Last Name First Name CIRCLE YOUR LECTURE BELOW: 8: am : am : pm Prof. Memon Prof. Naik Prof. Lucht EXAM # INSTRUCTIONS. This is a closed book examination. An equation sheet and all needed property tables are provided. In line with current ME policy, you may use only the TI-X IIS calculator for this exam. The single-line TI-XA is also acceptable although not recommended.. Do not hesitate to ask the instructor if you do not understand a problem statement.. Start each problem on the same page as the problem statement. Write on only one side of the page. Materials on the back side of the page will not be graded. There are blank pages following each of the three problems for your work. 4. Put only one problem on a page. A second problem on the same page will not be graded. 5. For your own benefit, please write clearly and legibly. Maximum credit for each problem is indicated below. 6. After you have completed the exam, at your seat, put your papers in order. This may mean that you have to remove the staple and re-staple. Do not turn in loose pages. 7. Once time is called you will have three minutes to turn in your exam. Points will be subtracted for exams turned in after these three minutes. Problem Possible Score 5 5 Total
Name Problem # ( points) Given: A rigid, well-insulated tank with a volume of. m initially contains air at a pressure p = kpa and a temperature of T =4 K. The tank is connected to a supply line containing air at a pressure pl kpa and a temperature TL K. The valve is opened and air flows into the rigid tank and then the valve is closed. The temperature immediately after the valve is closed is measured to be K. Find: (a) Draw a control volume on the diagram below. (b) State the assumptions that you are making and list the basic equations for your analysis. (c) Find the amount of mass () entering the tank. (d) Calculate the pressure (kpa) at state. Rigid Tank, Volume. m p = kpa T = 4 K Valve T = K Supply Line p L = kpa T L = K Assumptions: 4 () Well-insulated Q () Rigid tank W () ΔPE = (4) ΔKE = (5) uniform flow at inlet, hi hl (6) Air is ideal gas
Basic equations: dm mi mi m m de Q W mihi U U mu mu m m hl 8.4 R kmol K pmrat Ra.87 MW a 8.97 K kmol m p m m.87 RT a.87 K K m u h mu mu m m hl m u h From Table A : m.87 86.6 46.4.87 759.88.98 845.46.4.7 m m m.98.87.47 i m R T p.98.87 K a m m p 4 kpa K L L 4
4 Name Problem # (5 points) Given: A piston-cylinder system contains 4 of water vapor at an initial temperature of T = 5 C with an initial quality of x =. (the initial state of the fluid is saturated vapor). Heat transfer occurs from the piston-cylinder system to a reservoir with a temperature of 5 C. The heat transfer occurs until the saturated vapor is condensed completely, and then the heat transfer continues until at the final fluid state, the temperature T = 5 C. The ambient conditions aret C, p bar. Find: (a) Draw a diagram and control volume for the system at state. (b) State the assumptions that you are making and list the basic equations for your analysis. (c) Calculate the heat transfer Q () for the process. (d) Calculate the exergy destruction E d, () for the process. T x 5C. T res = 5 C Comp. Liq. T res = 5 C
5 Assumptions: () Closed system () ΔPE = () ΔKE = (4) Quasi-equilibrium process Basic equations: dm m m de Q W U U Q W During the condensation and cooling process, the piston is free to move and the pressure of the fluid in the cylinder remains constant. v v mp v v W mpd mp d v v Q m u u m p p m h h EITHER: ds Q Q S S T T E b T d, S S ms s b Q Q OR: de T d Q W p E d, T E E Q W p E d, E E U U p T S S T U U p T S S Q W p Q E d, E T S S d, T T b Q Q T S S T
6 At states and, from Table A-, T 5C x., p 475.8 kpa, u 559.5, m h 746.5, s 6.879, v.95 K T 5 C, p 475.8 kpa u u f 5C 9., h h f 5C 9., s s f 5C.78, K f v v 5C. m 5 Q mh h 9. 746.5 Q,49 Q,49 ms s.786.879 K 5 7.5 K 6.87 K Ed, T 9.5 K.8 4 K 5
7 Name Problem # (5 points) Given: An open water feedwater heater has two inlet streams and an exit stream. Inlet stream has a mass flow rate of 5 /s and the water has a pressure of bar and temperature of 5 C. Inlet stream has a mass flow rate of 5 /s and the water has a pressure of bar and temperature of 8 C. The water exits the feedwater heater as a saturated vapor at bar. The feedwater heater is also in contact with a 4 C temperature reservoir; heat transfer from the feedwater heater other than to or from this reservoir is negligible. The ambient conditions are T K, p bar. Find: (a) Draw a control volume on the diagram below. (b) State the assumptions that you are making and list the basic equations for your analysis. (c) Determine the rate of heat transfer Q (kw) to or from the feedwater heater. (d) Determine the rate of exergy destruction E d, (kw) for the feedwater heater. m =5 /s p = bar T =5 C Tres=4 C p = bar x =. m =5 /s p = bar T =8 C
8 Name System Sketch m =5 /s p = bar T =5 C Tres=4 C p = bar x =. Q m =5 /s p = bar T =8 C Assumptions: 4 () Open system () Steady state () Uniform flow at inlets and exits (4) ΔKE = (5) ΔPE = (6) Rigid control volume W (7) No heat loss to surroundings Basic equations: dm, m m m m m m / s de Q W V m V h gz m h gz V m h gz Q mh mh mh EITHER:
9 ds Q ms ms ms T d, b ms ms ms E T Q OR: Alternate approach: de T Q W p d f f f D, T T E Q m e m e m e Q m e m e m m e D, f f f f f f E T Q m e e m e e D, f f f f e e h h T s s f f e e h h T s s f f m e m e m e E At states, from Table A-4, T 5 C, p bar h 486., s 8.5 K At state, from Table A-: T 8 C, p bar compressed liquid h h f 8C 4.9, s s f 8C.75 K At state, from Table A-: p bar, x., saturated vapor h h g bar 75., s sg bar 6.999 K From the first law, Q mh mh mh 75. 5 86. 5.9 s s s Q, 5, 5 kw s Calculating the entropy generation we obtain: 4
EITHER:, 5 Q s ms ms ms 6.999 7.5K s K 5 8.5 5.75 s K s K kw.47.47 s K K kw Ed, T K.47,4 kw 6 K OR: Alternate solution e e h h T s s f f 86. 75. K 8.5 6.999 6.7 K e e h h T s s f f.9 75. K.75 6.999 65.4 K T ED, Q m e f e f m e f e f E D,, 5 5 6.7 5 65.4 67.5 s s s,4,4 kw 6 s