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physics
thermodynamics

Fundamentals of Thermodynamics 6th edition Richard E. Sonntag, Claus Borgnakke, Gordon J. Van Wylen - Solutions

Saturated vapor water at 150oC is expanded to a lower pressure with constant temperature. Find the changes in u and s when the final pressure isa. 100 kPab. 50 kPac. 10 kPa
Assume a heat engine with a given QH. Can you say anything about QL if the engine is reversible? If it is irreversible?
Determine the missing property among P, T, s, x for the following states:a. Ammonia 25oC, v = 0.10 m3/kgb. Ammonia 1000 kPa, s = 5.2 kJ/kg Kc. R-134a 5oC, s = 1.7 kJ/kg Kd. R-134a 50oC, s = 1.9 kJ/kg Ke. R-22100 kPa, v = 0.3 m3/kg
Consider a Carnot-cycle heat engine with water as the working fluid. The heat transfer to the water occurs at 300°C, during which process the water changes from saturated liquid to saturated vapor. The heat is rejected from the water at 40°C. Show the cycle on a T–s diagram and find the quality
In a Carnot engine with ammonia as the working fluid, the high temperature is 60°C and as QH is received, the ammonia changes from saturated liquid to saturated vapor. The ammonia pressure at the low temperature is 190 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 200°C 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 40°C, during which process the R-22 changes from saturated vapor to saturated liquid. The heat is transferred to the R-22 at 0°C. a. Show the cycle on a T–s diagram. b. Find the quality of the
Do Problem 8.34 using refrigerant R-134a instead of R-22. Consider a Carnot-cycle heat pump with R-22 as the working fluid. Heat is rejected from the R-22 at 40°C, during which process the R-22 changes from saturated vapor to saturated liquid. The heat is transferred to the R-22 at 0°C. a. Show
Water at 200 kPa, x = 1.0 is compressed in a piston/cylinder to 1 MPa, 250°C in a reversible process. Find the sign for the work and the sign for the heat transfer.
Water at 200 kPa, x = 1.0 is compressed in a piston/cylinder to 1 MPa, 350oC in a reversible process. Find the sign for the work and the sign for the heat transfer.
Ammonia at 1 MPa, 50oC is expanded in a piston/cylinder to 500 kPa, 20oC in a reversible process. Find the sign for both the work and the heat transfer.
One kilogram of ammonia in a piston/cylinder at 50°C, 1000 kPa is expanded in a reversible isothermal process to 100 kPa. Find the work and heat transfer for this process.
How can you change s of a substance going through a reversible process?
One kilogram of ammonia in a piston/cylinder at 50°C, 1000 kPa is expanded in a reversible isobaric process to 140°C. Find the work and heat transfer for this process.
One kilogram of ammonia in a piston/cylinder at 50°C, 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 50°C, 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 this
An insulated cylinder fitted with a piston contains 0.1 kg of water at 100°C, 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?
Compression and heat transfer brings R-134a in a piston/cylinder from 500 kPa, 50oC to saturated vapor in an isothermal process. Find the specific heat transfer and the specific work.
One kilogram of water at 300°C expands against a piston in a cylinder until it reaches ambient pressure, 100 kPa, at which point the water has a quality of 90.2%. It may be assumed that the expansion is reversible and adiabatic. What was the initial pressure in the cylinder and how much work is
Water in a piston/cylinder at 400oC, 2000 kPa is expanded in a reversible adiabatic process. The specific work is measured to be 415.72 kJ/kg out. Find the final P and T and show the P-v and the T-s diagram for the process.
A piston/cylinder has 2 kg ammonia at 50°C, 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 piston cylinder has R-134a at –20oC, 100 kPa which is compressed to 500 kPa in a reversible adiabatic process. Find the final temperature and the specific work.
A closed tank, V = 10 L, containing 5 kg of water initially at 25°C, is heated to 175°C by a heat pump that is receiving heat from the surroundings at 25°C. Assume that this process is reversible. Find the heat transfer to the water and the change in entropy.
Does the statement of Clausius require a constant T for the heat transfer as in a Carnot cycle?
A cylinder containing R-134a at 10°C, 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.
A heavily-insulated cylinder fitted with a frictionless piston, as shown in Fig. P8.51 contains ammonia at 5°C, 92.9% 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 50°C. How much work is
A piston/cylinder has 2 kg water at 1000 kPa, 250°C which is now cooled with a constant loading on the piston. This isobaric process ends when the water has reached a state of saturated liquid. Find the work and heat transfer and sketch the process in both a P-v and a T-s diagram.
Water at 1000 kPa, 250°C is brought to saturated vapor in a piston/cylinder with an isothermal process. Find the specific work and heat transfer. Estimate the specific work from the area in the P-v diagram and compare it to the correct value.
Water at 1000 kPa, 250°C is brought to saturated vapor in a rigid container, shown in Fig. P8.54. Find the final T and the specific heat transfer in this isometric process.
Estimate the specific heat transfer from the area in the T-s diagram and compare it to the correct value for the states and process in Problem 8.54.
Water at 1000 kPa, 250°C is brought to saturated vapor in a piston/cylinder with an isobaric process. Find the specific work and heat transfer. Estimate the specific heat transfer from the area in the T-s diagram and compare it to the correct value.
A heavily insulated cylinder/piston contains ammonia at 1200 kPa, 60°C. The piston is moved, expanding the ammonia in a reversible process until the temperature is −20°C. During the process 600 kJ of work is given out by the ammonia. What was the initial volume of the cylinder?
Water at 1000 kPa, 250°C is brought to saturated vapor in a piston/cylinder with an adiabatic process. Find the final T and the specific work. Estimate the specific work from the area in the P-v diagram and compare it to the correct value.
A rigid, insulated vessel contains superheated vapor steam at 3 MPa, 400°C. 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 that
A reversible process adds heat to a substance. If T is varying does that influence the change in s?
A piston/cylinder contains 2 kg water at 200°C, 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 200°C and the whole process may be assumed reversible. Sketch the process in a P-V diagram and
One kg water at 500oC and 1 kg saturated water vapor both at 200 kPa are mixed in a constant pressure and adiabatic process. Find the final temperature and the entropy generation for the process.
The unrestrained expansion of the reactor water in Problem 5.48 has a final state in the two-phase region. Find the entropy generated in the process. A water-filled reactor with volume of 1 m3 is at 20 MPa, 360°C and placed inside a containment room as shown in Fig. P5.48. The room is well
A mass and atmosphere loaded piston/cylinder contains 2 kg of water at 5 MPa, 100°C. Heat is added from a reservoir at 700°C to the water until it reaches 700°C. Find the work, heat transfer, and total entropy production for the system and surroundings.
Ammonia is contained in a rigid sealed tank unknown quality at 0oC. When heated in boiling water to 100oC its pressure reaches 1200 kPa. Find the initial quality, the heat transfer to the ammonia and the total entropy generation.
An insulated cylinder/piston contains R-134a at 1 MPa, 50°C, 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 25°C, 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 liquid
A piston cylinder has 2.5 kg ammonia at 50 kPa, -20oC. Now it is heated to 50oC at constant pressure through the bottom of the cylinder from external hot gas at 200oC. Find the heat transfer to the ammonia and the total entropy generation.
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 300°C. It is claimed that the water does 124 kJ of work during this process. Is this
A piston cylinder loaded so it gives constant pressure has 0.75 kg saturated vapor water at 200 kPa. It is now cooled so the volume becomes half the initial volume by heat transfer to the ambient at 20oC. Find the work, the heat transfer and the total entropy generation.
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 piston/cylinder contains 1 kg water at 150 kPa, 20°C. The piston is loaded so pressure is linear in volume. Heat is added from a 600°C source until the water is at 1 MPa, 500°C. Find the heat transfer and the total change in entropy.
A piston/cylinder hAs ammonia at 2000 kPa, 80oC with a volume of 0.1 m3. The piston is loaded with a linear spring and outside ambient is at 20oC, shown in Fig. P8.71. The ammonia now cools down to 20oC at which point it has a quality of 10%. Find the work, the heat transfer and the total entropy
A cylinder/piston contains water at 200 kPa, 200°C 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 20°C, show that this process does not
One kilogram of ammonia (NH3) is contained in a spring-loaded piston/cylinder, Fig. P8.73, as saturated liquid at −20°C. Heat is added from a reservoir at 100°C until a final condition of 800 kPa, 70°C is reached. Find the work, heat transfer, and entropy generation, assuming the process is
A piston/cylinder device keeping a constant pressure has 1 kg water at 20oC and 1 kg of water at 100oC both at 500 kPa separated by a thin membrane. The membrane is broken and the water comes to a uniform state with no external heat transfer. Find the final temperature and the entropy generation
A piston cylinder hAs constant pressure of 2000 kPa with water at 20oC. It is now heated up to 100oC. Find the heat transfer and the entropy change using the steam tables. Repeat the calculation using constant heat capacity and incompressibility.
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 23°C to 18°C in an 18°C house, what is the net entropy change associated with this process?
A 4 L jug of milk at 25°C is placed in your refrigerator where it is cooled down to the refrigerators inside constant temperature of 5°C. Assume the milk has the property of liquid water and find the entropy generated in the cooling process.
A foundry form box with 25 kg of 200°C hot sand is dumped into a bucket with 50 L water at 15°C. Assuming no heat transfer with the surroundings and no boiling away of liquid water, calculate the net entropy change for the process.
A 5-kg steel container is cured at 500oC. An amount of liquid water at 15oC, 100 kPa is added to the container so a final uniform temperature of the steel and the water becomes 75oC. Neglect any water that might evaporate during the process and any air in the container. How much water should be
A substance has heat transfer out. Can you say anything about changes in s if the process is reversible? If it is irreversible?
A pan in an autoshop contains 5 L of engine oil at 20oC, 100 kPa. Now 2 L of hot 100oC oil is mixed into the pan. Neglect any work term and find the final temperature and the entropy generation.
Find the total work the heat engine can give out as it receives energy from the rock bed as described in Problem 7.61 (see Fig.P 8.81). write the entropy balance equation for the control volume that is the combination of the rock bed and the heat engine.
Two kg of liquid lead initially at 500°C are poured into a form. It then cools at constant pressure down to room temperature of 20°C as heat is transferred to the room. The melting point of lead is 327°C and the enthalpy change between the phases, hif, is 24.6 kJ/kg. The specific heats are in
A 12 kg steel container has 0.2 kg superheated water vapor at 1000 kPa, both at 200oC. The total mass is now cooled to ambient temperature 30oC. How much heat transfer was taken out and what is the total entropy generation?
A 5 kg aluminum radiator holds 2 kg of liquid R-134a both at –10oC. The setup is brought indoors and heated with 220 kJ from a heat source at 100oC. Find the total entropy generation for the process assuming the R-134a remains a liquid.
A piston/cylinder of total 1 kg steel contains 0.5 kg ammonia at 1600 kPa both masses at 120oC. Some stops are placed so a minimum volume is 0.02 m3, shown in Fig. P8.85. Now the whole system is cooled down to 30oC by heat transfer to the ambient at 20oC, and during the process the steel keeps same
A hollow steel sphere with a 0.5-m inside diameter and a 2-mm thick wall contains water at 2 MPa, 250°C. The system (steel plus water) cools to the ambient temperature, 30°C. 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 piston/cylinder setup contains air at 100 kPa, 400 K which is compressed to a final pressure of 1000 kPa. Consider two different processes (i) a reversible adiabatic process and (ii) a reversible isothermal process. Show both processes in P-v and a T-s diagram. Find the final temperature and the
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 process the volume triples. Analyze each of the
A substance is compressed adiabaticly so P and T go up. Does that change s?
Consider a small air pistol with a cylinder volume of 1 cm3 at 250 kPa, 27°C. 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 and
Oxygen gas in a piston cylinder at 300 K, 100 kPa with volume 0.1 m3 is compressed in a reversible adiabatic process to a final temperature of 700 K. Find the final pressure and volume using Table A.5.
Oxygen gas in a piston cylinder at 300 K, 100 kPa with volume 0.1 m3 is compressed in a reversible adiabatic process to a final temperature of 700 K. Find the final pressure and volume using constant heat capacity from Table A.8.
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), and
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, assuming a. Variable specific heat, Table A.8 b. Constant specific heat, value from Table
A piston/cylinder, shown in Fig. P8.95, 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
Two rigid tanks, shown in Fig. P8.96, 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)
A spring loaded piston cylinder contains 1.5 kg air at 27oC and 160 kPa. It is now heated in a process where pressure is linear in volume, P = A + BV, to twice the initial volume where it reaches 900 K. Find the work, the heat transfer and the total entropy generation assuming a source at 900 K.
A rigid storage tank of 1.5 m3 contains 1 kg argon at 30°C. Heat is then transferred to the argon from a furnace operating at 1300°C 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 rigid tank contains 2 kg of air at 200 kPa and ambient temperature, 20°C. 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 80°C. Is this possible?
In a steady state single flow s is either constant or it increases. Is that true?
Friction in a pipe flow causes a slight pressure decrease and a slight temperature increase. How does that affect entropy?
A pump receives water at 100 kPa, 15°C and a power input of 1.5 kW. The pump has an isentropic efficiency of 75% and it should flow 1.2 kg/s delivered at 30 m/s exit velocity. How high an exit pressure can the pump produce?
A small air turbine with an isentropic efficiency of 80% should produce 270 kJ/kg of work. The inlet temperature is 1000 K and it exhausts to the atmosphere. Find the required inlet pressure and the exhaust temperature.
Repeat Problem 9.42 assuming the turbine and the pump each have an isentropic efficiency of 85%.
Repeat Problem 9.41 assuming the steam turbine and the air compressor each have an isentropic efficiency of 80%. 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
Steam enters a turbine at 300°C, 600 kPa and exhausts as saturated vapor at 20 kPa. What is the isentropic efficiency?
A turbine receives air at 1500 K, 1000 kPa and expands it to 100 kPa. The turbine has an isentropic efficiency of 85%. Find the actual turbine exit air temperature and the specific entropy increase in the actual turbine.
The small turbine in Problem 9.38 was ideal. Assume instead the isentropic turbine efficiency is 88%. Find the actual specific turbine work and the entropy generated in the turbine.
Air enters an insulated turbine at 50°C, and exits the turbine at - 30°C, 100 kPa. The isentropic turbine efficiency is 70% and the inlet volumetric flow rate is 20 L/s. Calculate turbine inlet pressure and the turbine power output?
Carbon dioxide, CO2, enters an adiabatic compressor at 100 kPa, 300 K, and exits at 1000 kPa, 520 K. Find the compressor efficiency and the entropy generation for the process.
Air enters an insulated compressor at ambient conditions, 100 kPa, 20°C, at the rate of 0.1 kg/s and exits at 200°C. The isentropic efficiency of the compressor is 70%. What is the exit pressure? How much power is required to drive the compressor? Assume the ideal and actual compressor has the
A flow of water at some velocity out of a nozzle is used to wash a car. The water then falls to the ground. What happens to the water state in terms of V, T and s?
Assume an actual compressor has the same exit pressure and specific heat transfer as the ideal isothermal compressor in Problem 9.8 with an isothermal efficiency of 80%. Find the specific work and exit temperature for the actual compressor..
A water-cooled air compressor takes air in at 20°C, 90 kPa and compresses it to 500 kPa. The isothermal efficiency is 80% and the actual compressor has the same heat transfer as the ideal one. Find the specific compressor work and the exit temperature.
A nozzle in a high pressure liquid water sprayer has an area of 0.5 cm2. It receives water at 250 kPa, 20°C and the exit pressure is 100 kPa. Neglect the inlet kinetic energy and assume a nozzle isentropic efficiency of 85%. Find the ideal nozzle exit velocity and the actual nozzle mass flow rate.
A nozzle is required to produce a flow of air at 200 m/s at 20°C, 100 kPa. It is estimated that the nozzle has an isentropic efficiency of 92%. What nozzle inlet pressure and temperature is required assuming the inlet kinetic energy is negligible?
Redo Problem 9.79 if the water pump has an isentropic efficiency of 85% (hose, nozzle included).
Find the isentropic efficiency of the nozzle in example 6.4.
Air flows into an insulated nozzle at 1 MPa, 1200 K with 15 m/s and mass flow rate of 2 kg/s. It expands to 650 kPa and exit temperature is 1100 K. Find the exit velocity, and the nozzle efficiency.
A coflowing 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
A vortex tube has an air inlet flow at 20°C, 200 kPa and two exit flows of 100 kPa, one at 0°C and the other at 40°C. The tube has no external heat transfer and no work and all the flows are steady and have negligible kinetic energy. Find the fraction of the inlet flow that comes out at 0°C. Is

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