The English unit problems are: New Old New Old New Old 61 new 71 67 81 75 62 58 72 new 82 83 63 60 73 68 83 77 64 63 74 new 84 64 65 61 75 69 85 71 66 80 76 70 86 73 67 62 77 72 87 78 68 new 78 new 69 65 79 79 70 66 80 84 Page 2 CHAPTER 10 The correspondence between the new problem set and the previous 4th edition chapter 8 problem set. The English unit problems are: New Old New Old New Old 61 new 71 67 81 75 62 58 72 new 82 83 63 60 73 68 83 77 64 63 74 new 84 64 65 61 75 69 85 71 66 80 76 70 86 73 67 62 77 72 87 78 68 new 78 new 69 65 79 79 70 66 80 84 This is a control mass.
Solution: C. Compressor out to ambient. Minimum work in is the reversible work. SSSF, 1 inlet and 2 exit energy Eq. Compare this to the actual work which was found to be SSSF, 1 inlet and 2 exits.
Use Eq. Table B. Assume that the rate of heat transfer from the cold space, Q. C , is the same as from the freezer, Q. F , find an expression for the minimum power into the heat pump.
Refrigerator heat pump , SSSF, no external flows except heat transfer. Energy Eq. A amount rejected to ambient Reversible gives minimum work in as from Eq.
Determine the minimum compressor work input. Compressor, SSSF, minimum work in is reversible work. The two sources are then mixed in an SSSF mixing chamber to generate the desired state as output.
Determine the rate of irreversibility of the mixing process. Calculate the heat transfer for the overall process. Stops in the cylinder are placed to restrict the enclosed volume to 0. The water is now heated until the piston reaches the stops.
Find the necessary heat transfer. Show the P—v diagram and find the work and heat transfer for the process. Solution: Take CV as the water. Properties from table B. The piston is allowed to move, and the R expands until it exists as saturated vapor.
During this process the R does 7. Determine the final temperature, assuming the process is adiabatic. Solution: Take CV as the R Find the initial and final volumes and the total heat transfer required. Solution: Take CV as the nitrogen. Find the final temperature and specific work and heat transfer for the process.
Water in the piston cylinder. When the valve is cracked open, Ra flows slowly into cylinder B. The piston mass requires a pressure of kPa in cylinder B to raise the piston. The process ends when the pressure in tank A has fallen to kPa. Calculate the heat transfer for the process. The Ra. This system is heated until the pressure in the balloon reaches kPa. For this process, it can be assumed that the pressure in the balloon is directly proportional to the balloon diameter. How does pressure vary with volume and what is the heat transfer for the process?
R which is a control mass. The piston has a mass of kg, with cross-sectional area of cm2, and the ambient pressure is kPa.
The pin is released, which allows the piston to move. Determine the final state of the water, assuming the process to be adiabatic. If the piston is at the bottom, the spring exerts a force such that a pressure of kPa inside is required to balance the forces. The system now cools until the pressure reaches 1 MPa. Find the heat transfer for the process. The spring is mounted so at zero cylinder volume a balancing pressure inside is kPa. The cylinder contains 0.
Heat is now transferred to the water until the cylinder pressure reaches kPa. How much work is done by the water during this process and what is the heat transfer? The 0. Conservation of mass: Energy eq. Tank A contains 0. The valve is opened, and the two tanks eventually come to a uniform state.
Assuming the process to be adiabatic, show the final state u,v is two-phase and iterate on final pressure to match required internal energy. Heat is now added until the water reaches a saturated vapor state. Find the initial volume, final pressure, work, and heat transfer terms and show the P—v diagram.
The 5 kg water. Find the heat transfer during the process. The valve is opened and saturated vapor flows from A into B until the pressures become equal. Find the total heat transfer to the Ra during the process.
Let the valve be opened and transfer enough heat to both tanks so all the liquid disappears. Find the final temperature in the cylinder and the heat transfer for the process. Water in cylinder. The room is well insulated and initially evacuated. Due to a failure, the reactor ruptures and the water fills the containment room. Find the minimum room volume so the final pressure does not exceed kPa.
A cylinder containing 1 kg of ammonia has an externally loaded piston. Ammonia going through process 1 - 2 - 3. Control mass. The piston cross-sectional area is 0.
A total of 62 kJ of heat is now added to the R Verify that the final pressure is around kPa and find the final temperature of the R The capsule breaks and its contents fill the entire volume. If the final pressure should not exceed kPa, what should the vessel volume be?
Larger vessel. The external piston force is proportional to cylinder volume cubed. Heat is transferred out of the cylinder, reducing the volume and thus the force until the cylinder pressure has dropped to kPa. Find the work and heat transfer for this process. The refrigerant mass is 5 kg, and during this process kJ of heat is removed. Find the initial and final volumes and the necessary work. Ra, this is a control mass.
Consider a piston cylinder with 0. A piston cylinder setup similar to Problem 4. The volume is 0. Find the mass of the fluid and show the P—v diagram. Find the work and heat transfer. R, this is a control mass. Properties in Table B. Find the final state P2, u2 and the specific work and heat transfer. How much energy will be available for heating during the nighttime hours? The mass of concrete.
Assume the brake pads are 0. Find the temperature increase in the brake assembly. Car looses kinetic energy and brake system gains internal u. No heat transfer short time and no work term. Assuming no heat transfer with the surroundings, what is the final temperature?
Copper block and the oil bath. The vessel is heated until the water inside is saturated vapor. Considering the vessel and water together as a control mass, calculate the heat transfer for the process. Vessel and water. This is a control mass of constant volume. Find the change in enthalpy using constant specific heat from Table A. Argon b. Oxygen c. Room A of 0. The plate is removed and the air comes to a uniform state without any heat transfer.
Find the final pressure and temperature. Total tank. Control mass of constant volume. Side A has air at kPa, K, and side B has air at 1. Find the mass in both A and B, and the final T and P. State 1A: Table A. Determine the final pressure, temperature, and the heat transfer for the process.
This is a control mass going through a polytropic process. Find the change in the specific internal energy, using the water table and the ideal gas water table in combination. Solution: State 1: Table B. Consider the following methods and indicate the most accurate one. Constant specific heat, value from Table A.
Constant specific heat, value at average temperature from the equation in Table A. Variable specific heat, integrating the equation in Table A. Enthalpy from ideal gas tables in Table A. The piston is then locked with a pin and heat is transferred to a final temperature of K. Find P, T, and h for states 2 and 3, and find the work and heat transfer in both processes. A line with a safety valve that opens at kPa is attached to the water side of the cylinder.
Assume no heat transfer to the water and that the water is incompressible. Show possible air states in a P—v diagram, and find the air temperature when the safety valve opens. How much heat transfer is needed to bring the air to K? The piston in B is loaded with the outside atmosphere and the piston mass in the standard gravitational field.
The valve is now opened, and the air comes to a uniform condition in both volumes. Assuming no heat transfer, find the initial mass in B, the volume of tank A, the final pressure and temperature and the work, 1W2. The tank is cooled to K. Find the final pressure and the heat transfer for the process. What is the percent error in the heat transfer if the specific heat is assumed constant at the room temperature value?
Calculate the heat transfer. Determine if piston will drop. Then find T and check. Air at K, volume 0. Find the total heat transfer to the air when all the water has been pushed out. The gas is now allowed to expand until the piston reaches a set of fixed stops at L cylinder volume. This process is polytropic, with the polytropic exponent n equal to 1. Additional heat is now transferred to the gas, until the final temperature reaches K.
Determine a The final pressure inside the cylinder. The mass of carbon dioxide. Constant mass has process 1 - 2 - 3. The external force on the piston is now varied in such a manner that the Ra slowly expands in a polytropic process to kPa, 20oC. Calculate the work and the heat transfer for this process. The mass of Ra.
Find the final volume, then knowing P1, V1, P2, V2 the polytropic exponent can be determined. Argon is an ideal monatomic gas Cv is constant. Now heat is transferred to the cylinder to a final pressure of kPa. Find the heat transfer in the process. Determine the final pressure inside the cylinder, the work done by the propane, and the heat transfer during the process.
Considering a control mass of the air and water, determine the work done by the system and the heat transfer to the cylinder. It is expected to carry four kg workers to the top of a m tall building in less than 2 min.
The elevator cage will have a counterweight to balance its mass. What is the smallest size power electric motor that can drive this unit? Suppose that the ventilation system fails in an auditorium containing people.
Assume the energy goes into the air of volume m3 initially at K and kPa. Find the rate degrees per minute of the air temperature change. The vent valve is accidentally closed so that the pressure inside slowly rises.
How long time will it take to reach a pressure of kPa? Once in the liquid region then v is not strong function of P. The room has 50 kg wood, 25 kg steel and air, with all material at K, kPa. Air, wood and steel. Heat is rejected from the system, and the piston moves until 6. Find the final temperature of the ammonia. The system undergoes a quasi-equilibrium polytropic expansion to kPa, during which the system receives a heat transfer of What is the final temperature of the R?
A valve connecting the tank and balloon is opened slightly and remains so until the pressures equalize. Calculate the final pressure and the work and heat transfer during the process. From the solution to problem 4. The work was found as The external force on the piston now varies in such a manner that the piston moves, increasing the volume. It is noted that the temperature is 25oC when the last drop of liquid Ra evaporates. The process continues to a final state of 40oC, kPa.
Assume the pressure is piecewise linear in volme and determine the final volume in the cylinder and the work and heat transfer for the overall process. The mass of Ra, which goes through process 1 - 2- 3. The tank is now heated to K. The amount of butane. C4H10 is polyatomic so the specific heat is a strong funciton of temperature. Calculate the work and heat transfer. This balloon contains helium gas at K, kPa, with a 0. The balloon is heated until the volume reaches 2 m3.
During the process the maximum pressure inside the balloon is kPa. What is the temperature inside the balloon when pressure is maximum? What are the final pressure and temperature inside the balloon? Determine the work and heat transfer for the overall process. The initial volumes of A and B are each L, and the initial pressure on each side is kPa. Heat is transferred to both A and B until all the liquid in B evaporates.
The upper part A contains air at ambient temperature, 20C, and the initial volume is L. Heat is now transferred from a heat source to part B, causing the piston to move upward until the volume of B reaches L. Neglect the piston mass, such that the pressures in A and B are always equal and assume the temperature in A remains constant during the process. What is the increase in potential energy of the car and how much volume should the pump displace to deliver that amount of work?
No change in kinetic or internal energy of the car, neglect hoist mass. What is the change in total energy of the hammerhead? Hammerhead The hammerhead does not change internal energy i. The tank is then cooled to 20 F. Heat is transferred to the system causing the piston to rise until it reaches a set of stops at which point the volume has doubled. It is now cooled to F.
Find the final temperature and plot the P-v diagram for the process. Calculate the work and the heat transfer for the process. It contains water at 25 F, which is then heated until the water becomes saturated vapor. To what temperature should the water be heated to lift the piston? If it is heated to saturated vapor find the final temperature, volume, and the heat transfer. A cylinder containing 2 lbm of ammonia has an externally loaded piston. Assume the brake pads are 1 lbm mass with heat capacity of 0.
Find the mass in both A and B and also the final T and P. PV State 1: Table C. Reference source not found. It is expanded in a constant-pressure process to twice the initial volume state 2. The piston is then locked with a pin, and heat is transferred to a final temperature of R. The piston is loaded with a linear spring, mass, and the atmosphere. Find the final temperature, volume, and the work and heat transfer. Find the work done on the spring.
V linear from 1 to a, see figure. To find state 2: From P2 to line to V2 so we need V1 to fix the line location. Assume that the volume is 1 in. If the air pressure is 1 atm in the cylinder as the bullet leaves the gun, find a. The final volume and the mass of air. The work done by the air and work done on the atmosphere. The work to the bullet and the bullet exit velocity. Air at R, volume 10 ft3 under the piston is heated so that the piston moves up, spilling the water out over the side.
Properties in Table C. Room A has 0. The pin is pulled, releasing the piston and both rooms come to equilibrium at 90 F. It is expected to carry four lbm workers to the top of a ft-tall building in less than 2 min. The room has lbm of wood, 50 lbm of steel and air, with all material at R, 1 atm. Assuming all the mass heats up uniformly how long time will it take to increase the temperature 20 F? New Old New Old New Old 1 83 25 49 2 new 26 50 3 new 27 new 51 4 84 28 new 52 5 85 29 92 53 6 new 30 96 54 7 new 31 new 55 8 32 56 9 86 33 88 57 10 89 mod 34 new 58 11 97 35 93 59 12 98 36 87 60 13 99 37 61 14 94 38 62 15 95 39 a 63 16 new 40 b 64 17 41 65 18 new 42 66 new 19 90 43 67 new 20 91 44 68 new 21 new 45 69 22 new 46 70 23 47 71 24 48 new 72 The advanced problems start with number 6.
The volumetric flow rate is 0. What is the velocity of the air flowing in the duct? They have carefully measured the average flow velocity to be 5. Changes in kinetic and potential energies are negligible. Calculate the required heat transfer per kilogram of carbon dioxide flowing through the heater. Heater SSSF single inlet and exit. Energy Eq. It then flows into a superheater also at kPa where it exits at kPa, K. Find the rate of heat transfer in the boiler and the superheater.
Continuity Eq. What should the inlet temperature be so that no water will condense inside the pipe? Find the rate of heat transfer to the water. If the. Heat exchanger, SSSF, 1 inlet and exit for air and water each. For an insulated condenser, find the flow rate of cooling water. Heat exchanger. Find the best estimate for the heat transfer.
Find the rate of heat transfer to the mixing chamber. Mixing chamber. SSSF with 2 flows in and 1 out, heat transfer in. Both flow rates are 0.
Mixing chamber, SSSF, no work term. Q Table B. It flows out of the nozzle at kPa, K. If the nozzle is insulated find the exit velocity. Nozzle SSSF one inlet and exit, insulated so it is adiabatic. Determine the temperature or quality, if saturated and the exit area of the nozzle.
Nozzle, SSSF, 1 inlet and 1 exit , insulated so no heat transfer. The inlet cross-sectional area of the diffuser is mm2. Determine the exit pressure and temperature of the air. Determine the exit temperature if the gas is argon, helium or nitrogen. Diffuser, SSSF, 1 inlet, 1 exit, no q, w. The diameter of the exit pipe is so much larger than the inlet pipe that the inlet and exit velocities are equal.
Find the exit temperature of the helium and the ratio of the pipe diameters. What is the temperature as it leaves the valve assuming no changes in kinetic energy and no heat transfer? Valve SSSF. Calculate the exit temperature assuming no changes in the kinetic energy and ideal-gas behavior. Repeat the answer for real-gas behavior. Determine the state and the velocity of the water at the exit. Find the flow rate for the second line.
SSSF, 2 inlets, 1 exit, no q, w. Find the rate of heat transfer and the exit pipe diameter. Assuming no heat transfer and no changes in kinetic energy, find the total turbine power output. Turbine SSSF, 1 inlet and 2 exit flows. Assuming the velocities to be low and the process to be adiabatic, find the required mass flow rate of air through the turbine. Find the total power out of the adiabatic turbine.
If the turbine produces kW, find the exhaust temperature and quality if saturated. The electric generators driven by water-powered turbines deliver MW of power. If the water is High pressure steam enters at point 1 with 2. There is a heat loss of kW. Find the exhaust velocity and the power output of the engine.
W 1 Engine 2 3. The exit line enters a pipe that goes up to an elevation 20 m above the pump and river, where the water runs into an open channel. Find the required pump work. SSSF, 1 inlet, 1 exit. At the compressor discharge, air exits at 1. The power input to the compressor is kW. Determine the mass flow rate of air through the unit.
One is 0. The control volume rejects 1. Determine the flow rate of air at the inlet at state 2. Find the specific compressor work and the specific heat transfer.
Q Table A. Piping diameters are mm from steam generator to the turbine and 75 mm from the condenser to the steam generator. Determine the power output of the turbine and the heat transfer rate in the condenser. Rather than generating this from a pump and boiler, the setup in Fig. Find the power the turbine now cogenerates in this process.
Mass flow rates and the various states in the cycle are shown in the accompanying table. The cycle includes a number of heaters in which heat is transferred from steam, taken out of the turbine at some intermediate pressure, to liquid water pumpedfrom the condenser on its way to the steam drum. The heat exchanger in the reactor supplies MW, and it may be assumed that there is no heat transfer in the turbines.
Assume the moisture separator has no heat transfer between the two turbinesections, determine the enthalpy and quality h , x. Determine the power output of the low-pressure turbine. Determine the power output of the high-pressure turbine. Find the ratio of the total power output of the two turbines to the total power delivered by the reactor. Determine the quality of the steam leaving the reactor. What is the power to the pump that feeds water to the reactor?
Reactor feedwater pump. Determine the temperature of the water leaving the intermediate pressure heater, T , assuming no heat transfer to the surroundings. Determine the pump work, between states 13 and Find the power removed in the condenser by the cooling water not shown. Find the power to the condensate pump. Do the energy terms balance for the low pressure heater or is there a heat transfer not shown?
The high-pressure water at 1. If the turbine should produce 1 MW, find the required mass flow rate of hot geothermal water in kilograms per hour. A valve on the tank is now opened and air flows out until the pressure drops to kPa. What is the heat transfer? The valve is opened, and air flows into the tank until the pressure reaches kPa. Determine the final temperature and mass inside the tank, assuming the process is adiabatic.
Develop an expression for the relation between the line temperature and the final temperature using constant specific heats. Tank: Continuity Eq. A valve is cracked open, and carbon dioxide escapes slowly until the tank pressure has dropped to kPa.
At this point the valve is closed. Find the final mass inside and the heat transferred to the tank during the process. Calculate the heat transferred from the tank during this process. USUF as flows comes in. The turbine operates to a tank pressure of 0. Assuming the entire process is adiabatic, determine the turbine work. The valve is opened allowing air to flow into the tank until the pressure inside is 6 MPa.
This filling process occurs rapidly and is essentially adiabatic. The tank is then placed in storage where it eventually returns to room temperature. What is the final pressure? The valve is now opened, allowing air to flow into the balloon until the pressure inside reaches kPa, at which point the valve is closed. The final temperature inside the balloon is K.
The pressure is directly proportional to the diameter of the balloon. Find the work and heat transfer during the process. A valve on the tank is opened, and air escapes until half the original mass is gone, at which point the valve is closed. What is the pressure inside then? The boiler tank has a volume of L and initially contains saturated liquid with a very small amount of vapor at kPa.
Heat is now added by the burner, and the pressure regulator does not open before the boiler pressure reaches kPa, which it keeps constant. The saturated vapor enters the turbine at kPa and is discharged to the atmosphere as saturated vapor at kPa. The burner is turned off when no more liquid is present in the as boiler. Find the total turbine work and the total heat transfer to the boiler for this process.
A valve on the top of the tank is opened, and steam is allowed to escape. During the process any liquid formed collects at the bottom of the vessel, so that only saturated vapor exits. Calculate the total mass that has escaped when the pressure inside reaches 1 MPa. Vessel: Mass flows out. The valve is opened, allowing air to flow into the tank until the pressure reaches 1. Assume the air and tank are always at the same temperature and find the final temperature.
A valve at the bottom of the tank is opened, and liquid is slowly withdrawn. Heat transfer takes place such that the temperature remains constant. Find the amount of heat transfer required to the state where half the initial mass is withdrawn. CV: vessel 0. Assume no heat transfer and that the bottle is closed when the pressure reaches line pressure. Find the final temperature and mass in the bottle. The supply line valve is closed when the pressure inside reaches Find the final mass and temperature in the container.
Initially the cylinder is empty and the spring force is zero. The valve is then opened until the cylinder pressure reaches kPa. Find the air mass that enters, the work, and heat transfer. Air is let in until the volume doubles, during which process there is a heat transfer of 50 kJ out of the balloon. Find the final temperature and the mass of air that enters the balloon. It may be assumed that LNG has the same properties as pure methane. Heat is transferred to the tank and saturated vapor at K flows into the a steady flow heater which it leaves at K.
The process continues until all the liquid in the storage tank is gone. Calculate the total amount of heat transfer to the tank and the total amount of heat transferred to the heater. A valve is now opened, allowing gas to flow out until the diameter reaches 1. The balloon then continues to cool until the diameter is 1. Process 1 - 2 - 3. Flow out in 1- 2, USUF. A pressure-relief valve on the top of the tank is set at kPa when tank pressure reaches that value, mass escapes such that the tank pressure cannot exceed kPa.
The line valve is now opened, allowing 10 kg of R to flow in from the line, and then this valve is closed. Heat is transferred slowly to the tank, until the final mass inside is kg, at which point the process is stopped. There is both an inlet flow from the line and en exit flow through the relief valve, USUF, no work. The valve is now opened for a short time to let steam in to a final volume of 10 L. The final uniform state is twophase and there is no heat transfer in the process.
What is the final mass inside the cylinder? The valve is opened, allowing ammonia to flow into the tank. At what pressure should the valve be closed if the manufacturer wishes to have 15 kg of ammonia inside at the final state? The valve is opened, and the bag slowly inflates at constant temperature to a final diameter of 2 m.
After this the pressure and diameter are related according to A maximum pressure of kPa is recorded for the whole process. Find the heat transfer to the bag during the inflation process. A valve on the cylinder is opened and R flows out until half the initial mass is left.
Find the final state of the R, P , x , and the 2 2 heat transfer to the cylinder. The R Flow out, use average so USUF. All pipes have diameter of 4 in. Find the flow work into and out of the pump and the kinetic energy in the flow. It is shown in Fig. Calculate the required heat transfer per lbm of carbon dioxide flowing through the heater. The cooling is done by lake water at 70 F that returns to the lake at 90 F. Nozzle : Continuity Eq. The inlet cross-sectional area of the diffuser is 0.
At the exit, the area is 1. Valve SSSF 1 2. Find the mass flow rate for the second line. Assuming no heat transfer and no changes in kinetic energy, find the total turbine work.
The electric generators driven by water-powered turbines deliver 1. If the water is 65 F, find the minimum amount of water running through the turbines. The exit line enters a pipe that goes up to an elevation 60 ft above the pump and river, where the water runs into an open channel. Assume the process is adiabatic and that the water stays at 50 F. Piping diameters are 8 in.
Determine also the flow rate of cooling water through the condenser, if the cooling water increases from 55 to 75 F in the condenser. If the turbine should produce hp, find the required mass flow rate of hot geothermal water in pound-mass per hour. The valve is opened, and mass flows in until the tank is half full of liquid, by volume at 80 F. The piston crosssectional area is 0. The system is shown in Fig. Heat is transferred so the final temperature of the R is 30 F.
Find the final state of the R, P2, x2 , and the heat transfer to the cylinder. Pressure drop in all lines. Compare the result with that of Problem 7. Find the plant thermal efficiency. Assuming the same pump work and heat transfer to the boiler is given, how much turbine power could be produced if the plant were running in a Carnot cycle? Estimate the amount of power needed to operate the air-conditioner. Clearly state all assumptions made.
It rejects kJ to a K energy reservoir and the cycle produces kJ of work as output. Is this cycle reversible, irreversible, or impossible? What is the theoretically smallest power motor required to operate this freezer? Any actual machine requires a larger input.
For a maximum of 1. Heat pump. Definition of the coefficient of performance and the fact that the maximum is for a Carnot heat pump. The house gains 0. Find the maximum outside temperature for which the heat pump provides sufficient cooling. The heat pump must remove the gain or leak heat transfer to keep it at a constant temperature. Substitute in for QL and multiply with Tamb - Thouse :.
What is the possible thermal efficiency of such a heat engine? A heat engine receives a Q H from the bed and rejects heat to the ambient at K. The rock bed therefore cools down and as it reaches K the process stops. Find the energy the rock bed can give out. What is the heat engine efficiency at the beginning of the process and what is it at the end of the process?
Solution: Assume the whole setup is reversible and that the heat engine operates in a Carnot cycle. A coefficient of performance of 8. How do you evaluate this? Find the amount of energy the freezer must remove from the Ra and the extra amount of work input to the freezer to do the process. What is the maximum thermal efficiency? Determine the maximum thermal efficiency of the power plant. Is it misleading to use the temperatures given to calculate this value?
Find the amount of energy that must be removed from the milk and the additional work needed to drive the refrigerator. Determine the minimum electric power to drive the heat pump as a function of the two temperatures. Assume that the house is losing energy to the outside as described in the previous problem. Find the maximum and minimum outside temperature for which this unit is sufficient. Solution: Analyse the unit in heat pump mode.
Assume that the house is gaining energy from the outside directly proportional to the temperature difference. At this temperature the enthalpy of evaporation is A Carnot refrigeration cycle is analyzed for the production of 1 kmol of liquid helium at 4. What is the work input to the refrigerator and the coefficient of performance for the cycle with an ambient at K? A reservoir, shown in Fig. This work is used to drive the refrigerator. Solution: Equate the work from the heat engine to the refrigerator.
If the total waste energy is 5 MW find the rate of energy delivered at the high temperature. Solution: Waste supply:. In this process a strong magnetic field is imposed on a paramagnetic salt, maintained at 1 K by transfer of energy to liquid helium boiling at low pressure. The salt is then thermally isolated from the helium, the magnetic field is removed, and the salt temperature drops. Assume that 1 mJ is removed at an average temperature of 0.
Find the work input to the heat pump and the coefficient of performance with an ambient at K. To achieve this an additional stage of cooling is required beyond that described in the previous problem, namely nuclear cooling. This process is similar to magnetic cooling, but it involves the magnetic moment associated with the nucleus rather than that associated with certain ions in the paramagnetic salt. Find the work input to a Carnot heat pump and its coefficient of performance to do this assuming the ambient is at K.
Heat transfer through the walls and ceilings is estimated to be kJ per hour per degree temperature difference between the inside and outside. The condensers are to be cooled with river water see Fig. Estimate the temperature rise of the river downstream from the power plant. Which fuel would you buy and why? Find the required minimum heat transfer area. Solution: 7. Find the required power input to the heat pump. The heat engine drives a heat pump that delivers QH2 at Troom using the atmosphere as the cold reservoir.
Is this a better set-up than direct room heating from the furnace? Is it? The collected energy powers a heat engine which rejects heat at 40 C.
If the heat engine should deliver 2. Find the rate of work into the heat pump. It is heated to K by heat transfer from a reversible heat pump that receives energy from the ambient at K besides the work input. Use constant specific heat at K. Integrate dW with temperature to find the required heat pump work. 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. It rejects heat at a given low temperature TL.
To design the heat engine for maximum work output show that the high temperature, TH. The heat engine runs until the air temperature has dropped to K and then stops. Assume constant specific heat capacities for air and find how much work is given out by the heat engine. A not max. The high and low temperatures are K and K respectively. Find the specific volume and pressure at all 4 states in the cycle assuming constant specific heats at K..
During the heat rejection the pressure changes from 90 kPa to kPa. Find the high and low temperature heat transfer and the net cycle work per unit mass hydrogen. Make a listing of the coefficient of performance and compare those to corresponding Carnot cycle devices operating between the same temperature reservoirs. Solution: Discussion English Unit Problems. Solution: From solution to problem 6. Assume the same pump work and heat transfer to the boiler as given, how much turbine power could be produced if the plant were running in a Carnot cycle?
Estimate the amount of power needed to operate the airconditioner. A heat engine receives a QH from the bed and rejects heat to the ambient at R. The rock bed therefore cools down and as it reaches R the process stops.
The condenser cooling water comes from a cooling tower at 60 F. Similarly, the H2O leaves the cooling tower and enters the condenser at 60 F, and leaves the condenser at some higher temperature. 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 proportional to the temperature difference as Q. Solution: Max Perf. For several different summer outdoor temperatures estimate the percent savings in electricity if the house is kept at 77 F instead of 68 F. A reservoir is available at F and the ambient temperature is 80 F, as shown in Fig. Thus, work can be done by a cyclic heat engine operating between the F reservoir and the ambient. The energy is supplied by a heat pump with a low temperature of 50 F.
The collected energy powers a heat engine which rejects heat at F. The heat is supplied by a Carnot heat pump operating from a low-temperature reservoir at 60 F. It is heated to R by heat transfer from a reversible heat pump that receives energy from the ambient at R besides the work input. Use constant specific heat at 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 temperature has dropped to R and then stops. The high and low temperatures are R and R respectively. Find the specific volume and pressure at all 4 states in the cycle assuming constant specific heats at 80 F. New 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Old new 1 2 3 new 4 5 new 7 8 9 10 11 new 13 new 15 6 16 12 17 new new new 25 New 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 Old new 29 28 27 new new new 20 21 22 30 31 new new 33 34 new 35 36 37 38 39 new 40 41 New 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 Old 61 new 42 43 44 45 46 new 48 new 49 51 53 54 new 56 57 new 58 55 60 59 14 52 new New 82 Old 50 The problems that are labeled advanced are: New 76 77 78 Old 23 26 32 New 79 80 81 Old 47 new new The English unit problems are: New 83 84 85 86 87 88 89 90 91 92 93 94 Old new mod new New 95 96 97 98 99 Old new new New Old new new new new new 8.
Show that these cycles satisfy the inequality of Clausius. Show the cycle on a T—s diagram and find the quality of the water at the beginning and end of the heat rejection process. Determine the net work output per kilogram of water and the cycle thermal efficiency.
From the definition of the Carnot cycle, two constant s and two constant T processes.
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