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19.45:
We will need to use Equations (19.3),
(
29
.
4),

(17
and
1
2
W
Q
U
V
V
p
W

=
∆

=
a)
The work done by the system during the process: Along
ab
or
cd,
W
=0. Along
bc,
(
29
(
29
.
,
Along
.
a
c
a
ad
a
c
c
bc
V
V
p
W
ad
V
V
p
W

=

=
b)
The heat flow into the system during the process:
.
W
U
Q
+
∆
=
(
29
(
29
(
29
(
29
(
29
(
29
(
29
(
29
(
29
(
29
(
29
(
29
(
29
a
c
a
a
c
adc
a
c
a
adc
a
c
c
a
c
a
c
c
b
c
a
b
abc
a
c
c
abc
d
c
dc
d
c
dc
a
c
a
a
d
ad
a
d
ad
a
c
c
b
c
bc
b
c
bc
a
b
ab
a
b
ab
V
V
p
U
U
Q
V
V
p
W
adc
c
a
V
V
p
U
U
V
V
p
U
U
U
U
Q
V
V
p
W
abc
c
a
U
U
Q
U
U
U
V
V
p
U
U
Q
U
U
U
V
V
p
U
U
Q
U
U
U
U
U
Q
U
U
U

+

=

=

+

=

+

+

=

=
+

=

=
∆

+

=

=
∆

+

=

=
∆
+

=

=
∆
.
:
path
along
state
to
state
From
.
:
path
along
state
to
state
From
c)
.
0
so
,
.
so
,
.
so
,
.
0
so
,
Assuming
.
and
,
,
adc
abc
adc
abc
a
c
W
W
Q
Q
p
p
d) To understand this difference, start from the relationship
.
U
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Unformatted text preview: W Q ∆ + = The internal energy change U ∆ is path independent and so it is the same for path abc and path adc . The work done by the system is the area under the path in the pVplane and is not the same for the two paths. Indeed, it is larger for path abc. Since U ∆ is the same and W is different, Q must be different for the two paths. The heat flow Q is path dependent....
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