SOLUCIONARIO EX P2

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FÓRMULAS
GÁS IDEAL:
CICLO OTTO:
DIESEL:
BOMBA DE AQUECIMENTO E REFRIGERADORES
7.15 A gasoline engine produces 20 hp using 35 kW of heat transfer from burning fuel. What is its thermal efficiency and how much power is rejected to the ambient?
7.19 A coal fired power plant has an efficiency of 35% and produces net 500 MW of electricity. Coal releases 25 000 kJ/kg as it burns so how much coal is used per hour? 
From the definition of the thermal efficiency and the energy release by the combustion called heating value HV we get
7.25 A water cooler for drinking water should cool 25 L/h water from 18oC to 10oC using a small refrigeration unit with a COP of 2.5. Find the rate of cooling required and the power input to the unit.
7.30 A car engine delivers 25 hp to the driveshaft with a thermal efficiency of 30%. The fuel has a heating value of 40 000 kJ/kg. Find the rate of fuel consumption and the combined power rejected through the radiator and exhaust. 
Solution:
7.31 R-410a enters the evaporator (the cold heat exchanger) in an A/C unit at -20oC, x = 28% and leaves at -20oC, x = 1. The COP of the refrigerator is 1.5 and the mass flow rate is 0.003 kg/s. Find the net work input to the cycle
SEGUNDA LEI E PROCESSOS
7.38
7.43 The water in a shallow pond heats up during the day and cools down during the night. Heat transfer by radiation, conduction and convection with the ambient thus cycles the water temperature. Is such a cyclic process reversible or irreversible? 
Solution: 
All the heat transfer takes place over a finite ΔT and thus all the heat transfer processes are irreversible. 
Conduction and convection have ΔT in the water, which is internally irreversible and ΔT outside the water which is externally irreversible. The radiation is absorbed or given out at the water temperature thus internally (for absorption) and externally (for emission) irreversible.
CICLOS DE CARNOT E TEMPERATURAS ABSOLUTAS
7.45 Carnot cycle heat engine has an efficiency of 40%. If the high temperature is raised 10% what is the new efficiency keeping the same low temperature?
7.51 A car engine burns 5 kg fuel (equivalent to addition of QH) at 1500 K and rejects energy to the radiator and the exhaust at an average temperature of 750 K. If the fuel provides 40 000 kJ/kg what is the maximum amount of work the engine can provide?
7.59 Calculate the amount of work input a refrigerator needs to make ice cubes out of a tray of 0.25 kg liquid water at 10oC. Assume the refrigerator works in a Carnot cycle between –8oC and 35oC with a motor-compressor of 750 W. How much time does it take if this is the only cooling load?
7.65 A thermal storage is made with a rock (granite) bed of 2 m3 which is heated to 400 K using solar energy. A heat engine receives a QH from the bed and rejects heat to the ambient at 290 K. The rock bed therefore cools down and as it reaches 290 K the process stops. Find the energy the rock bed can give out. What is the heat engine efficiency at the beginning of the process and what is it at the end of the process?
7.70 Sixty kilograms per hour of water runs through a heat exchanger, entering as saturated liquid at 200 kPa and leaving as saturated vapor. The heat is supplied by a Carnot heat pump operating from a low-temperature reservoir at 16°C. Find the rate of work into the heat pump.
VARIAÇÃO FINITA DE TEMPERATURA, TROCA DE CALOR
7.78 The ocean near Havaii has 20oC near the surface and 5oC at some depth. A power plant based on this temperature difference is being planned. How large an efficiency could it have? If the two heat transfer terms (QH and QL) both require a 2 degree difference to operate what is the maximum efficiency then?
7.79 A refrigerator keeping 5oC inside is located in a 30oC room. It must have a high temperature ΔT above room temperature and a low temperature ΔT below the refrigerated space in the cycle to actually transfer the heat. For a ΔT of 0, 5 and 10oC respectively calculate the COP assuming a Carnot cycle
7.91 On a cold (–10oC) winter day a heat pump provides 20 kW to heat a house maintained at 20oC and it has a COPHP of 4. How much power does the heat pump require? The next day a winter storm brings the outside to -15oC, assuming the same COP and the same house heat transfer coefficient for the heat loss to the outside air. How much power does the heat pump require then?
CICLO DE CARNOT DE GÁS IDEAL
7.92 Hydrogen gas is used in a Carnot cycle having an efficiency of 60% with a low temperature of 300 K. During the heat rejection the pressure changes from 90 kPa to 120 kPa. Find the high and low temperature heat transfer and the net cycle work per unit mass of hydrogen
7.93 Carbon dioxide is used in an ideal gas refrigeration cycle, reverse of Fig. 7.24. Heat absorption is at 250 K and heat rejection is at 325 K where the pressure changes from 1200 kPa to 2400 kPa. Find the refrigeration COP and the specific heat transfer at the low temperature.
7.94 An ideal gas Carnot cycle with air in a piston cylinder has a high temperature of 1200 K and a heat rejection at 400 K. During the heat addition the volume triples. Find the two specific heat transfers (q) in the cycle and the overall cycle efficiency.
CAPITULO 8
INEGUALDADE DE CLAUSIUS
8.18 A heat engine receives 6 kW from a 250oC source and rejects heat at 30oC. Examine each of three cases with respect to the inequality of Clausius
8.19 Use the inequality of Clausius to show that heat transfer from a cold space towards a warmer space without work is an impossible process i.e. a heat pump with no work input
8.22 Let the steam power plant in Problem 7.35 have 700oC in the boiler and 40oC during the heat rejection in the condenser. Does that satisfy the inequality of Clausius? Repeat the question for the cycle operated in reverse as a refrigerator
ENTROPIA DE SUBSTANCIA PURA
8.27
8.31Two kg water at 200 kPa with a quality of 25% has its temperature raised 20oC in a constant pressure process. What is the change in entropy?
PROCESSOS REVERSÍVEIS
8.41 R-410a at 1 MPa and 60oC 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 for this process.
8.48 One kilogram of carbon dioxide in a piston/cylinder at 120°C, 1400 kPa, shown in Fig. P8.48, is expanded to 800 kPa in a reversible adiabatic process. Find the work and heat transfer.
8.54 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.
ENTROPIA DE UM LIQUIDO OU SÓLIDO
8.70 
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 change of the milk
8.73 
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 added and how much was the entropy changed?
8.76 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 steel-water entropy change?
ENTROPIA DE GASES IDEAIS
8.89 
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.
8.98 
Argon in a light bulb is at 90 kPa and 20oC when it is turned on and electric input now heats it to 60oC. Find the entropy increase of the argon gas.
PROCESSOS POLITRÓPICOS
8.107 
A piston/cylinder contains air at 300 K, 100 kPa. It is now compressed in a reversible adiabatic process to a volume 7 times as small.Use constant heat capacity and find the final pressure and temperature, the specific work and specific heat transfer for the process.
GERAÇÃO DE ENTROPIA
8.128 
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 for the process.
8.137 
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.
8.146 
A rigid container with volume 200 L is divided into two equal volumes by a partition, shown in Fig. P8.146. Both sides contain nitrogen, one side is at 2 MPa, 200°C, and the other at 200 kPa, 100°C. The partition ruptures, and the nitrogen comes to a uniform state at 70°C. Assume the temperature of the surroundings is 20°C, determine the work done and the net entropy change for the process.
TAXAS OU FLUXO DE ENTROPIA
8.161 
Reconsider the heat pump in the previous problem and assume it has a COP of 2.5. What are the fluxes of entropy in and out of the heat pump and the rate of entropy generation inside it?
8.165 
A car engine block receives 2 kW at its surface of 450 K from hot combustion gases at 1500 K. Near the cooling channel the engine block transmits 2 kW out at its 400 K surface to the coolant flowing at 370 K. Finally, in the radiator the coolant at 350 K delivers the 2 kW to air which is at 25 C. Find the rate of entropy generation inside the engine block, inside the coolant and in the radiator/air combination.
ESTADO ESTACIONARIO REVERSIVEL
9.20
A compressor in a commercial refrigerator receives R-410a at -25oC and x = 1. The exit is at 2000 kPa and the process assumed reversible and adiabatic. Neglect kinetic energies and find the exit temperature and the specific work
9.27 
A flow of 2 kg/s saturated vapor R-410a at 500 kPa is heated at constant pressure to 60oC. The heat is supplied by a heat pump that receives heat from the ambient at 300 K and work input, shown in Fig. P9.27. Assume everything is reversible and find the rate of work input.
9.39 
A reversible adiabatic compression of an air flow from 20oC, 100 kPa to 200 kPa is followed by an expansion down to 100 kPa in an ideal nozzle. What are the two processes? How hot does the air get? What is the exit velocity?
9.44 
A two-stage compressor having an interstage cooler takes in air, 300 K, 100 kPa, and compresses it to 2 MPa, as shown in Fig. P9.44. The cooler then cools the air to 340 K, after which it enters the second stage, which has an exit pressure of 15.74 MPa. Both stages are adiabatic, and reversible. Find q in the cooler, total specific work, and compare this to the work required with no intercooler. 
Solution:
PROCESSO TRANSIENTE
9.50 
An underground salt mine, 100 000 m3 in volume, contains air at 290 K, 100 kPa. The mine is used for energy storage so the local power plant pumps it up to 2.1 MPa using outside air at 290 K, 100 kPa. Assume the pump is ideal and the process is adiabatic. Find the final mass and temperature of the air and the required pump work
TRABALHO DE EIXO REVERSIVEL, EQUAÇÃO DE BERNOULLI
9.66 
A small pump is driven by a 2 kW motor with liquid water at 150 kPa, 10°C entering. Find the maximum water flow rate you can get with an exit pressure of 1 MPa and negligible kinetic energies. The exit flow goes through a small hole in a spray nozzle out to the atmosphere at 100 kPa. Find the spray velocity.
ESTADO ESTACIONARIO, PROCESSO IRREVERSIVEL
9.92 
Air at 1000 kPa, 300 K is throttled to 500 kPa. What is the specific entropy generation?
9.99 
A counter flowing heat exchanger has one line with 2 kg/s at 125 kPa, 1000 K entering and the air is leaving at 100 kPa, 400 K. The other line has 0.5 kg/s water coming in at 200 kPa, 20°C and leaving at 200 kPa. What is the exit temperature of the water and the total rate of entropy generation?
PROCESSO TRANSIENTE
9.109 
A 1-m3 rigid tank contains 100 kg R-410a at ambient temperature, 15°C. A valve on top of the tank is opened, and saturated vapor is throttled to ambient pressure, 100 kPa, and flows to a collector system. During the process the temperature inside the tank remains at 15°C. The valve is closed when no more liquid remains inside. Calculate the heat transfer to the tank and total entropy generation in the process.
9.112 
An 0.2 m3 initially empty container is filled with water from a line at 500 kPa, 200°C until there is no more flow. Assume the process is adiabatic and find the final mass, final temperature and the total entropy generation.
EFICIENCIA DO DISPOSITIVO
9.146 
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 same exit pressure. 
Solution:
CICLO SIMPLES DE RANKINE
CICLO DE REAQUECIMENTO
AQUECEDORES COM ALIMENTAÇÃO ABERTO
11.42 
A Rankine cycle operating with ammonia is heated by some low temperature source so the highest T is 120oC at a pressure of 5000 kPa. Its low pressure is 1003 kPa and it operates with one open feedwater heater at 2033 kPa. The total flow rate is 5 kg/s. Find the extraction flow rate to the feedwater heater assuming its outlet state is saturated liquid at 2033 kPa. Find the total power to the two pumps.
11.45 
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 fraction of extraction steam flow and the two specific pump work inputs. 
Solution:
AQUECEDORES COM ALIMENTAÇÃO FECHADA
CICLOS NÃO IDEAIS
11.65 
A steam power plant operates with a high pressure of 4 MPa and has a boiler exit of 600oC receiving heat from a 700oC source. The ambient at 20oC provides cooling to maintain the condenser at 60oC, all components are ideal except for the turbine which has an isentropic efficiency of 92%. Find the ideal and the actual turbine exit qualities. Find the actual specific work and specific heat transfer in all four components. 
Solution:
COGERAÇÃO
11.72 
A boiler delivers steam at 10 MPa, 550°C to a two-stage turbine as shown in Fig. 11.17. After the first stage, 25% of the steam is extracted at 1.4 MPa for a process application and returned at 1 MPa, 90°C to the feedwater line. The remainder of the steam continues through the low-pressure turbine stage, which exhausts to the condenser at 10 kPa. One pump brings the feedwater to 1 MPa and a second pump brings it to 10 MPa. Assume the first and second stages in the steam turbine have isentropic efficiencies of 85% and 80% and that both pumps are ideal. If the process application requires 5 MW of power, how much power can then be cogenerated by the turbine? 
Solution:
CICLOS DE REFRIGERAÇÃO
11.91 
A small heat pump unit is used to heat water for a hot-water supply. Assume that the unit uses ammonia and operates on the ideal refrigeration cycle. The evaporator temperature is 15°C and the condenser temperature is 60°C. If the amount of hot water needed is 0.1 kg/s, determine the amount of energy saved by using the heat pump instead of directly heating the water from 15 to 60°C. 
Solution:
CICLOS DE ABSORÇÃO DE AMONIA
CICLO DE BRAYTON
12.20 
A Brayton cycle produces net 50 MW with an inlet state of 17oC, 100 kPa and the pressure ratio is 14:1. The highest cycle temperature is 1600 K. Find the thermal efficiency of the cycle and the mass flow rate of air using coldair properties.
CICLO DE MOTOR A JATO
12.48 
Consider an air standard jet engine cycle operating in a 280 K, 100 kPa environment. The compressor requires a shaft power input of 4000 kW. Air enters the turbine state 3 at 1600 K, 2 MPa, at the rate of 9 kg/s, and the isentropic efficiency of the turbine is 85%. Determine the pressure and temperature entering the nozzle at state 4. If the nozzle efficiency is 95%, determine the temperature and velocity exiting the nozzle at state 5. 
Solution:
12.51 
The turbine in a jet engine receives air at 1250 K, 1.5 MPa. It exhausts to a nozzle at 250 kPa, which in turn exhausts to the atmosphere at 100 kPa. The isentropic efficiency of the turbine is 85% and the nozzle efficiency is 95%. Find the nozzle inlet temperature and the nozzle exit velocity. Assume negligible kinetic energy out of the turbine.
CICLO OTTO
12.65 
Suppose we reconsider the previous problem and instead of the standard ideal cycle we assume the expansion is a polytropic process with n = 1.5. What are the exhaust temperature and the expansion specific work?
12.70 
Answer the same three questions for the previous problem, but use variable heat capacities (use table A.7). 
A gasoline engine takes air in at 290 K, 90 kPa and then compresses it. The combustion adds 1000 kJ/kg to the air after which the temperature is 2050 K. Use the cold air properties (i.e. constant heat capacities at 300 K) and find the compression ratio, the compression specific work and the highest pressure in the cycle. 
Solution:
12.75 
An Otto cycle has the lowest T as 290 K and the lowest P as 85 kPa, the highest T is 2400 K and combustion adds 1200 kJ/kg as heat transfer. Find the compression ratio and the mean effective pressure. 
Solution:
CICLO DIESEL
12.92 
The worlds largest diesel engine has displacement of 25 m3 running at 200 RPM in a two stroke cycle producing 100 000 hp. Assume an inlet state of 200 kPa, 300 K and a compression ratio of 20:1. What is the mean effective pressure?
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