Environmental Engineering Reference
In-Depth Information
Solution
DME has the same overall chemical formula as ethanol (it is an isomer); thus,
based on the previous example, we can easily write out the reaction equation
for stoichiometric combustion:
CH
3
OCH
3
+3 O
2
+3
ð
:
76N
2
Þ!
2CO
2
+3H
2
O+11
:
28N
2
Recognizing that no work is done by or on the system and that the system is
adiabatic (no heat flows), the energy balance is very much simplified as
X
=
X
Products
h
0
h
0
Δ
h
Δ
h
n
in per mole fuel
f
+
n
out per mole fuel
f
+
in
out
Reactants
Thus, H
Products
=H
Reactants
.
For the left-hand side of the equation, only
h
f
,
DME
remains, leading to the
equation
+3×
393,546 +
ð
T
ad
241, 845 +
ð
T
ad
h
f
,
DME
=2×
−
298
:
15
c
p
,
CO
2
dT
−
298
:
15
c
p
,
H
2
O
dT
28 × 0 +
ð
T
ad
+11
:
298
:
15
c
p
,
N
2
dT
which is equal to
−
h
f
,
DME
+2×
0=
ð
−
393, 546
Þ
+3×
ð
−
241, 845
Þ
+R
u
ð
T
ad
298
:
15
dT
A
+
B
T+
C
T
2
+
D
T
3
+
E
T
4
with
A
=2
a
1
,
CO
2
+3
a
1
,
H
2
O
+11
:
28
a
1
,
N
2
B
=2
a
2
,
CO
2
+3
a
2
,
H
2
O
+11
28
a
2
,
N
2
C
=2
a
3
,
CO
2
+3
a
3
,
H
2
O
+11
:
:
28
a
3
,
N
2
D
=2
a
4
,
CO
2
+3
a
4
,
H
2
O
+11
:
28
a
4
,
N
2
E
=2
a
5
,
CO
2
+3
a
5
,
H
2
O
+11
:
28
a
5
,
N
2
Integration with partial substitution of the numbers yields
0=
−−
ð
184, 100
Þ
+2×
ð
−
393,546
Þ
+3×
ð
−
241, 845
Þ
2
4
+
1
2
B
T
ad
−
+
1
3
C
T
ad
−
3
5
15
2
15
3
A
T
ad
−
ð
298
:
15
Þ
298
:
298
:
+
1
4
D
T
ad
−
+
1
5
E
T
ad
−
+8
:
3143 ×
15
4
15
5
:
:
298
298
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