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Fundamentals of Thermodynamics 6th edition Richard E. Sonntag, Claus Borgnakke, Gordon J. Van Wylen - Solutions
A geothermal source provides 10 kg/s of hot water at 500 kPa, 150C flowing into a flash evaporator that separates vapor and liquid at 200 kPa. Find the three fluxes of availability (inlet and two outlets) and the irreversibility rate.
Air flows at 1500 K, 100 kPa through a constant pressure heat exchanger giving energy to a heat engine and comes out at 500 K. What is the constant temperature the same heat transfer should be delivered at to provide the same availability?
Refrigerant R-12 at 30C, 0.75 MPa enters a SSSF device and exits at 30C, 100 kPa. Assume the process is isothermal and reversible. Find the change in availability of the refrigerant.
A wooden bucket (2 kg) with 10 kg hot liquid water, both at 85C, is lowered 400m down into a mineshaft. What is the availability of the bucket and water with respect to the surface ambient at 20C?
A rigid container with volume 200 L is divided into two equal volumes by a partition. Both sides contains nitrogen, one side is at 2 MPa, 300C, and the other at 1 MPa, 50C. The partition ruptures, and the nitrogen comes to a uniform state at 100C. Assuming the surroundings
An air compressor is used to charge an initially empty 200-L tank with air up to 5 MPa. The air inlet to the compressor is at 100 kPa, 17C and the compressor isentropic efficiency is 80%. Find the total compressor work and the change in availability of the air.
Air enters a compressor at ambient conditions, 100 kPa, 300 K, and exits at 800 kPa. If the isentropic compressor efficiency is 85%, what is the second-law efficiency of the compressor process?
Steam enters a turbine at 25 MPa, 550C and exits at 5 MPa, 325C at a flow rate of 70 kg/s. Determine the total power output of the turbine, its isentropic efficiency and the second law efficiency.
A compressor is used to bring saturated water vapor at 1 MPa up to 17.5 MPa, where the actual exit temperature is 650C. Find the irreversibility and the second-law efficiency.
A flow of steam at 10 MPa, 550C goes through a two-stage turbine. The pressure between the stages is 2 MPa and the second stage has an exit at 50 kPa. Assume both stages have an isentropic efficiency of 85%. Find the second law efficiencies for both stages of the turbine.
Consider the two-stage turbine in the previous problem as a single turbine from inlet to final actual exit and find its second-law efficiency.
Consider the two-stage turbine in the previous problem as a single turbine from inlet to final actual exit and find its second-law efficiency. Discuss.
The simple steam power plant shown in Problem 6.39 has a turbine with given inlet and exit states. Find the availability at the turbine exit, state 6. Find the second law efficiency for the turbine, neglecting kinetic energy at state 5.
Steam is supplied in a line at 3 MPa, 700C. A turbine with an isentropic efficiency of 85% is connected to the line by a valve and it exhausts to the atmosphere at 100 kPa. If the steam is throttled down to 2 MPa before entering the turbine find the actual turbine specific work. Find the
The condenser in a refrigerator receives R-134a at 700 kPa, 50C and it exits as saturated liquid at 25C. The flow rate is 0.1 kg/s and the condenser has air flowing in at ambient 15C and leaving at 35C. Find the minimum flow rate of air and the heat exchanger
A piston/cylinder arrangement has a load on the piston so it maintains constant pressure. It contains 1 kg of steam at 500 kPa, 50% quality. Heat from a reservoir at 700C brings the steam to 600C. Find the second-law efficiency for this process. Note that no formula is given for
Air flows into a heat engine at ambient conditions 100 kPa, 300 K, Energy is supplied as 1200 kJ per kg air from a 1500 K source and in some part of the process a heat transfer loss of 300 kJ/kg airs happens at 750 K. The air leaves the engine at 100 kPa, 800 K. Find the first and the second law
Consider the high-pressure closed feedwater heater in the nuclear power plant described in Problem 6.42. Determine its second-law efficiency.
Air enters a steady-flow turbine at 1600 K and exhausts to the atmosphere at 1000 K. The second law efficiency is 85%. What is the turbine inlet pressure?
Consider the two turbines in Problem 9.72. What is the second-law efficiency for the combined system?
Air in a piston/cylinder arrangement is at 110 kPa, 25C, with a volume of 50 L. It goes through a reversible polytropic process to a final state of 700 kPa, 500 K, and exchanges heat with the ambient at 25C through a reversible device. Find the total work (including the external
Refrigerant-22 is flowing in a pipeline at 10C, 600 kPa, with a velocity of 200 m/s, at a steady flow rate of 0.1 kg/s. It is desired to decelerate the fluid and increase its pressure by installing a diffuser in the line (a diffuser is basically the opposite of a nozzle in this respect).
A piston/cylinder contains ammonia at 20C, quality 80%, and a volume of 10 L. A force is now applied to the piston so it compresses the ammonia in an adiabatic process to a volume of 5 L, where the piston is locked. Now heat transfer with the ambient takes place so the ammonia
Consider the irreversible process in Problem 8.34. Assume that the process could be done reversibly by adding heat engines/pumps between tanks A and B and the cylinder. The total system is insulated, so there is no heat transfer to or from the ambient. Find the final state, the work given out to
Consider the irreversible process in Problem 8.34. Assume that the process could be done reversibly by adding heat engines/pumps between tanks A and B and the cylinder. The total system is insulated, so there is no heat transfer to or from the ambient. Find the final state, the work given out to
A rock bed consists of 6000 kg granite and is at 70C. A small house with lumped mass of 12000 kg wood and 1000 kg iron is at 15C. They are now brought to a uniform final temperature with no external heat transfer. a. For a reversible process, find the final temperature and the work
Consider the heat engine in Problem 10.47. The exit temperature was given as 800 K, but what are the theoretical limits for this temperature? Find the lowest and the highest, assuming that the heat transfers are as given. For an exit temperature that is the average of the highest and lowest
Consider two rigid containers each of volume 1 m3 containing air at 100 kPa, 400 K. An internally reversible Carnot heat pump is then thermally connected between them so it heats one up and cools the other down. In order to transfer heat at a reasonable rate, the temperature difference between the
Calculate the reversible work and irreversibility for the process described in Problem 5.122, assuming that the heat transfer is with the surroundings at 68 F.
The compressor in a refrigerator takes refrigerant R-134 a in at 15 lbf/in.2, 0 F and compresses it to 125 lbf/in.2, 100 F. With the room at 70 F find the reversible heat transfer and the minimum compressor work.
A supply of steam at 14.7 lbf/in. 2, 320 F is needed in a hospital for cleaning purposes at a rate of 30 lbm/s, a supply of steam at 20 lbf/in.2, 500 F is available from a boiler and tap water at 14.7 lbf/in.2, 60 F is also available. The two sources are then mixed in an SSSF mixing chamber to
A 4-lbm piece of iron is heated from room temperature 77 F to 750 F by a heat source at 1100 F. What is the irreversibility in the process?
Fresh water can be produced from saltwater by evaporation and subsequent condensation. An example is shown where 300-lbm/s saltwater, state 1, comes from the condenser in a large power plant. The water is throttled to the saturated pressure in the flash evaporator and the vapor, state 2, is then
Air flows through a constant pressure heating device as shown. It is heated up in a reversible process with a work input of 85 Btu/lbm air flowing. The device exchanges heat with the ambient at 540 R. The air enters at 540 R, 60 lbf/in 2. Assuming constant specific heat develops an expression for
Air enters the turbocharger compressor of an automotive engine at 14.7 lbf/in2, 90 F, and exits at 25 lbf/in 2, as shown. The air is cooled by 90 F in an intercooler before entering the engine. The isentropic efficiency of the compressor is 75%. Determine the temperature of the air entering the
Calculate the irreversibility for the process described, assuming that the heat transfer is with the surroundings at 61 F.
A control mass gives out 1000 Btu of energy in the form ofa. Electrical work from a batteryb. Mechanical work from a springc. Heat transfer at 700 F
A steady stream of R-22 at ambient temperature, 50 F, and at 110 lbf/in 2 enters a solar collector. The stream exits at 180 F, 100 lbf/in 2, calculate the change in availability of the R-22 between these two states.
A 20-lbm iron disk brake on a car is at 50 F. Suddenly the brake pad hangs up, increasing the brake temperature by friction to 230 F while the car maintains constant speed. Find the change in availability of the disk and the energy depletion of the car’s gas tank due to this process alone. Assume
Air in a piston/cylinder arrangement shown is at 200 kPa, 300 K with a volume of 0.5 m3. If the piston is at the stops, the volume is 1 m3 and a pressure of 400 kPa is required to raise the piston. The air is then heated from the initial state to 1500 K by a 1900 K reservoir. Find the total
Calculate the availability of the system (aluminum plus gas) at the initial and final states of Problem 8.113, and also the irreversibility.
Consider the springtime melting of ice in the mountains, which gives cold water running in a river at 34 F while the air temperature is 68 F. What is the availability of the water (SSSF) relative to the temperature of the ambient?
A geothermal source provides 20 lbm/s of hot water at 80 lbf/in 2, 300 F flowing into a flash evaporator that separates vapor and liquid at 30 lbf/in 2. Find the three fluxes of availability (inlet and two outlets) and the irreversibility rate.
A wood bucket (4 lbm) with 20 lbm hot liquid water, both at 180 F, is lowered 1300 ft down into a mineshaft. What is the availability of the bucket and water with respect to the surface ambient at 70 F?
An air compressor is used to charge an initially empty 7-ft3 tank with air up to 750 lbf/in 2. The air inlet to the compressor is at 14.7 lbf/in 2, 60 F and the compressor isentropic efficiency is 80%. Find the total compressor work and the change in energy of the air.
A compressor is used to bring saturated water vapor at 150 lbf/in 2 up to 2500 lbf/in 2, where the actual exit temperature is 1200 F. Find the irreversibility and the second law efficiency.
The simple steam power plant has a turbine with given inlet and exit states. Find the availability at the turbine exit, state 6. Find the second law efficiency for the turbine, neglecting kinetic energy at state 5.
Steam is supplied in a line at 450 lbf/in 2, 1200 F. A turbine with an isentropic efficiency of 85% is connected to the line by a valve and it exhausts to the atmosphere at 14.7 lbf/in 2. If the steam is throttled down to 300 lbf/in 2 before entering the turbine find the actual turbine specific
A piston/cylinder arrangement has a load on the piston so it maintains constant pressure. It contains 1 lbm of steam at 80 lbf/in 2, 50% quality. Heat from a reservoir at 1300 F brings the steam to 1000 F. Find the second-law efficiency for this process. Note that no formula is given for this
Air flows into a heat engine at ambient conditions 14.7 lbf/in.2, 540 R. Energy is supplied as 540 Btu per lbm air from a 2700 R source and in some part of the process a heat transfer loss of 135 Btu per lbm air happens at 1350 R. The air leaves the engine at 14.7 lbf/in 2, 1440 R. Find the first-
Consider a gasoline engine for a car as an SSSF device where air and fuel enters at the surrounding conditions 77 F, 14.7 lbf/in 2 and leaves the engine exhaust manifold at 1800 R, 14.7 lbf/in 2 as products assumed to be air. The engine cooling system removes 320 Btu/lbm air through the engine to
Consider the two turbines what is the second-law efficiency of the combined system?
Adv Refrigerant-22 is flowing in a pipeline at 40 F, 80 lbf/in 2, with a velocity of 650 ft/s, at a steady flow rate of 0.2 lbm/s, tt is desired to decelerate the fluid and increase its pressure by installing a diffuser in the line (a diffuser is basically the opposite of a nozzle in this respect).
Adv water in a piston/cylinder is at 14.7 lbf/in 2, 90 F, the cylinder has stops mounted so that Vmin = 0.36 ft3 and Vmax = 18 ft3. The piston is loaded with a mass and outside P0, so a pressure inside of 700 lbf/in 2 will float it. Heat of 14000 Btu from a 750 F source is added. Find the total
A rock bed consists of 12000 lbm granite and is at 160 F. A small house with lumped mass of 24000 lbm wood and 2000 lbm iron is at 60 F. They are now brought to a uniform final temperature with no external heat transfer.a. For a reversible process, find the final temperature and the work done in
Air in a piston/cylinder arrangement, is at 30 lbf/in 2, 540 R with a volume of 20 ft3, if the piston is at the stops the volume is 40 ft3 and a pressure of 60 lbf/in 2 is required. The air is then heated from the initial state to 2700 R by a 3400 R reservoir. Find the total irreversibility in the
A steam power plant as operating in a Rankine cycle has saturated vapor at 3.5 MPa leaving the boiler. The turbine exhausts to the condenser operating at 10 kPa. Find the specific work and heat transfer in each of the ideal components and the cycle efficiency.
Consider a solar-energy-powered ideal Rankine cycle that uses water as the working fluid. Saturated vapor leaves the solar collector at 175°C, and the condenser pressure is 10 kPa. Determine the thermal efficiency of this cycle.
A utility runs a Rankine cycle with a water boiler at 3.5 MPa and the cycle have the highest and lowest temperatures of 450°C and 45°C respectively. Find the plant efficiency and the efficiency of a Carnot cycle with the same temperatures.
A steam power plant operating in an ideal Rankine cycle has a high pressure of 5 MPa and a low pressure of 15 kPa. The turbine exhaust state should have a quality of at least 95% and the turbine power generated should be 7.5 MW. Find the necessary boiler exit temperature and the total mass flow
A supply of geothermal hot water is to be used as the energy source in an ideal Rankine cycle, with R-134a as the cycle working fluid. Saturated vapor R-134a leaves the boiler at a temperature of 85°C, and the condenser temperature is 40°C. Calculate the thermal efficiency of this cycle.
Do Problem 11.5 with R-22 as the working fluid.
Do Problem 11.5 with ammonia as the working fluid.
Consider the ammonia Rankine-cycle power plant shown in, a plant that was designed to operate in a location where the ocean water temperature is 25°C near the surface and 5°C at some greater depth.a. Determine the turbine power output and the pump power input for the cycle.b. Determine the mass
Do Problem 11.8 with R-134a as the working fluid in the Rankine cycle.
Consider the boiler in Problem 11.5 where the geothermal hot water brings the R- 134a to saturated vapor. Assume a counter flowing heat exchanger arrangement. The geothermal water temperature should be equal to or greater than the R-134a temperature at any location inside the heat exchanger. The
Do the previous problem with R-22 as the working fluid.
The power plant in Problem 11.1 is modified to have a super heater section following the boiler so the steam leaves the super heater at 3.5 MPa, 400°C. Find the specific work and heat transfer in each of the ideal components and the cycle efficiency.
A steam power plant has a steam generator exit at 4 MPa, 500°C and a condenser exit temperature of 45°C. Assume all components are ideal and find the cycle efficiency and the specific work and heat transfer in the components.
Consider an ideal Rankine cycle using water with a high-pressure side of the cycle at a supercritical pressure. Such a cycle has a potential advantage of minimizing local temperature differences between the fluids in the steam generator, such as the instance in which the high-temperature energy
Steam enters the turbine of a power plant at 5 MPa and 400C, and exhausts to the condenser at 10 kPa. The turbine produces a power output of 20 000 kW with an isentropic efficiency of 85%. What is the mass flow rate of steam around the cycle and the rate of heat rejection in the condenser?
Consider an ideal steam reheat cycle where steam enters the high-pressure turbine at 3.5 MPa, 400°C, and then expands to 0.8 MPa. It is then reheated to 400°C and expands to 10 kPa in the low-pressure turbine. Calculate the cycle thermal efficiency and the moisture content of the steam leaving
The reheat pressure effect the operating variables and thus turbine performance. Repeat Problem 11.16 twice, using 0.6 and 1.0 MPa for the reheat pressure.
The effect of a number of reheat stages on the ideal steam reheat cycle is to be studied. Repeat Problem 11.16 using two reheat stages, one stage at 1.2 MPa and the second at 0.2 MPa, instead of the single reheat stage at 0.8 MPa.
A closed feedwater heater in a regenerative steam power cycle heats 20 kg/s of water from 100°C, 20 MPa to 250°C, 20 MPa. The extraction steam from the turbine enters the heater at 4 MPa, 275°C, and leaves as saturated liquid. What is the required mass flow rate of the extraction steam?
An open feedwater heater in a regenerative steam power cycle receives 20 kg/s of water at 100C, 2 MPa. The extraction steam from the turbine enters the heater at 2 MPa, 275C, and all the feedwater leaves as saturated liquid. What is the required mass flow rate of the extraction
A power plant with one closed feedwater heater has a condenser temperature of 45°C, a maximum pressure of 5 MPa, and boiler exit temperature of 900°C. Extraction steam at 1 MPa to the feedwater heater condenses and is pumped up to the 5 MPa feedwater lines where all the water goes to the boiler
A power plant with one open feedwater heater has a condenser temperature of 45°C, a maximum pressure of 5 MPa, and boiler exit temperature of 900°C. Extraction steam at 1 MPa to the feedwater heater is mixed with the feedwater line so the exit is saturated liquid into the second pump. Find the
A steam power plant operates with a boiler output of 20 kg/s steam at 2 MPa, 600C. The condenser operates at 50 C dumping energy to a river that has an average temperature of 20 C. There is one open feedwater heater with extraction from the turbine at 600 kPa and its exit is saturated liquid. Find
Consider an ideal steam regenerative cycle in which steam enters the turbine at 3.5 MPa, 400°C, and exhausts to the condenser at 10 kPa. Steam is extracted from the turbine at 0.8 MPa for an open feedwater heater. The feedwater leaves the heater as saturated liquid. The appropriate pumps are used
Repeat Problem 11.24, but assume a closed instead of an open feedwater heater. A single pump is used to pump the water leaving the condenser up to the boiler pressure of 3.5 MPa. Condensate from the feedwater heater is drained through a trap to the condenser.
A steam power plant has high and low pressures of 25 MPa and 10 kPa, and one open feedwater heater operating at 1 MPa with the exit as saturated liquid. The maximum temperature is 800°C and the turbine has a total power output of 5 MW. Find the fraction of the flow for extraction to the feedwater
Do Problem 11.26 with a closed feedwater heater instead of an open and a drip pump to add the extraction flow to the feed water line at 25 MPa. Assume the temperature is 175°C after the drip pump flow is added to the line. One main pump brings the water to 25 MPa from the condenser.
Consider an ideal combined reheat and regenerative cycle in which steam enters the high-pressure turbine at 3.5 MPa, 400°C, and is extracted to an open feedwater heater at 0.8 MPa with exit as saturated liquid. The remainder of the steam is reheated to 400°C at this pressure, 0.8 MPa, and is fed
An ideal steam power plant is designed to operate on the combined reheat and regenerative cycle and to produce a net power output of 10 MW. Steam enters the high-pressure turbine at 8 MPa, 550°C, and is expanded to 0.6 MPa, at which pressure some of the steam is fed to an open feedwater heater,
The low pressure turbine in a reheat and regenerative cycle receives 10 kg/s steam at 600 kPa, 550 C. The turbine exhausts to a condenser operating at 10 kPa. The condenser cooling water temperature is restricted to a maximum of 10 C increase so what is the needed flow rate of the cooling water?
A steam power plant has a high pressure of 5 MPa and maintains 50°C in the condenser. The boiler exit temperature is 600°C. All the components are ideal except the turbine which has an actual exit state of saturated vapor at 50°C. Find the cycle efficiency with the actual turbine and the turbine
A steam power cycle has a high pressure of 3.5 MPa and a condenser exit temperature of 45°C. The turbine efficiency is 85%, and other cycle components are ideal. If the boiler superheats to 800°C, find the cycle thermal efficiency.
A steam power plant operates with a high pressure of 5 MPa and has a boiler exit temperature of 600 C receiving heat from a 700 C source. The ambient at 20 C provides cooling for the condenser so it can maintain 45C inside. All the components are ideal except for the turbine which has an
Repeat Problem 11.26 assuming the turbine has an isentropic efficiency of 85%.
Steam leaves a power plant steam generator at 3.5 MPa, 400°C, and enters the turbine at 3.4 MPa, 375°C. The isentropic turbine efficiency is 88%, and the turbine exhaust pressure is 10 kPa. Condensate leaves the condenser and enters the pump at 35°C, 10 kPa. The isentropic pump efficiency is
For the steam power plant described in Problem 11.1, assume the isentropic efficiencies of the turbine and pump are 85% and 80%, respectively. Find the component specific work and heat transfers and the cycle efficiency.
A small steam power plant has a boiler exit of 3 MPa, 400°C while it maintains 50 kPa in the condenser. All the components are ideal except the turbine which has an isentropic efficiency of 80% and it should deliver a shaft power of 9.0 MW to an electric generator. Find the specific turbine work ,
In a particular reheat-cycle power plant, steam enters the high-pressure turbine at 5 MPa, 450°C and expands to 0.5 MPa, after which it is reheated to 450°C. The steam is then expanded through the low-pressure turbine to 7.5 kPa. Liquid water leaves the condenser at 30°C, is pumped to 5 MPa, and
A supercritical steam power plant has a high pressure of 30 MPa and an exit condenser temperature of 50°C. The maximum temperature in the boiler is 1000°C and the turbine exhaust is saturated vapor there is one open feedwater heater receiving extraction from the turbine at 1MPa, and its exit is
In one type of nuclear power plant, heat is transferred in the nuclear reactor to liquid sodium. The liquid sodium is then pumped through a heat exchanger where heat is transferred to boiling water. Saturated vapor steam at 5 MPa exits this heat exchanger and is then superheated to 600C in
A co-generating steam power plant operates with a boiler output of 25 kg/s steam at 7 MPa, 500C. The condenser operates at 7.5 kPa and the process heat is extracted as 5 kg/s from the turbine at 500 kPa, state 6 and after use is returned as saturated liquid at 100 kPa, state 8. Assume all
A 10 kg/s steady supply of saturated-vapor steam at 500 kPa is required for drying a wood pulp slurry in a paper mill. It is decided to supply this steam by cogeneration, that is, the steam supply will be the exhaust from a steam turbine. Water at 20C, 100 kPa, is pumped to a pressure of 5
An industrial application has the following steam requirement: one 10-kg/s stream at a pressure of 0.5 MPa and one 5-kg/s stream at 1.4 MPa (both saturated and slightly superheated vapor). It is obtained by cogeneration, whereby a high pressure boiler supplies steam at 10 MPa, 500C to a
In a co-generating steam power plant the turbine receives steam from a high-pressure steam drum and a low-pressure steam drum as shown in Fig. P11.44, the condenser is made as two closed heat exchangers used to heat water running in a separate loop for district heating. The high-temperature heater
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