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chbe2120spring2011hw5 - ChBE 2120 Spring 2011 Homework 5...

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ChBE 2120 Spring 2011, Homework 5 Extended deadline: Sunday, February 27, 2011, by 8:05 am We will consider two CSTR problems. The first problem deals with a unimolecular reaction A Æ B, while the second deals with a bimolecular reaction 2A Æ B. Part 1 We will derive the steady-state mass and energy balances for this CSTR in class. For the unimolecular reaction, they are: 0 = FC A0 – FC A – k 0 *exp(-E a /RT)*V*C A ( 1 ) 0 = -FC B + k 0 *exp(-E a /RT)*V*C A ( 2 ) 0 = F ρ c p (T 0 -T) - Δ H rxn *k 0 *exp(-E a /RT)*V*C A (3) Equation (2) can express C B in terms of C A and T, so we will ignore it for now (it is not a free variable). In this case, however, we can also rearrange equation (1) to express C A in terms of T, as follows: V RT E k F FC C a A A ⎛ − + = exp 0 0 Assume: C A0 = 100 mol/m 3 Initial concentration F = 0.1 m 3 /s Flow in V = 1 m 3 Reactor volume E a = 5,000 J/mol Activation energy for reaction Δ H rxn = -5,420,000 J/mol Heat of reaction R = 8.314 J/(K mol) Universal gas constant k 0 = 1 s -1 Prefactor for reaction ρ = 1000 kg/m3 Density (water) c p = 4184 J/(kg K) Heat capacity (water) T 0 = 298 K Inlet temperature The unknowns are temperature T and concentration C A . Plug your new equation for C A , derived from equation (1), into equation (3) to get an equation in T only. Do the following steps: (1) Define the function f(x) = 0 for this problem. Write a function called hw5CstrFo_myGtAccountId.m that takes a value of the unknown and returns the value of the function f . (2) You will be implementing and performing the false position method in order to solve this problem. To do so, you will need to identify two T values that are likely to enclose your root. You should plot your function and choose two values that look like they may bracket a solution. You do not need to turn in your plot or code to make the plot for this step.
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(3) Write a Matlab function called falsePosition_myGtAccountId.m that performs the false position method for this problem. The code should run until the magnitude of the function at the guess during any step of your false position method is less than ε tol = 10 -6 . Make sure to comment your code and include your name in a comment line.
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chbe2120spring2011hw5 - ChBE 2120 Spring 2011 Homework 5...

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