AREN 2110: Thermodynamics Review Problems, part 2 Fall 2004

Transcription

1 1. Engineers are designing a refrigerator that will take in heat from a cold box kept at -3 o C and reject heat to a room maintained at 22 o C. They want to know the highest performance theoretically possible for a refrigerator operating under those conditions, in order to understand the limits for their new device. a) Draw the process diagram for the refrigeration cycle with the highest possible coefficient of performance. The minimum entropy of the system = S 1 and the maximum entropy = 4S 1. Use the temperature-entropy graph below. Number process endpoints and put arrows to show direction. T vs S T (K) S (KJ/K) 5 b) Calculate the coefficient of performance for this refrigeration cycle from part a c) Calculate the cooling capacity of this refrigerator from part a, in terms of S 1. 1

2 d) Calculate the required work input for the refrigeration cycle from part a), in terms of S 1. e) What is the maximum amount of entropy change in the system for any one process, in terms of S 1? f) In which process is the maximum heat transferred? How much is the maximum heat transfer in terms of S 1? g) What is the generated entropy for the entire cycle, in terms of S 1? 2

3 2. Air is expanded in an adiabatic turbine to produce 1,000 kw power, as below. Inlet: P = 1,000 kpa T = 500 o C Outlet: P = 100 kpa T = 200 o C a) Calculate the mass flow rate of air required. b) Calculate the rate of entropy generated in the surroundings. c) If the turbine process were reversible, the entropy generated in the surroundings would - justify your answer -: 3

4 1. Increase 2. Decrease 3. Stay the same 4. Can't tell 3. Answer the five the multiple-choice questions below by circling the best choice (or choices if indicated). Justify all answers. Partial credit will be given for a good attempt to analyze the question even if the answer is incorrect. a) According to the 1 st Law of Thermodynamics, the maximum efficiency of a heat engine could be - justify your answer -: 5. 1 Q 6. 1 Q 7. T 1 T out L H in 8. none of the above b) Steam entering a turbine at 10 MPa and 350 o C is expanded in a reversible adiabatic process. The entropy of the steam at the turbine outlet will be - justify your answer: kj/kg-k kj/kg-k kj/kg-k 4. none of the above c) Air is throttled in an adiabatic throttling valve to reduce the pressure. The entropy of the air from inlet to outlet will - justify your answer - 1. stay the same 2. increase 3. decrease 4. cannot tell from information given 4

5 d) It is possible for a process that is adiabatic to be (circle ALL that are correct) - justify your answer 1. reversible and isentropic 2. isentropic and irreversible 3. isothermal and reversible 4. isothermal and irreversible e) The process of saturated steam condensing to saturated liquid at constant pressure in a heat exchanger cannot be - choose one and justify your answer: 1. irreversible 2. reversible 3. isentropic 4. isothermal 5

6 4. Water is heated by an electric heater in an insulated hot water heater tank. The water entering the tank is 15 o C and the heated water leaving the tank is 65 o C. In order to be used in showers, the hot water has to be cooled by adding 15 o C water to reach the desired shower water temperature of 45 o C. Assume the shower pipes are insulated as well. a) Calculate the annual electric power requirement for a family that takes four 15-minute showers per day every day and the shower water flow rate is 15 kg/min. (HINT: this is a 1 st law problem. Recall that enthalpy for an incompressible liquid is a function of temperature only! That is all liquid water at the same temperature has the same enthalpy) b) If the cost of electricity is $0.075 per kilowatt-hour (kwh), calculate the annual cost of showering 6

7 c) What is the annual total entropy generation rate for heater and shower in kj/k-yr? HINT: entropy for an ideal incompressible liquid is a function of temperature only! Than is, all liquid water at the same temperature has the same entropy.) d) In an effort to conserve energy, the family has replaced the shower head with a water-saving shower that reduces the flow to 7 kg/min. What are the savings in annual power cost? 7