ME 200 Final Exam December 12, :00 a.m. to 10:00 a.m.

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1 CIRCLE YOUR LECTURE BELOW: First Name Last Name 7:30 a.m. 8:30 a.m. 10:30 a.m. 1:30 p.m. 3:30 p.m. Mongia Abraham Sojka Bae Naik ME 200 Final Exam December 12, :00 a.m. to 10:00 a.m. INSTRUCTIONS 1. This is a closed book examination. You are provided with an equation sheet and all needed property tables are provided. 2. Do not hesitate to ask the instructor if you do not understand a problem statement. 3. 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 1, 2, and 3 for your work. 4. Put only one problem on a page. Another problem on the same page will not be graded. 5. Label your system(s) and list relevant assumptions for problems 1, 2, and 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. 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. Problem Possible Score Total 100 1

2 Problem 1 (30 points) R-134a flows steadily through a refrigeration cycle shown below with a mass flow rate of 1.1 lbm/s. The refrigerant enters the poorly insulated compressor at 20 psia and 20 F (state 1) and is compressed to 180 psia and 140 F (state 2). The compressor requires 47 HP of power input and its average surface temperature is 80 F. The refrigerant exits the condenser at 180 psia and 95 F (state 3) and the pressure drops to 20 psia (state 4) through the throttling valve. (a) Calculate the COP of the refrigeration cycle. (b) Determine the rate of heat transfer (Btu/s) for the compressor. (c) Calculate the rate of entropy generation (Btu/s-R) for the compressor. (d) Show the cycle on T-s diagram. Label the states clearly, show temperature and specific entropy values, and indicate appropriate lines of constant pressure. Identify your system(s), list assumptions, and start with basic equations. 2

3 Problem 1 (continued) 3

4 Problem 1 (continued) 4

5 Problem 2 (35 points) A six-cylinder Diesel engine operates on the ideal air-standard Diesel cycle. The engine speed is 3000 rpm. Air is at 95 kpa and 300 K at the start of compression and its volume is m 3 (state 1). Air is compressed isentropically and engine compression ratio (r = V 1 /V 2 ) is 17 (state 2). Heat is added at constant pressure (P 2 = P 3 ) to the compressed air until temperature increases to 2200 K (state 3) and the corresponding cut-off ratio (r c = V 3 /V 2 ). Air expands isentropically (state 4) and heat is rejected at constant volume (V 4 = V 1 ) to complete the thermodynamic cycle. Consider variable specific heats for air. Do not interpolate; use closest values in property tables. (a) Determine the cut-off ratio. (b) What is the thermal efficiency (%) of the cycle? (c) Calculate the total power output (kw) of the engine. Identify your system, list assumptions, and start with basic equations. 5

6 Problem 2 (continued) First Name Last Name 6

7 Problem 2 (continued) First Name Last Name 7

8 Problem 3 (20 points) 5 kg of steam inside a piston-cylinder device initially at 20 bar and 500 C expands to 10 bar via a polytropic process such that Pv 2 = constant. The temperature of the surroundings is 27 C. Do not interpolate; use closest values in property tables. n 1 dv v n v n 1 (a) Determine the heat transfer (kj) during the process. (b) Calculate the total entropy generation (kj/k) during the expansion process. Identify your system, list assumptions, and start with basic equations. 8

9 Problem 3 (continued) 9

10 Problem 4 (15 points) Show all work to receive credit. (a) An isentropic process in a closed system must always be reversible and adiabatic. (3 points) True False Insufficient Information (b) Which of the following correctly provides explanation for the nearly isothermal pumping process in an ideal Rankine cycle? (3 points) Constant Pressure Reversible Process Incompressible Isentropic Process Constant Volume Adiabatic Process None of the above (c) For a reversible compressor operating at steady state with negligible changes in kinetic and potential energy, which type of compression process requires the least amount of work input? (3 points) Isothermal Isobaric Isentropic Insufficient Information (d) Consider air (ideal gas with constant specific heats) at 1600 K entering an adiabatic gas turbine. The temperature of air at the end of isentropic expansion is 820 K while at the end of actual expansion is 900 K. Calculate the isentropic efficiency (%) of the gas turbine. (3 points) 10

11 Problem 4 (continued) (e) Heat is transferred to air inside a piston-cylinder device initially at P 1 and V 1 such that its volume doubles to V2 = 2V 1. Piston area is A and the spring constantt is k. Show the expansion process on P-V diagram for case I and case II. ( 3 points) 11

12 ME 200 Fall 2011 Final Exam Answers 1(a) 2.1 1(b) Btu/s, heat rejected 1(c) Btu/s-R 1(d) Not attached 2(a) 2.5 2(b) 53.7% 2(c) 2310 kw 3(a) kj, heat rejected 3(b) kj/k 4(a) False 4(b) Incompressible Isentropic Process 4(c) Isothermal 4(d) 89.7% 4(e) Not attached

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