ME 200 Thermodynamics I, Spring 2013 CIRCLE YOUR LECTURE BELOW: Div. 5 7:30 am Div. 2 10:30 am Div. 4 12:30 am Prof. Naik Prof. Braun Prof. Bae Div. 3 2:30 pm Div. 1 4:30 pm Div. 6 4:30 pm Prof. Chen Prof. Chen Prof. Hall FINAL EXAM INSTRUCTIONS: This is closed book and closed notes exam. You are only allowed to use the basic equation sheet and property tables attached here, a pen/pencil, and a simple calculator. Show your work clearly and follow the standard problem solving procedure for problems 2 to 4. Although you may not be able to complete the calculations for some of the problems, significant credit for problems 2 to 4 will be given if you draw control mass/volume and list all assumptions, basic equations and methods by which you propose to solve the problem correctly. Do not hesitate to ask the instructor if you do not understand a problem statement. For your own benefit, please write clearly and legibly. Work only on one side of each page. If you need extra space, work on the extra paper available, and clearly indicate problem to which the work refers. If you give multiple solutions, you will receive only a partial credit although one of the solutions might be correct. Delete the solution you do not want graded. Maximum credit for each problem is indicated below. Important Note: The use of PDAs, ipads and other tablets, cell phones, laptop computers, or any other sources of communication (wireless or otherwise) are strictly prohibited during examinations. Doing so is cheating. If you bring a cell phone or other communication device to the examination, they must be turned off prior to the start of the exam, placed in your backpack, and the backpack stored below your seat, and only picked up as you leave the examination room for the final time. They are not to be turned on again until after you have exited the examination room. Otherwise it will be considered a form of cheating and treated as such. Problem Possible Score 1 50 2 50 3 50 4 50 Total 200 1
Problem 1: (50/200 points) The standard problem solving procedure is not required for Problem 1. If required, you should support your answers by providing appropriate arguments, equations, tables, or charts in order to receive a full score. Place your final answer in the box provided. (a) (5 points) Please identify which of the following parameters is not a property: temperature, reduced temperature, pressure, relative pressure, reduced pressure, heat, and specific heat. (b) (5 points) Does h fg increase, decrease, or remain the same when pressure increases? Explain. (c) (5 points) A room is heated by an iron that is left plugged in. Take the entire room, including the iron, as the system. Is this a heat or work interaction? Explain. (d) (5 points) When two water streams are mixed in an adiabatic mixing chamber, can the mixture temperature be lower than the temperature of both stream under a certain condition? Explain. (e) (5 points) In the absence of any friction and other irreversibilities, can a heat engine have an efficiency of 100 percent on the earth? Explain. 2
Problem 1: (Continued) (f) (5 points) Does a cycle for which enough information) Explain. 0 violate the Clausius inequality? (Yes, No, or Not W (g) (5 points) From class we learned that an Otto cycle is more efficient than a Diesel cycle if both cycles operate at the same compression ratio. Is a real diesel engine typically more efficient or less efficient than a gasoline (Otto) engine? Explain. (h) (5 points) A steam power plant operates on a simple, ideal Rankine cycle. Steam enters the turbine as a saturated vapor. Now the heat input in the boiler is increased so that the steam enters the turbine as a superheated vapor, while the boiler pressure and condenser pressure remain unchanged. Does the net work of the cycle increase, decrease, or remain the same? Explain. (i) (10 points) Which requires more work to compress 1 kg/s of steam by a compressor or to compress 1 kg/s liquid water by a pump from 1 bar to 10 bar? Assume internally reversible and adiabatic compression and neglect kinetic and potential energy effects. Explain. 3
Problem 2: (50/200 points) Given: A new air-standard power cycle is proposed. Air undergoes the following four processes inside a piston-cylinder device. Process 1-2: Isothermal compression from P 1 = 100 kpa and T 1 = 300 K to P 2 = 1000 kpa, transferring 198.3 kj/kg heat to the environment; Process 2-3: Constant volume process during which heat is added q 23 = 1000 kj/kg; Process 3-4: Isentropic (reversible and adiabatic) expansion to P 4 = 100 kpa; Process 4-1: Constant pressure process during which heat is rejected. Neglect kinetic and potential energy effects. Assume constant specific heats for air. R air = 0.287 kj/kg K, c v = 0.718 kj/kg K, c p = 1.005 kj/kg K, k = 1.4 Find: (a) Draw the processes of the cycle in the T-s diagram on the next page. Clearly label the states and mark the direction of the process. Do not show any property values on the diagram. The P-v diagram for the cycle is shown on the next page as an example; (b) Complete Table P-1 on the next page (If calculations are need, please show them to receive credits.); (c) Calculate thermal efficiency (%) of the cycle. System sketch: Please show the control mass used. Assumptions: Basic equations: 4
Solution: (a) P 3 T 2 1 4 v s (b) Table P-1 State Pressure Temperature Specific volume Specific internal energy (kpa) (K) (m 3 /kg) (kj/kg) 1 100 300 0.861 215.4 2 1000 300 0.0861 215.4 3 4 100 (c) 5
6
7
Problem 3: (50/200 points) Given: A vapor compression refrigeration cycle uses steam as the working fluid. The evaporator absorbs heat at 35 F. The saturated steam at state 1 has a mass flow rate of 1.0 lb/s and passes a poorly insulated compressor. The steam pressure is increased to 5 psi a after the compression. The heat transfer from the compressor to the surrounding is 100 Btu/s so that h 2 = h 2s. The boundary and surrounding temperature of the compressor is measured to be 540 R. Then the steam rejects heats to the surrounding by the condenser and then passes through the throttling device and evaporator to complete the cycle. Assume there are no pressure drop in condenser and evaporator. Neglect kinetic and potential energy changes. Do not interpolate but use the closest table values. Find: (a) Draw the processes for the cycle on the T-s chart on the next page. Clearly label the states and mark the direction of the processes. Do not show any property values on the chart; (b) Complete Table P-2 on the next page (If calculations are need, please show them to receive credits.); (c) Calculate the work input to the compressor; in Btu/s; (d) Determine the isentropic efficiency of the compressor; (e) Calculate the COP of the refrigerator; (f) Calculate the entropy generation of the compressor, in Btu/s or. System sketch: Please show the control volume used for the compressor. x 3 =0 P 2 =5 psia Condenser T cv =540 R 4 Assumptions: Evaporator T 1 =35 F x 1 =1 Basic equations: 8
Solution: (a) T (b) Table P-2 (c) State P (psi a ) T ( F) h (Btu/lb) s (Btu/lb- R) x or phase 1 0.0999 35 1 2 & 2s 5 SHV 3 5 162.21 130.17 0.2349 0 4 0.0999 35 s 9
10
11
Problem 4: (50/200 points) Given: An inventor has developed a two-phase compressor that consists of an adiabatic phase separation tank, an adiabatic and reversible pump, an adiabatic and reversible compressor, and an adiabatic mixing chamber, as shown in the schematic diagram below. The inventor claims that the use of the two-phase compressor enables an isothermal heat addition and therefore is closer to a Carnot cycle. A two-phase water-steam mixture with a flow rate of 25 kg/s enters the compressor at a pressure of 0.8 bar at state 1. Liquid is separated from the vapor in the adiabatic phase separation tank. The liquid is compressed in the reversible adiabatic pump while the vapor is compressed in the reversible adiabatic compressor. Both flows are mixed in the adiabatic mixing chamber to produce the saturated liquid with a pressure of 6 MPa (state 2) at the exit. Neglect the kinetic and potential energy effects. Assume the water liquid is incompressible. Do not interpolate but use the closest table values. Note that m 1 1 b x m. 1 Find: (a) Depict properly all of the state points (1, 1a, 1b, 2a, 2b, and 2) on the T-s diagram on the next page and show lines of constant pressure of P 1 and P 2 ; (b) Complete Table P-3 in the following page (If calculations are need, please show them to receive credits.); (c) Determine the specific work input requirement for the pump, in kj/kg; (d) Determine the overall entropy generation for the two-phase compressor, in kw/k; (e) Identify which the following components has irresibilities in the two-phase compressor: (1) 2-phase separator, (2) pump, (3) compressor, (4) mixing chamber, (5) none of these. System sketch: Please show the control volume you used for part (d). Assumptions: 12
Basic equations: Solution: (a) T (b) Table P-3 (c) State P (MPa) 1 0.08 h (kj/kg) s (kj/kg K) x/phase 1a 0.08 391.66 1.2329 0 1b 0.08 2665.8 7.4346 1 2a 6 2b 6 2 6 0 s (-) 13
14
15