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CONSTRUCTA Fridge Manual do Utilizador Página 2

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Heat engine.
Heat engine undergoing the Carnot
cycle.
Work is done by the gas in expansion
Work must be done on the gas to compress it to the initial state
Heat transfer in the Carnot cycle
In the Carnot cycle the magnitude of the heat
transferred at T is proportional to the absolute
temperature T.
hh
cc
QT
QT
=
B
hh
A
V
QRTln
V
=
C
cc
D
V
QRTln
V
=
P
V
T
h
T
c
Q
h
Q
c
1
2
3
4
A
B
C
D
Isothermal expansion and compression
Adiabatic expansion and compression
T
h
V
B
γ-1
= T
c
V
c
γ-1
T
h
V
A
γ-1
= T
c
V
D
γ-1
From the relations
C
B
AD
V
V
VV
=
(here Q is
always positive)
c
h
hc
QQ
TT
=
Efficiency of the Carnot cycle
c
h
Q
e1
Q
=−
c
h
T
e1
T
=
−
becomes
The efficiency only depends on the ratio of the absolute
temperatures.
The efficiency would be 100% if Q
c
=0.
This is only possible if T
c
= 0 K (i.e absolute Zero)
A temperature of absolute zero cannot be attained.
(Third law of thermodynamics)
P
V
T
h
T
c
Q
h
Q
c
1
2
3
4
A
B
C
D
Carnot’s Theorem
All Carot engines operating between temperatures T
h
and T
c
have the same efficiency.
No other heat engine operating between these temperatures
can have a greater efficiency
c
h
T
e1
T
=−
Stirling Engine
42
QQ =
41
31
in
outin
QQ
QQ
Q
QQ
e
+
−
=
−
=
V
P
Q
2
Q
1
Q
3
Q
4
Isothermal T
h
Isothermal T
c
Maximum efficiency is less
than the Carnot efficiency.
c
3
h
1
T
Q
T
Q
=
⎟
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎜
⎝
⎛
+
=
1
4
carnot
Q
Q
1
1
ee
w
2
=w
4
=0
then
For isothermal
processes same
volume change
then Efficiency lower due to extra heat added.
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