible and
A reversible SSSF device receives a flow of 1 kg/s air at 400 K, 450 kPa and the air leaves at 600 K, 100 kPa. Heat transfer of 800 kW is added from a 1000 K reservoir, 100 kW rejected at 350 K and some heat transfer takes place at 500 K. Find the heat transferred at 500 K and the rate of work
One technique for operating a steam turbine in part-load power output is to throttle the steam to a lower pressure before it enters the turbine. The steam line conditions are 2 MPa, 400C, and the turbine exhaust pressure is fixed at 10 kPa. Assuming the expansion inside the turbine to be
Carbon dioxide at 300 K, 200 kPa is brought through a SSSF device where it is heated to 500 K by a 600 K reservoir in a constant pressure process. Find the specific work, heat transfer and entropy generation.
One type of feedwater heater for preheating the water before entering a boiler operates on the principle of mixing the water with steam that has been bled from the turbine. For the states calculate the rate of net entropy increase for the process, assuming the process to be steady flow and
Air at 327C, 400 kPa with a volume flow 1 m3/s runs through an adiabatic turbine with exhaust pressure of 100 kPa Neglect kinetic energies and use constant specific heats. Find the lowest and highest possible exit temperature. For each case find also the rate of work and the rate of entropy
A certain industrial process requires a steady supply of saturated vapor steam at 200 kPa, at a rate of 0.5 kg/s. Also required is a steady supply of compressed air at 500 kPa, at a rate of 0.1 kg/s. Both are to be supplied by the process shown in Fig. P9.20. Steam is expanded in a turbine to
Air enters a turbine at 800 kPa, 1200 K, and expands in a reversible adiabatic process to 100 kPa. Calculate the exit temperature and the work output per kilogram of air, usinga. The ideal gas tables, Table A.7b. Constant specific heat, value at 300 K from table A.5c. Constant specific heat, value
Consider a steam turbine power plant operating at supercritical pressure. As a first approximation, it may be assumed that the turbine and the pump processes are reversible and adiabatic. Neglecting any changes in kinetic and potential energies, calculatea. The specific turbine work output and the
A supply of 5 kg/s ammonia at 500 kPa, 20C is needed. Two sources are available one is saturated liquid at 20C and the other is at 500 kPa, 140C. Flows from the two sources are fed through valves to an insulated SSSF mixing chamber, which then produces the desired output
A turbo charger boosts the inlet air pressure to an automobile engine. It consists of an exhaust gas driven turbine directly connected to an air compressor. For a certain engine load the conditions are given in the figure. Assume that both the turbine and the compressor are reversible and adiabatic
A stream of ammonia enters a steady flow device at 100 kPa, 50C, at the rate of 1 kg/s. Two streams exit the device at equal mass flow rates; one is at 200 kPa, 50C, and the other as saturated liquid at 10C. It is claimed that the device operates in a room at 25C on
An initially empty 0.1 m3 canister is filled with R-12 from a line flowing saturated liquid at 5C. This is done quickly such that the process is adiabatic. Find the final mass, liquid and vapor volumes, if any, in the canister. Is the process reversible?
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