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Chapter 4  Section B  NonNumerical Solutions
4.5
For consistency with the problem statement, we rewrite Eq. (4.8) as:
h
C
P
i=
A
+
B
2
T
1
(τ
+
1
)
+
C
3
T
2
1
(τ
2
+
τ
+
1
)
where
τ
≡
T
2
/
T
1
. Define
C
P
am
as the value of
C
P
evaluated at the arithmetic mean temperature
T
am
.
Then:
C
P
am
=
A
+
BT
am
+
CT
2
am
where
T
am
≡
T
2
+
T
1
2
=
T
1
τ
+
T
1
2
=
T
1
(τ
+
1
)
2
and
T
2
am
=
T
2
1
4
(τ
2
+
2
τ
+
1
)
Whence,
C
P
am
=
A
+
B
2
T
1
(τ
+
1
)
+
C
4
T
2
1
(τ
2
+
2
τ
+
1
)
Define
δ
as the difference between the two heat capacities:
δ
≡h
C
P
i−
C
P
am
=
CT
2
1
µ
τ
2
+
τ
+
1
3
−
τ
2
+
2
τ
+
1
4
¶
This readily reduces to:
δ
=
CT
2
1
12
(τ
−
1
)
2
Making the substitution
τ
=
T
2
/
T
1
yields the required answer.
4.6
For consistency with the problem statement, we rewrite Eq. (4.8) as
h
C
P
i=
A
+
B
2
T
1
(τ
+
1
)
+
D
τ
T
2
1
where
τ
≡
T
2
/
T
1
. Define
C
P
am
as the value of
C
P
evaluated at the arithmetic mean temperature
T
am
.
Then:
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This note was uploaded on 01/29/2011 for the course CHEM 101 taught by Professor Brown during the Spring '10 term at The University of Akron.
 Spring '10
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