FinalExamME525SP2008withanswers - Name ME 525 Final Exam...

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1 Name___________________________ May 1, 2008 Prof. Lucht ME 156 1. POINT DISTRIBUTION Problem #1 35 points Problem #2 35 points Problem #3 45 points Problem #4 45 points 2. EXAM INSTRUCTIONS Write your name on each sheet. Equation sheets and tables are provided. When working the problems, list all assumptions, and begin with the basic equations. If you do not have time to complete numerical evaluation of terms, remember that the significant credit on each problem will be given for setting up the problem correctly and obtaining the correct analytical solution. ME 525 Final Exam

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2 ME 525 Final Exam 1 May 2008 Name___________________________ 1. (35 points) A mixture of H 2 and Cl 2 is placed in a constant-volume reactor at a pressure of 100 kPa = 1.0 bars and at 300 K. The mole fractions of H 2 and Cl 2 are 0.7 and 0.3, respectively, and the mixture is nonreactive at 300 K. At time t = 0, the temperature in the reactor is raised very suddenly to 900 K, while the pressure is increased to 3 bars. After time t =0 + , the reactor temperature at 900 K. Consider the following reaction mechanism:  43 1 21 11 6 2 2 22 83 3 23 70 . 5 3 4 24 1.15 10 / 1.49 10 / 2 10 exp 10,000/ / 2 10 exp 1000/ / k Cl M Cl Cl M k m gmol s k Cl Cl M Cl M k m gmol s k Cl H HCl H k T m gmol s k H Cl HCl Cl k T T m gmol s       (a) Verify that the rate coefficient expressions given above for k 1 and k 2 are consistent with chemical equilibrium. The Gibbs free energies of formation for the chlorine atom (Cl) and diatomic chlorine (Cl 2 ) at 900 K are +71,200 J/gmol, and 0 J/gmol, respectively. . (b) Assume that the concentrations of the radicals H• and Cl• can be evaluated from steady state expressions, and that they reach these concentrations levels very quickly. Develop an expression for the formation rate of HCl at the initial time t = 0 + from the rate mechanism given above. Calculate the initial rate of formation of HCl in gmol/m 3 -s . Answer: +162 gmol/(m 3 s)
3 ME 525 Final Exam 1 May 2008 Name___________________________ 2. (35 points) The flame height of turbulent nonpremixed jet flames can be found from the Delachatsios correlations:  * 1/2 / f stoich je Lf L d  2/5 * * 1/5 2 13.5 5, 23 5 10 . 0 7 f ff f Fr L for Fr L for Fr Fr  where 1/4 3/2 v fj e fe s t o i c h Tgd Fr f T     2 9.8 / v jf stoich e d jet exit diameter T flame temperature rise g m s f stoich mixture fraction uniform exit velocity   (a) Calculate the flame length for a butane (C 4 H 10 ) jet issuing from a 1-mm-diameter circular nozzle with a uniform jet exit velocity of 50 m/sec.

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FinalExamME525SP2008withanswers - Name ME 525 Final Exam...

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