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# hw 2 - C C = 0 2 Given the parameter values k 1 = 1 k 2 = 2...

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Homework #2 ChE 361 Spring 2010 Problem 1. Consider the following matrix: A = " - 4 - 3 2 1 # 1. Find the eigenvalues and eigenvectors. 2. Verify your results with Matlab. 3. Do these eigenvectors provide a basis for R 2 . Why? Problem 2. Consider a CSTR in which the following reactions occur: A B, B C, C B. The reaction rates per unit volume of the three reactions are r 1 = k 1 C A , r 2 = k 2 C B , and r 3 = k 3 C C respectively. The reactor has constant volumetric flow rate q and pure component A feed at concentration C Ai . The volume of the reactor is denoted V . 1. Perform steady-state mass balances on the three reaction species to obtain the following algebraic equation system: q V ( C Ai - C A ) - k 1 C A = 0 , - q V C B + k 1 C A - k 2 C B + k 3 C C = 0 , - q V C C + k 2
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Unformatted text preview: C C = 0 2. Given the parameter values k 1 = 1, k 2 = 2, k 3 = 3, q V = 1, and C Ai = 6, show that the linear algebra problem for determining C A , C B , and C C can be posed as Ax = b where: A = -2 1-3 3 2-4 , b = -6 3. Use Gaussian elimination to solve the linear algebraic system. 4. Determine the eigenvalues and eigenvectors for the matrix A . 5. Validate your results with Matlab. Problem 3. Problem Set 19.2, Problem 4. Validate your result with Matlab. Problem 4. Problem Set 19.2, Problem 14. Validate your result with Matlab. 1...
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