ChBE 2120 Homework 7
Due: Friday June 29 at 8 am
Objectives of this assignment
•
Understand the differences between various methods for onedimensional rootfinding
•
Implement the NewtonRaphson method for multidimensional rootfinding
Part I.
Consider the steadystate 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 rootfinding, 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).
•
NewtonRaphson: Beginning with
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 Summer '07
 Gallivan
 pH, Secant method, Rootfinding algorithm, 4.184 kJ, energy balance equation, Antoine equation, bisection C. Hand

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