Final Exam 224 Elements of Fluid Mechanics and Thermodynamics

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1 Final Exam 224 May 20, 1999 MAE Elements of Fluid Mechanics and Thermodynamics Professor F. L. Dryer Two Hours - Solve all of Problems 1-4 INSTRUCTIONS: Complete answers to all of the problems below. You need not restate the problem as part of the solution, but you must explain your methodology carefully and in detail, including the specific assumptions you use. Specifically note in each case the table(s) you use for obtaining property information. No credit will be given unless the reasoning which led to your answer is clear. Reasoning is more important than a numerically correct answer. Schematics should be used and considered as part of your solutions. (Below, the phrase "thermodynamic schematic" refers to a schematic of the problem which includes a definition of the thermodynamic system and notes devices/processes affecting its thermodynamic parameters.) Use T-S, H-S, P-V, etc. diagrams where possible to help clarify your answers. Be careful to define all of the symbols (e.g. T H, Q C, etc.) you use in your solutions and the units of each term in numerical problems, including the final answer. Materials: Only the following materials may be used in this exam: One 8 1/2" x 11 1/2" sheet (front and back) of crib notes that you have personally prepared; the Moran and Shapiro Appendix booklet containing the text book appendix tables, charts, and figures (no personal notes or crib material in the booklet); and, a calculator. No prior exams, problem sets, or problem set solutions are permitted. Please sign and turn in the quiz sheets with your exam booklet(s). Also, sign and turn in your crib sheets with your exam. The exam sheets and your crib sheet will be returned with your graded exam. This exam is to be completed in two hours. Where not explicitly noted, all dimensions of terms are expressed in appropriate "SI" units. Solutions On May 14 (1:30-3:00 p.m.) and May 16 (7:00-9:00 p.m.), two review sessions were held. About 5 students were present on Friday, and about 15 were present on Sunday night. On Sunday night, the attending A/I's and I gave the review sessions. We went over explicitly, the last problem set which contained a problem similar to problem 4, and I went over hypothetical problems that essentially are Problems 1, 2, and 3 on the exam. Problem 2 was a homework problem as well. I also gave explicit instructions on best ways to prepare crib sheets. Particularly I suggested that a crib sheet for this exam should have essential notes required for the student to perform any of the problems assigned during the thermodyanmics section of the course. What follows are the questions and solutions to the Final exam.

2 Problem 1. [20 Points] Liquid ethanol at 25 C, 1 atm enters a combustion chamber operating at steady state and burns with air which is entering the chamber at 227 C, 1 atm. The fuel flow rate is 25 kg/s and the air-fuel ratio on a mass basis is 7.5. The products of combustion consisting of CO 2, CO, H 2 O, and N 2 leave the combustor at 1000 K and 1 atm. Consider all species to be ideal gases, and ignore potential and kinetic energy effects. a.) Determine the molar air fuel ratio for the reaction. Write an appropriate molar reaction equation to represent this process. b.) Find an expression for the rate of heat transfer from the combustion chamber, kj/s. Develop the expression with appropriate schematic and procedure for its solution, but DO NOT SOLVE.

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6 Problem 2. [20 points] No single constant equation of state is accurate over a wide range of states. However, a number are useful over a limited range of states. One such equation is: v = (RT/p) - b/t 3, b = constant. a) [10 Points] Determine an expression for the exact differential, dv. b) [5 Points] Prove that the answer in part a is an exact differential. c) [5 Points] Determine a thermodynamic relationship between C p and C v for this equation of state.

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9 Problem 3. [20 Points] A system consisting of air initially at 300 K and 1 bar experiences the two different types of interactions described below. In each case, the system is brought from the initial state to a state where the temperature is 500 K. The volume of the system may be changed by the (reversible) movement of a piston. The air may be modeled as an ideal gas. The molecular weight of air is The Universal gas constant is kj/kg-k. a.) [10 Points] For each case described below: a) draw a thermodynamic schematic of the problem, and b) determine the entropy production, in kj/kg-k: i.) The temperature rise is brought about by adiabatically stirring the air with a paddle wheel, while the piston is moved such that the pressure is constant during the process. ii.) The temperature rise is brought about by heat transfer from a reservoir at 600 K. The temperature of the boundary where heat transfer occurs is 600 K, while the piston is moved such that the pressure remains constant. b.) [4 Points] Draw a P-V diagram for each case. State whether the areas under the P-V diagram for each of the problems above represents the work performed. Explain your answer. c.) [4 Points] Draw a T-S diagram for each case. State whether the areas under the T-S diagram for each of the problems above represent the heat transferred. Explain your answer. d.) [2 Points] Show that the entropy produced in case ii. is always less than that produced in case i. and, under what hypothetical condition, the entropy produced in each case would approach one another.

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13 Problem 4. [20 Points] An insulated open feedwater heat exchanger has two inlets and one outlet. At inlet 1, water vapor enters at 10.0 MPa and 520 C. At inlet 2, liquid water enters at 10.0 MPa with an internal energy of kj/kg. The mass flow rate is 10 kg/s at each inlet. A small stirrer mixes the two streams together inside the heat exchanger. The work done by the stirrer is 10 Kilowatts.. The exit pressure is also 10 MPa. Draw a diagram of the problem and label the systems you use in determining the answers to the following: a.) What is the exit temperature of the stream in degrees C? Locate the inlet and outlet states on a P-V diagram. b.) What is the entropy production of the heater?

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16 Problem 5. [20 Points] Answer each of the following questions, as directed. a.) [3 Points] Consider a reversible heat engine driven by two reservoirs, both of which are at temperatures well above the ambient temperature. Suppose one can change either (but not both) of the reservoir temperatures, T h (hot) and T c (cold), by an amount T d. To increase the thermal efficiency of a reversible cycle operating between reservoirs at T h and T c, would it be better to increase T h while keeping T c constant, or decrease T c while keeping T h constant? Discuss. b.) [4 Points] A tray of ice cubes is placed in a food freezer having an ideal coefficient of performance of 10. If the room temperature is 32 C, will the ice cubes remain frozen or will they melt? c.) [3 Points] An ordinary household refrigerator receives electrical work from its surroundings while discharging energy by heat transfer to its surroundings. Is this a violation of the Kelvin- Planck statement? Explain. d.) [3 Points] Discuss the purpose of using reheat and super heat in a Rankine power cycle. Use a thermodynamic schematic and a T-S diagram in your discussions. e.) [3 Points] Discuss the purpose of adding intercooling to a Brayton cycle, with and without regeneration and in particular how it affects compressor work, heat addition, turbine work and thermal efficiency. Use a thermodynamic schematic and a T-S diagram in your discussions. f.) [4 Points] For each of the following processes, specify whether the entropy change of the closed system is positive, negative, zero, or indeterminate. i.) Two kilograms of water vapor undergoing an internally reversible process. ii.) Three kilograms of argon, modeled as an ideal gas undergoing an isothermal process to a higher pressure. iii.) Three kilograms of Refrigerant 134A undergoing an isothermal process. iv.) One kilogram of oxygen, modeled as an ideal gas, undergoing a constant pressure process to a lower temperature.

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20 BONUS POINTS FOR EXAM (10 Points). Provide the numerical solution for Problem 1. (b) Have a wonderful summer. See you in the fall!