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MidTerm Review 7 p.m. Thursday evening
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The Carnot Cycle
P
Volume
A
B
C
D
-work
net
Efficiency = work
out
/q
in
isothermal
isothermal
a
d
i
b
t
c
How efficient can this engine be?
We need to calculate how
much work we can get out of
this system for a given
amount of heat input

3
The Carnot Cycle
Volume
A
B
C
D
-work
net
Efficiency = work
out
/q
in
isothermal
isothermal
a
d
i
b
t
c
How efficient can this engine be?
Clicker Question
The adiabatic processes must be
considered when calculating the
efficiency
True
False

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The Carnot Cycle
P
Volume
A
B
C
D
-work
net
Work out the various pathways first
Isothermal
Temp -
T
H
How efficient?
A
Æ
B
−
=
=
A
B
H
AB
AB
V
V
nRT
q
w
ln

5
The Carnot Cycle
P
Volume
A
B
C
D
-work
net
Work out the various pathways first
Isothermal
Temp -
T
H
How efficient?
B
Æ
C
( )
H
L
V
BC
BC
T
T
nc
w
U
−
−
=
=
∆
q=0
Adiabatic
∆
T =
T
H
Æ
T
L

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The Carnot Cycle
P
Volume
A
B
C
D
-work
net
Work out the various pathways first
Isothermal
Temp -
T
H
How efficient?
Skipping to D
Æ
A
( )
L
H
V
DA
DA
T
T
nc
w
U
−
−
=
=
∆
q=0
Adiabatic
∆
T =
T
L
Æ
T
H
( )
DA
H
L
V
BC
BC
w
T
T
nc
w
E
−
=
−
−
=
=
∆
Note that this exactly cancels out
w
BC

7
The Carnot Cycle
P
Volume
A
B
C
D
-work
net
pathway C
Æ
D
Isothermal Temp -
T
L
How efficient?
−
=
=
C
D
L
CD
CD
V
V
nRT
q
w
ln
Since
w
BC
= -w
DA
, all work is along
pathways A
Æ
B and C
Æ
D
Thus
,
w
BC
+w
DA
=
0
i.e. all work is along pathways A
Æ
B and C
Æ
D

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The Carnot Cycle
P
Volume
A
B
C
D
-work
net
How efficient?
+
−
=
D
C
L
A
B
H
total
V
V
nRT
V
V
nRT
w
ln
ln
Why don’t we worry about w
BC
+w
DA
contributions?
−
=
=
C
D
L
CD
CD
V
V
nRT
q
w
ln
−
=
−
=
A
B
H
AB
AB
V
V
nRT
q
w
ln