EXAM # 1 ME 300 SP2017

Transcription

1 CIRCLE YOUR LECTURE BELOW: 8:3 am :3 am 3:3 pm Prof. Lucht Prof. Chen Prof. Goldenstein EXAM # ME 3 SP7 INSTRUCTIONS. Please place all your electronics, including but not limited to cell phones, computers, watches, tablets, etc., into your bag and store your bag under your seat.. 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-3X IIS calculator for this exam. The single-line TI-3XA is also acceptable although not recommended. 3. Do not hesitate to ask the instructor if you do not understand a problem statement. 4. 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. 5. Put only one problem on a page. A second problem on the same page will not be graded. 6. If you give multiple solutions, you will receive only a partial credit although one of the solutions might be correct. Cross out any solutions that you do not want to be graded. 7. For your own benefit, please write clearly and legibly. Maximum credit for each problem is indicated below. 8. 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. 9. 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.. Keep your eyes on your own paper. If you are caught cheating you will get a zero for the exam and your name will be turned over to the Dean of Students. Problem Possible Score Total

2 Problem # (3 points) Circle the correct answer for each question. There is one and only one correct answer for each question. () (4 points) What happens to specific volume of an ideal gas when the pressure is doubled and the absolute temperature is halved? Doubled Quartered Quadrupled () (4 points) Is the statement correct: Exergy is destroyed whenever there is a change in entropy? Yes No Insufficient information to judge (3) (4 points) For an ideal gas, are temperature and volume independent properties? Yes No Insufficient information to judge (4)(4 points) A system undergoes a process from an initial state to a final state. For the given change in entropy S S, for which process will the entropy generation σ be the greatest? Adiabatic process Isothermal heat rejection process Isothermal heat addition process

3 3 (5) (4 points) A piston-cylinder device contains an ideal gas. What happens to the entropy of the gas during a reversible, isothermal process? Never increases Sometimes increases Insufficient information (6) (4 points) A saturated liquid-vapor mixture of water has a temperature of 5 C. Given no further information about the state of the mixture, which of the following thermodynamic properties can be determined? Enthalpy Pressure Specific enthalpy Specific volume (7) (4 points) Is this statement correct: Only irreversible effects destroy exergy during thermodynamic processes? Yes No Insufficient information to judge 8. (4 points) For which of the following processes is entropy always generated? Frictionless work addition Heat transfer across a finite temperature gradient Isothermal heat transfer

4 4 Problem # (34 points) Given: A rigid, well-insulated tank initially contains air at a pressure p. bars and a temperature oft 95 K. The tank is connected to a supply line containing air at a pressure pl 3 bars and a temperature TL 6 K. The valve is opened and air flows into the rigid tank for a period of time, and then the valve is closed. The air temperature in the tank immediately after the valve is closed is R.87 K. In this problem, if measured to be 7 K. The specific gas constant for air is a you need to use the expression for the absolute entropy of an ideal gas, st (, p) s o ( T) Rln ( p p) assume p atm bar., Find: (a) Draw an appropriate 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 p (kpa) at state. (e) Calculate the entropy generation σ (/K) for the control volume that you have drawn for the tank filling process. Assumptions: () Well-insulated Q () Rigid tank W

5 5 (3) ΔPE (4) ΔKE (5) uniform flow at inlet, hi hl (6) Air is ideal gas Basic equations: dm de ds m m m m i Q Q T a b p mr T i W + ( ) mh U U mu mu m m h i i L + ms + σ S S m s ms m m s + σ i i L Solution: ( h ) m u c mu mu m m hl m u h From Table A : u.49 u 5.33 hl 67. m (. ) (. ) m m m i ( d) p (. ).87 ( 95 K ) a p 3 a 3 m mrt 3 (.847 m ) L L K ( 8.38 ).87 ( 7 K ) mrt K p 99 kpa m m 3

6 6 EITHER e σ ms ms m m s m s s + m s s L L L p 9.9 s sl s sl Raln ln +.8 pl K K 3 K p L 3 sl s sl s Raln ln.533 p K K K σ ( 8.38 ) ( ) K K K OR e σ ms ms m m s L p 9.9 s s Ra ln ln +.74 p K K K pl 3 sl s sl Raln ln p K K K p s s Ra ln ln p K K K σ ( 8.38 ) +.74 ( ) ( 6.38 ) K K K K

7 7 Problem #3 (34 points) Given: Steam flows through a turbine at a mass flowrate of m 5 s. At the turbine inlet, the temperature of the steam is T 5 C and the pressure is p 6. bars. At the exit, T C and p.7 bars. Stray heat transfer at the rate of kw occurs from the piston-cylinder system to the surroundings at T C, p. bar. Assume that the outside surface of the turbine is at the ambient temperature T. Find: (a) Draw an appropriate control volume for your analysis on the diagram below. (b) State the assumptions that you are making and list the basic equations for your analysis. (c) Calculate the turbine output power W ( kw ). (d) Calculate the rate of exergy destruction E d, ( kw ) for the control volume that you have drawn. (e) Calculate the exergetic efficiency ε t of the turbine as the ratio of actual work per unit mass flow to the difference in flow exergy between the initial and final states. (a) (b) Assumptions: () Open system () ΔPE (3) ΔKE (4) Steady state (5) Uniform flow at inlet, exit (6) Rigid control volume pdv work

8 8 Basic equations: dm m m m de V Q W + m V h + + gz m h + W Q + m h h + gz EITHER: ds Q + ms ms + σ T b Q σ + m s s E T σ d, Tb OR: Alternate approach: de T Q W + p Tb E W + m e e D, f f d + me me E f f D, e e h h T s s f f Solution: (c) At states and, from Table A-4, T 5 C, p 6. bars h 34., s K T C, p.7 bars h 68., s W Q + m ( h h) s s W kw s K EITHER

9 9 Q s Tb 93.5 K s K s K ( d) σ m ( s s ) E d, T σ ( 93.5 K ) kw sk f f e f 936 ( e) e e ( h h ) T ( s s ) ( K) e f ( t ) W m W t 35 kw εt.75 e e m e s f f f f ( e ) ( 5 )( 936 ) K OR ( d) E D, W + m ( e f e f ) e f e f ( h h) T( s s) ( 93.5 K) K e f e f 936 E D, ( 35 kw ) kw s ( e) ( W t m ) W t εt e e m e e f f f 35 kw.75 ( 5 s )( 936 f )