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# Final - CHEE 3334 Fall'98 FINAL EXAM Michael Nikolaou...

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CHEE 3334 Fall ’98 Michael Nikolaou FINAL EXAM Open-book, open-notes. Total points 100. Please, budget your time ! Do NOT try to read the book during the exam! Write neatly! Do NOT use your programmable calculator to find results you are asked to compute in a certain way--after all, the calculator may find the wrong answer or not all answers! Show all work. Return this sheet with your exam . GOOD LUCK! (30 pts.) 1. The reactions products side C B A _ + occur in a batch reactor. If y 1 ( t ) and y 2 ( t ) denote the concentrations of A and C inside the reactor, then the following ordinary differential equations (ODE) describe how y 1 and y 2 evolve with time: 2 1 2 2 2 2 1 1 ) ( 10 ) ( 2 ) ( ) ( 10 t y t y dt dy t y t y dt dy + - = + - = Let the initial conditions be ( 29 1 0 1 = y and ( 29 0 0 2 = y . Consider a grid of points t k t k δ = * , with 01 . 0 = δ t and ,... 2 , 1 , 0 = k a. For the above equations, do one step of Euler’s method, to compute ) ( 1 1 t y and ) ( 1 2 t y . b. Approximate the derivatives dt dy / 1 and dt dy / 2 at t 1 by centered finite divided differences, and develop a recursive formula for the solution of the above two ODE.

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Final - CHEE 3334 Fall'98 FINAL EXAM Michael Nikolaou...

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