The Carnot Cycle (Heat Engine)
6-7 THE CARNOT CYCLE
The Reversed Carnot Cycle (Refrigerator, Heat Pump)
P
P
TH
1
TH
1
QH
QH
2
4
TH
Q=0
Wnet ,out
Wnet ,in
Q=0
Q=0
4
2
3
QL
Sadi Carnot (1822-1888)
V1
The Carnot Cycle consists
V4
V2
Reversible Processes
V3
V1
V2
W
2
V4
TL
V
V3
TL
3
V3
2
V2
3
V3
4
V4
continues
to expand
-Q
-W
3
QL
V
gas
1
Q
TL
TL
of 4 reversible processes
1
TH
Q=0
2
V2
2
• the paths coinside
4
V4
1
V1
• heat transfer is due to infinitely
small difference in temperature
• at thermal equilibrium
V1
1
gas
Irreversible Processes
∆T > 0
insulated
insulated
QH
• heat transfer is due to finite
difference in temperature
• heat generation by friction
6-8 CARNOT PRINCIPLES
QL
Isothermal expansion
at TH
heat QH is added
Adiabatic expansion
Q=0
Temperature dropped to TL
Isothermal compression
Adiabatic compression
at TL
Q=0
Temperature raised to TH
heat QL is rejected
Efficiency of two Heat Engines operating between the same two reservoirs at TL and TH
TH
C1
η irreversible < η reversible
η IR < η R
Violation of Carnot Principles
yields violation of the
IR
2nd Law of Thermodynamics
C2
η R1 = η R2
R1
R2
η reversible 1 = η reversible 2
TL
6-9 THE THERMODYNAMIC TEMPERATURE SCALE
For reversible heat engine operating between TL and TH :
QL
T
= L
QH
TH
Kelvin Scale of Absolute Temperature
6-10 THE CARNOT HEAT ENGINE The efficiency of heat engine operating on a reversible Carnot cycle between TL and TH :
ηC = 1 −
6-11 THE CARNOT HEAT PUMP
QL
T
= 1 − L
QH
TH
Carnot Heat Pump:
COPCHP =
1
Q
1− L
QH
Carnot
Efficiency
ηC is the highest possible efficiency
of the heat engine operating between
two reservoirs at TL and TH
Carnot Refrigerator:
=
1
T
1− L
TH
COPCR =
1
1
=
QH
TH
−1
−1
QL
TL
INSTITUT NATIONAL DES SCIENCES APPLIQUEES, LYON