ChBE 2120A Homework 7 Summer 2007

ChBE 2120A Homework 7 Summer 2007 - ChBE 2120 Homework 7...

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ChBE 2120 Homework 7 Due: Friday June 29 at 8 am Objectives of this assignment Understand the differences between various methods for one-dimensional root-finding Implement the Newton-Raphson method for multi-dimensional root-finding Part I. Consider the steady-state energy balance equation we derived in the first lecture: V C RT E k H T T c F A a rxn p ⎛ − Δ = exp ) ( 0 0 ρ Use the properties of water: = 1000 kg/m 3 , c p = 4.184 kJ/(kg K), and the process settings F = 1 m 3 /s, T 0 = 273 K, V = 1 m 3 , and C A = 1 mol/m 3 . For the reaction, heat of reaction Δ H rxn = 500 kJ/mol, reaction constant k 0 = 20,000 s -1 , and activation energy E a = 10 kJ/mol. Your task is to solve for temperature T . A. Set this equation up in the form for root-finding, and plot the function f from 300 to 600 K, and print out four plots. B. Sketching. For each of the four methods we learned in class, sketch 3 iterations (each on a separate plot). Newton-Raphson: Beginning with
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ChBE 2120A Homework 7 Summer 2007 - ChBE 2120 Homework 7...

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