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320 MAE Thermodynamics HW 4 Assignment
February 18, 2009 The homework is due Friday March 6, 2009. Each problem is worth the points indicated. I encourage you to work in small groups to learn this material. However, copying of the solution from another is not acceptable.
1. Multiple Choice: a. Air (cp = 1.005 kJ/kg-k) is heated from 27C to 327C. How much does the specific internal energy of the air change as a result of this heating? (5 points) A) 301.5 kJ/kg decrease B) 301.5 kJ/kg increase C) 215.4 kJ/kg decrease D) 215.4 kJ/kg increase Answer: .
b. Water is heated on an electrical range with a power rating of 1.5 kW for a period of 18 minutes. The initial and final temperatures of the water are 15 C and 85 C and 70 percent of the electrical heat is transferred to the water. What is the mass of water? (5 points) A) 1.4 kg B) 3.9 kg C) 5.5 kg D) 9.2 kg Answer: .
c. A piston-cylinder device contains 5 kg of air at 400 kPa and 30 C. During a quasi-equilibrium isothermal expansion process, 15 kJ of boundary work is done by the system, and 3 kJ of work is done on the system by a paddle wheel. The heat transfer during this process is (5 points) A) Q = 2.4 kJ B) Q = 12 kJ C) Q = 18 kJ D) Q = 60 kJ Answer: .
P (kPa)
2. A piston-cylinder arrangement contains 0.1 kg of air (treated as ideal gas) and undergoes the cycle shown in the figure. (a) Show that 1 kPa-m3 = 1 kJ. (b) Determine the temperatures at Points 1, 2, and 3. (c) Find the work done in the Process from Point 1 to Point 2, the work done in the Process from Point 2 to Point 3, and the work done in the Process from Point 3 to Point 1. (d) Calculate the net heat transfer for this cycle. (20 points)
800
2
T = constant
100
1
0.08
3
V (m3)
3. Determine the enthalpy change (in kJ/kg) for nitrogen when heated from 27 C to 927 C by (a) using the idea gas table, (b) using the average specific heat, (c) integrating Cp(T) (the specific heat as a function of temperature), (d) compare the results from Methods (a) and (b) to that from Method (c) and quantitatively evaluate the error. (20 points)
1
4. Nitrogen expands from the initial state (100 C and 600 kPa) to a final state in such a way that it can approximated be by a polytropic process with n = 1.2. The pressure at the final state is 749.54 mmHg and the final temperature is 276.7 K. (a) Sketch the process on a P-v diagram and place the specific volume values of the initial and the final states on the v-axis. (b) Calculate the work done during the process. (c) Calculate the heat transfer during the process and tell whether the nitrogen gas has adsorbed the heat from the surroundings or not. (15 points) 5. A rigid, well-insulated tank contains 3 kg of a two-phase liquid-vapor mixture of water, initially at 200 kPa with quality of 84%. A paddle wheel stirs the mixture until only saturated vapor remains in the tank. Kinetic and potential energy effects are negligible. (a) Sketch the process on a P-v diagram and place the values of the specific volume of the initial and final states on the v-axis. (b) For the water, determine the amount of energy transferred by work, in kJ. (10 points) 6. A 30 L electrical radiator containing heating oil is placed in a 50 m3 room. Both the room and the oil in the radiator are initially at 10 C. The radiator, with a rating of 1.8 kW, is now turned on. At the same time, heat is lost from the room at an average rate of 0.35 kJ/s. After some time, the average temperature is measured to be 20 C for the air in the room, and 50 C for the oil in the radiator. Taking the density and the specific heat of the oil to be 950 kg/m3 and 2.2 kJ/kg-C, respectively, determine how long the heater is kept on. Assume the room is well-sealed so that there are no air leaks. (10 points) 7. An insulated piston-cylinder device initially contains 0.3 m3 of carbon dioxide at 200 kPa and 27 C. An electric switch is turned on, and a 110 V source supplies current to a resistance heater inside the cylinder for a period of 10 min. The pressure is held constant during the process, while the volume is doubled. Determine the current that passes through the resistance heater. (10 points) We
CO2 200 kPa 27C
Suggested Book Problems to Review: These problems will not be collected, but are suggested as a review. Chapter 4: 1, 7, 12, 19, 26, 35, 39, 42, 48, 49, 60, 65, 68, 74, 79, 86, 94, 104, 119
2

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