ME 200 Exam 2 October 22, :30 p.m. to 7:30 p.m.

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1 CIRCLE YOUR LECTURE BELOW: First Name Solution Last Name 7:0 a.m. 8:0 a.m. 10:0 a.m. 11:0 a.m. Boregowda Boregowda Braun Bae :0 p.m. :0 p.m. 4:0 p.m. Meyer Naik Hess ME 00 Exam October, 015 6:0 p.m. to 7:0 p.m. INSTRUCTIONS 1. This is a closed book and closed notes examination. You are proided with an equation sheet and all the needed property tables.. 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 problems and for your work. 4. Put only one problem on a page. Another problem on the same page will not be graded. 5. Identify system boundary, list releant assumptions, and proide solution with appropriate basic equations for problems and. Do not specify Gien or Find on these problems. 6. If you gie multiple solutions, you will receie only a partial credit although one of the solutions might be correct. Delete the solution you do not want graded. 7. For your own benefit, please write clearly and legibly. Maximum credit for each problem is indicated below. 8. After you hae completed the exam, at your seat put your papers in order. This may mean that you hae to remoe the staple and re-staple. Do not turn in loose pages. 9. Once time is called you will hae three minutes to turn in your exam. Points will be subtracted for exams turned in after these three minutes. Problem Possible Score Total 100 1

2 Problem 1 (5 points) Answer the following questions. For Problem 1 only, assumptions need not be stated. No credit will be gien without correct justification een if the answer is correct. (a) Consider isothermal heating processes for two different fluids. What happens to internal energy during the heating process for the following types of fluids? (6 points) Ideal Gas Increases Decreases Remains Same Saturated Vapor Increases Decreases Remains Same For ideal gas, internal energy depends only on temperature or u C dt 0 Saturated apor becomes superheated apor upon isothermal heating; pressure must change either in non-flow or flow system (b) In a certain process, the temperature of an ideal gas increases by 800 K. The change in specific internal energy and specific enthalpy during this process is measured to be 1600 / and 100 /, respectiely. Are the gien measurements possible? Justify your answer with equation(s). (6 points) Yes No Insufficient Information hup For an ideal gas: P RT h u RT hurt hu u h impossible

3 Problem 1 (continued) (c) An ideal gas flows steadily through a rigid, constant area duct. Its temperature increases from inlet to exit (T > T 1 ) and its pressure decreases from inlet to exit (P < P 1 ) due to friction. What happens to its density from inlet to exit? Justify your answer with equation(s). (4 points) Increases Decreases Remains Same 1 P For an ideal gas: P RT density decreases since pressure decreases and RT temperature increases + What is the heat transfer for the duct? Justify your answer with equation(s). (4 points) Into the system Out of the system No heat transfer de Q W m h h g z z de Steady 0 ; Rigid W 0 ; Constant area 1 For ideal gas, enthalpy depends only on temperature h h1 when T T1 Q m h h (d) Which of the following most closely approaches an ideal gas state? (5 points) P << P critical, T << T critical P >> P critical, T << T critical P << P critical, T >> T critical P >> P critical, T >> T critical +5 Ideal gas is low density state i.e. applicable at low pressure and high temperature

4 Problem (5 points) Air flowing steadily at the rate of 10 /s is compressed from bar and 1 K (State 1) to.05 bar and K (State ) in a cryogenic application. Air exits the compressor with a elocity of 100 m/s. Critical pressure of air = 7.7 bar Critical temperature of air = 1 K Molecular weight of air = 8.97 /kmol Calculate the flow area (cm ) at the exit of the compressor. Identify system boundary, list assumptions, and proide solution with basic equations. m air 10 s Assumptions - Steady state - One-dimensional flow Basic Equation(s) dm mi i e m e Solution P.05 bar Reduced pressure of air at the compressor exit: PR 0.85 Pcritical 7.7 bar T K Reduced temperature of air at the compressor exit: TR 1.15 Tcritical 1 bar Figure A-1 for compressibility factor: Z 0.8 air is not ideal gas P ZRairT +5 4

5 Problem (continued) Specific olume of air at the compressor exit: R air 8.14 kmol-k K kmol Z R T P air K -K m kpa A Considering mass balance for the air compressor: m 1 air m m Flow area at the compressor exit: A + m m s 4 air m 1110 m m s A 11 cm 5

6 Problem (50 points) A power cycle using steam/water as the working substance is shown below. Steam/water flows steadily through the system at the rate of 5 /s. Heat is added in the boiler and rejected from the condenser. The turbine produces power while the pump consumes power. Steam enters the turbine at 100 bar and 400C (State 1) and expands to 0.1 bar and 90% quality (State ). Saturated liquid at 0.1 bar (State ) leaes the condenser and it is pumped to the boiler pressure (State 4) in an isothermal process. (a) Calculate the power deeloped (kw) by the turbine. (b) What is the rate of heat transfer (kw) for the boiler? (c) Apply an oerall energy balance for the power cycle as the system and erify that the oerall energy balance is satisfied with appropriate calculations. (d) Calculate thermal efficiency (%) of the power cycle. Identify system boundary, list assumptions, and proide solution with basic equations. Q boiler W pump m 5 s W turbine +5 Q condenser Assumptions - Steady state - One-dimensional flow - Ignore KE and PE changes - Boiler and condenser: No work W 0 - Turbine and pump: No heat transfer Q 0 - Incompressible liquid water in pump + 6

7 Problem (continued) Basic Equation(s) dm m 1 4 i me m m m m m de i e i i Q W m i hi gzi me hi gzi i e Solution (a) Considering energy balance for the turbine ( I), power deeloped by the turbine: W W m h h turbine 1 State 1: P 1 = 100 bar, T 1 = 400C Table A- for water: T sat (P 1 ) = 11.1C T 1 > T sat (P 1 ) superheated apor (SHV) Table A-4 for superheated water apor: h State : P = 0.1 bar, x = 0.9 saturated liquid-apor mixture (SLVM) Table A- for water: hf P and hfg P 9.8 h hf Pxhfg P W turbine s W turbine 18, kw (b) Considering energy balance for the boiler ( II), rate of heat transfer for the boiler: Q Qboiler mh1h 4 State 4: P 4 = 100 bar, T 4 = T = T sat (P ) = 45.81C Table A- for water: T sat (P 4 ) = 11.1C T 4 < T sat (P 4 ) sub-cooled liquid For incompressible liquid water in the pump: hupcwatert P h4 h 4P4 Ph4 h P4 P +4 7

8 Problem (continued) State : P = 0.1 bar, saturated liquid Table A- for water: P and h h P f m f h 4 m kpa 01.9 Q boiler s Q boiler 7,64.5 kw (c) Considering energy balance for the pump ( III), power consumed by the pump: W kw s Wpump m h h Considering energy balance for the condenser ( IV), rate of heat transfer for the condenser: Q ,88 kw s Qcondenser m h h Net rate of heat transfer for the power cycle: Q Q Q 7,64.5 kw 5,88 kw 18,56.5 kw cycle boiler condenser Net power output for the power cycle: W W W 18,778.8 kw 5. kw 18,56.5 kw cycle turbine pump Considering energy balance for the entire power cycle ( V): Q cycle W is alid cycle (d) Thermal efficiency of the power cycle: W W turbine W cycle pump 18,56.5 kw thermal thermal 5.6% Q Q 7,64.5 kw +4 in boiler 8

ME 200 Exam 2 October 16, :30 p.m. to 7:30 p.m.

ME 200 Exam 2 October 16, :30 p.m. to 7:30 p.m. CIRCLE YOUR LECTURE BELOW: First Name Solution Last Name 7:30 am 8:30 am 10:30 am 11:30 am Joglekar Bae Gore Abraham 1:30 pm 3:30 pm 4:30 pm Naik Naik Cheung ME 200 Exam 2 October 16, 2013 6:30 p.m. to