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Homework Set # 12: Shell mass/molar balance for components in a multi
component system
Problem #1:
Recall the example of evaporation of component A contained in a test tube in the lecture
note (or see section 18.2, 2
nd
edition, 17.2, 1
st
edition).
(a)
By neglecting the convective flux of component A, show that this leads to
()
1
12
21
AA
zz
cD
Nx
=
=−
−
A
x
(b)
What error is made in the determination of D in the example 18.22 (or 17.22, 1
st
edition) if the result in (a) is used?
Answer:
a.
Without the convection term, the total molar flux of A is equal to the diffusion flux of
A. For steady state
.
A
A
dx
N
cD
const
dz
=
Since c and D are constant, thus
( )
.
A
x
x
dx
const
dz
z
z
−
==
−
−
Therefore,
1
cD
=
−
A
x
b.
Error in the determination of D in the example 18.22
To get the solution of Example 18.22 by using the result in (a), we make the following
calculation with the help of the equation of state for an ideal gas.
( )( )( )( )
(
)
9
2
7.26
10
82.06
273
17.1
0.0641
/
/
/
755/760
33/755
0
Az
Az
NR
T
N
Dc
c
dx
dz
p
dx
dz
−
×
=
=
−−
−
⎡⎤
⎣⎦
m
s
Hence the error is
%
79
.
0
100
0636
.
0
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This note was uploaded on 09/01/2011 for the course PGE 312 taught by Professor Peters during the Fall '08 term at University of Texas at Austin.
 Fall '08
 Peters

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