MA2007 Tutorials AY2021S2 PDF

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School of Mechanical and Aerospace Engineering MA2007 Thermodynamics (Semester 2, 2020-2021) Tutorial 1 – Heat Engines & Refrigerators; Maximum Performance of Cycles 1. A steam power plant receives heat from a furnace at a rate of 280 GJ/h. Heat loses to the surrounding air from the steam as it passes through the pipes and other components are estimated to be about 8 GJ/h. If the waste heat is transferred to the cooling water at a rate of 145 GJ/h, determine: a) the net power output b) the thermal efficiency of this power plant [35.3 MW, 45.4%] 2. A household refrigerator with a COP of 1.5 removes heat from the refrigerated space at a rate of 60 kJ/min. Determine: a) the electric power consumed by the refrigerator b) the rate of heat transfer to the kitchen air [0.67 kW, 100 kJ/min] 3. A heat pump is used to maintain a house at a constant temperature of 23 °C. The house is losing heat to the outside air through the walls and the windows at a rate of 60,000 kJ/h while the energy contributed within the house from people, lights and appliances amounts to 4,000 kJ/h. For a COP of 2.5, determine the required power input to the heat pump. [Ans: 6.22 kW] 4. An innovative way of power generation involves the utilization of geothermal energy – the energy of hot water that exists naturally underground – as the heat source. If a supply of hot water at 140 °C is discovered at a location where the environmental temperature is 20 °C, determine the maximum thermal efficiency a geothermal power plant built at that location can have. How does it compare with steam power plants using fossil fuels (steam temperature around 500°C)? Also, what would happen to the efficiency if the environmental temperature drops to 0 °C or rises to 40 °C? [Ans: 29.1%, 62.1%, 33.9%, 24.2%] 5. A Carnot heat engine receives heat from a reservoir at 927 °C at a rate of 740 kJ/min and rejects the waste heat to the ambient air at 27 °C. The entire work output of the heat engine is used to drive a refrigerator that removes heat from the refrigerated space at -7 °C and transfers it to the same ambient at 27 °C. Determine (a) the maximum rate of heat removal from the refrigerated space and (b) the total rate of heat rejection to the ambient air. [Ans: (a) 4342 kJ/min, (b) 5082 kJ/min]

School of Mechanical and Aerospace Engineering MA2007 Thermodynamics (Semester 2, 2020-2021) Tutorial 2 – Carnot Cycle; Entropy and Increase of Entropy Principle 1. Consider a Carnot refrigeration cycle executed in a closed system in a saturated liquidvapor mixture region using 0.96 kg of refrigerant-134a as the working fluid. It is known that the maximum absolute temperature in the cycle is 1.2 times the minimum absolute temperature, and the net work input to the cycle is 22 kJ. If the refrigerant changes from saturated vapor to saturated liquid during the heat rejection process, (a) determine the minimum pressure in the cycle, and (b) plot the cycle on T-v and T-s diagrams. [Ans: 0.355 MPa] 2. Air is compressed by a 30 kW compressor from P1 to P2. The air temperature is maintained constant at 25 °C during the process as a result of heat transfer to the surrounding medium at 17 °C. Determine the rate of entropy change of the air on the basis of system. State the assumptions made in solving the problem. [Ans: -0.0101 kW/K] 3. A completely reversible heat pump produces heat at a rate of 300 kW to warm a house maintained at 24 °C. The exterior air which is at 7 °C serves as a source. Calculate the rate of entropy change of the two reservoirs and determine if this heat pump satisfies the second law according to the increase of entropy principle. [Ans: 1.01 kW/K, -1.01 kW/k, 0 kW/K]

4. Water vapour enters a turbine at 6 MPa and 400 °C and leaves the turbine at 100 kPa with the same specific entropy as that at the inlet. Calculate the difference between enthalpy of the water at the turbine inlet and exit. [Ans: -807.4 kJ/K]

School of Mechanical and Aerospace Engineering MA2007 Thermodynamics (Semester 2, 2020-2021) Tutorial 3 – Entropy change of Solids, Liquids and Gases

1. A 12-kg iron block initially at 350°C is quenched in an insulated tank that contains 100 kg of water at 22°C. Assuming the water that vaporizes during the process condenses back in the tank, determine the total entropy change during the process. [Ans: 1.92 kJ/kg] 2.

An adiabatic pump is to be used to compress saturated liquid R-134a at 80 kPa to a pressure of 2.5 MPa in a reversible manner. The measured enthalpy and specific volume at outlet are 12.94 kJ/kg and 0.0007120 m3/kg, respectively. Determine the work input using : (a) First law of thermodynamics from saturated tables, (b) Inlet specific volume and pressure values, and (c) Average specific volume and pressure values. Determine the errors in parts (b) and (c). [Ans: (a) 1.73 kJ/kg, (b) 1.73877 kJ/kg, 0.5%, (c) 1.73091 kJ/kg, 0.05%]

3. An insulated piston-cylinder device initially contains 300 L of air at 120 kPa and 17°C. Air is now heated for 15 min by a 200 W resistance heater placed inside the cylinder. The pressure of air is maintained constant during the process. Determine the entropy change of air, assuming constant specific heats (obtained at 450 K) [Ans: 0.385 kJ/K]

4. An insulated rigid tank is divided into two equal parts by a partition. One part of the tank contains 1.5 kg of air at 250 kPa and 40 °C while the other part is evacuated. The partition is now removed, and the air expands to fill the entire tank. Determine the total entropy change during this process. [Ans: 0.298kJ/K] 1.5 kg air

Vacuum 250 kPa 40 oC

School of Mechanical and Aerospace Engineering MA2007 Thermodynamics (Semester 2, 2020-2021) Tutorial 4 – Reversible Steady-Flow Processes; Isentropic Efficiency of Steady Flow Devices

1. Saturated refrigerant R134-a vapour at 0.14 MPa is compressed reversibly in an adiabatic compressor to 0.8 MPa. Determine the work input to the compressor. If instead of compressing the vapour, the refrigerant is first condensed to a liquid at the same pressure before it is pumped reversibly to the higher pressure, what is the pump power required? [Ans: (a) 36.23 kJ/kg, (b) 0.49 kJ/kg] 2. Air is compressed in a compressor from 95 kPa and 27 °C to 600 kPa following: a. A reversible adiabatic process. Determine the exit temperature and the power required by the compressor per unit mass flow b. An adiabatic process such that its exit temperature is 277 °C. Determine the power required by the compressor per unit mass flow and the isentropic efficiency. c. A polytropic process such that its exit temperature is 200 °C. Determine the power required by the compressor and the heat rejection rate per unit mass flow d. An isothermal process. Determine the power required by the compressor and the heat rejection rate per unit mass flow. Assume an average specific heat based on 400K for (a), (b) and (c) and 300K for (c). Neglect the changes in kinetic and potential energies. Indicate the processes on a P-v diagram with respect to lines of constant temperature. [Ans:(a) 505.6 K, 208.2 kJ/kg, (b) 253.3 kJ/kg, 82.2%, (c) 201.0 kJ/kg, 25.7 kJ/kg, (d) 158.7 kJ/kg, 158.7 kJ/kg] 3. Steam enters an adiabatic turbine at 8 MPa and 500 °C with a mass flow rate of 3 kg/s and leaves at 30 kPa. The isentropic efficiency of the turbine is 0.90. Neglecting the kinetic energy change of the steam, determine (a) the temperature at the turbine exit and (b) the power output of the turbine. [Ans: (a) 69.1°C, (b) 3057 kW] 4. Air at 100 kPa and 20 °C is compressed to 700 kPa steadily and adiabatically at a rate of 2 kg/s. Determine the power required to compress this air if the isentropic efficiency is 95%. [Ans: 459.3 kW]

School of Mechanical and Aerospace Engineering MA2007 Thermodynamics (Semester 2, 2020-2021) Tutorial 5 – Entropy Balance 1. A rigid tank is divided into two equal parts by a partition. One part of the tank contains 1.5 kg of compressed liquid water at 300 kPa and 60°C while the other part is evacuated. The partition is now removed, and the water expands to fill the entire tank. If the final pressure of the tank is 15 kPa, determine: (a) the final temperature in the tank and the heat transfer between the tank and the surroundings (b) the entropy generation during the process if the surroundings temperature is 300 K. [Ans: (a) 53.97°C, -37.5 kJ (b) 0.011 kJ/K] 1.5 kg compress ed liquid

Vacuum

300 kPa 60 oC

2. Air (Cp = 1.005 kJ/kg K) is to be preheated by hot exhaust gases in a cross-flow heat exchanger before it enters the furnace. Air enters the heat exchanger at 95 kPa and 20 °C at a rate of 1.6 m3/s. The combustion gases (Cp = 1.10 kJ/kg K) enters at 180 °C at a rate of 2.2 kg/s and leave at 95 °C. Determine the rate of heat transfer to the air, the outlet temperature of the air, and the rate of entropy generation. [Ans: 205.7 kW, 133.2 °C, 0.091 kW/K ] 3. Long cylindrical steel rods (ρ = 7833 kg/m3) and cp = 0.465 kJ/kg °C) of 10 cm diameter are heat treated by drawing them at a speed of 3 m/min through a 7 m long oven maintained at 900 °C . If the rods enter the oven at 30 °C and leave at 700 °C , determine (a) the rate of heat transfer to the rods in the oven and (b) the rate of entropy generation with the heat transfer process. [Ans: (a) 958.3 kW, (b) 0.85 kW/K]

4. Steam expands in a turbine steadily at a rate of 25,000 kg/h, entering at 8 MPa and 450 °C and leaving at 50 kPa as saturated vapour. If the power generated by the turbine is 4 MW, determine the rate of entropy generation for this process. Assume the surrounding medium is air at 25 °C. [Ans: 8.40 kW/K]

School of Mechanical and Aerospace Engineering MA2007 Thermodynamics (Semester 2, 2020-2021) Tutorial 6 – Refrigeration and Heat Pump Cycles-1 1. A refrigerator uses refrigerant-134a as the working fluid and operates on an ideal vaporcompression refrigeration cycle between 0.12 and 0.7 MPa. The mass flow rate of the refrigerant is 0.05 kg/s. Show the cycle on a T-s diagram with respect to saturation lines. Determine (a) the rate of heat removal from the refrigerated space and the power input to the compressor, (b) the rate of heat rejection to the environment, and (c) the coefficient of performance (COP). [Ans: (a) 7.41 kW, 1.83 kW; (b) 9.24 kW; (c)4.05] 2. Refrigerant-134a enters the compressor of a refrigerator at 140 kPa and -10 °C at a rate of 0.3 m3/min and leaves at 1 MPa. The isentropic efficiency of the compressor is 78 percent. The refrigerant enters the throttling valve at 0.95 MPa and 30 °C and leaves the evaporator as saturated vapor at -18.5 °C. Show the cycle on a T-s diagram, and determine (a) the power input to the compressor, (b) the rate of heat removal from the refrigerated space, and (c) the pressure drop and the heat rate of heat gain in the line between the evaporator and the compressor. [Ans: (a)1.88 kW; (b) 4.98 kW; (c) 1.72 kPa, 0.240 kW] 3. A heat pump using refrigerant-134a heats a house by using underground water at 8°C as the heat source. The house is losing heat at a rate of 60,000 kJ/h. The refrigerant enters the compressor at 280 kPa and 0 °C, and it leaves at 1 MPa and 60 °C. The refrigerant exits the condenser at 30 °C. Determine (a) the power output to the heat pump, (b) the rate of heat absorption from the water, and (c) the increase in electric power input if an electric resistance heater is used instead of a heat pump. [Ans: (a) 3.55 kW;(b) 13.12 kW; (c)13.12 kW]

4. An ideal gas refrigeration cycle using air as the working fluid is to maintain a refrigerated space at -23oC while rejecting heat to the surrounding medium at 27oC. If the pressure ratio of the compressor is 3 and using constant specific heats at room temperature, determine (a) the maximum and minimum temperatures in the cycle, (b) the COP, and (c) the refrigeration rate for a mass flow rate of 0.15 kg/s. [Ans: (a) 342.2 K, 219.2 K; (b) 2.70; (c) 46.43 kJ/s]

School of Mechanical and Aerospace Engineering MA2007 Thermodynamics (Semester 2, 2020-2021) Tutorial 7 – Refrigeration and Heat Pump Cycles-2

1. A two-evaporator compression refrigeration system as shown in the figure uses refrigerant134a as the working fluid. The system operates evaporator 1 at 0 oC, evaporator 2 at -26.4 oC, and the condenser at 800 kPa. The refrigerant is circulated through the compressor at a rate of 0.1 kg/s and the low-temperature evaporator serves a cooling load of 8 kW. Determine the cooling rate of the high-temperature evaporator, the power required by the compressor, and the COP of the system. The refrigerant is saturated liquid at the exit of the condenser and saturated vapour at the exit of each evaporator, and the compressor is isentropic.

[Ans: 6.58 kW, 4.50 kW, 3.24]

2. A gas refrigeration cycle with a pressure ratio of 3 uses helium (an ideal gas with constant specific heats) as the working fluid. The temperature of the helium is -10 °C at the compressor inlet and 50 °C at the turbine inlet. Assuming the isentropic efficiencies of 82% for both the turbine and the compressor, determine (a) the minimum temperature in the cycle, (b) the coefficient of performance (COP), and (c) the mass flow rate of the helium for a refrigeration rate of 12 kW. [Ans: (a) 228. 8 K; (b) 0.413; (c) 0.0676 kg/s]...