Final Exam MAE224May 20, 1999 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 theproblem 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 forobtaining property information. No credit will be given unless the reasoning which led to youranswer is clear. Reasoning is more important than a numerically correct answer. Schematicsshould be used and considered as part of your solutions. (Below, the phrase "thermodynamicschematic" refers to a schematic of the problem which includes a definition of the thermodynamicsystem 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. TH, QC, 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 ShapiroAppendix booklet containing the text book appendix tables, charts, and figures (no personalnotes or crib material in the booklet); and, a calculator. No prior exams, problem sets, or problemset solutions are permitted.

Please sign and turn in the quiz sheets with your exam booklet(s). Also, sign and turn in your cribsheets with your exam. The exam sheets and your crib sheet will be returned with your gradedexam.

This exam is to be completed in two hours. Where not explicitly noted, all dimensions of termsare expressed in appropriate "SI" units.______________________________________________________________________________

SolutionsOn May 14 (1:30 - 3:00 p.m.) and May 16 (7:00 - 9:00 p.m.), two review sessions wereheld. About 5 students were present on Friday, and about 15 were present on Sundaynight. On Sunday night, the attending A/I's and I gave the review sessions. We went overexplicitly, the last problem set which contained a problem similar to problem 4, and I wentover hypothetical problems that essentially are Problems 1, 2, and 3 on the exam. Problem2 was a homework problem as well.

I also gave explicit instructions on best ways to prepare crib sheets. Particularly Isuggested that a crib sheet for this exam should have essential notes required for thestudent to perform any of the problems assigned during the thermodyanmics section of thecourse.

What follows are the questions and solutions to the Final exam.

Problem 1. [20 Points] Liquid ethanol at 25 C, 1 atm enters a combustion chamber operating atsteady state and burns with air which is entering the chamber at 227 C, 1 atm. The fuel flow rateis 25 kg/s and the air-fuel ratio on a mass basis is 7.5. The products of combustion consisting ofCO2, CO, H2O, and N2 leave the combustor at 1000 K and 1 atm. Consider all species to be idealgases, and ignore potential and kinetic energy effects.

a.) Determine the molar air fuel ratio for the reaction. Write an appropriate molar reactionequation to represent this process.

b.) Find an expression for the rate of heat transfer from the combustion chamber, kJ/s. Developthe expression with appropriate schematic and procedure for its solution, but DO NOT SOLVE.

Problem 2. [20 points] No single constant equation of state is accurate over a wide range ofstates. However, a number are useful over a limited range of states. One such equation is:

v = (RT/p) - b/T3, 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 Cp and Cv for this equation ofstate.

Problem 3. [20 Points] A system consisting of air initially at 300 K and 1 bar experiences the twodifferent types of interactions described below. In each case, the system is brought from the initialstate 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 molecularweight of air is 28.97. The Universal gas constant is 8.314 kJ/kg-K.

a.) [10 Points] For each case described below: a) draw a thermodynamic schematic of theproblem, and b) determine the entropy production, in kJ/kg-K:

i.) The temperature rise is brought about by adiabatically stirring the air with a paddlewheel, 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. Thetemperature of the boundary where heat transfer occurs is 600 K, while the piston is moved suchthat the pressure remains constant.b.) [4 Points] Draw a P-V diagram for each case. State whether the areas under the P-V diagramfor 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 diagramfor 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 casei. and, under what hypothetical condition, the entropy produced in each case would approach oneanother.

Problem 4. [20 Points] An insulated open feedwater heat exchanger has two inlets and oneoutlet. At inlet 1, water vapor enters at 10.0 MPa and 520 C. At inlet 2, liquid water enters at10.0 MPa with an internal energy of 416.12 kJ/kg. The mass flow rate is 10 kg/s at each inlet. Asmall stirrer mixes the two streams together inside the heat exchanger. The work done by thestirrer is 10 Kilowatts. . The exit pressure is also 10 MPa. Draw a diagram of the problem andlabel 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 ona P-V diagram.b.) What is the entropy production of the heater?

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 attemperatures well above the ambient temperature. Suppose one can change either (but not both)of the reservoir temperatures, Th (hot) and Tc (cold), by an amount Td. To increase the thermalefficiency of a reversible cycle operating between reservoirs at Th and Tc, would it be better toincrease Th while keeping Tc constant, or decrease Tc while keeping Th constant? Discuss.

b.) [4 Points] A tray of ice cubes is placed in a food freezer having an ideal coefficient ofperformance of 10. If the room temperature is 32 C, will the ice cubes remain frozen or will theymelt?

c.) [3 Points] An ordinary household refrigerator receives electrical work from its surroundingswhile 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 athermodynamic schematic and a T-S diagram in your discussions.

e.) [3 Points] Discuss the purpose of adding intercooling to a Brayton cycle, with and withoutregeneration and in particular how it affects compressor work, heat addition, turbine work andthermal 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 theclosed 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.

_

_________________________

BONUS POINTS FOR EXAM (10 Points).

Provide the numerical solution for Problem 1. (b)

Have a wonderful summer. See you in the fall!