PHY 113 A General Physics I
9-9:50 AM MWF Olin 101
Plan for Lecture 32:
Chapter 22: Heat engines
1. Thermodynamic cycles; work and heat
efficiency
2. Carnot cycle
3. Otto cycle; diesel cycle
4. Note – in this class, we will not focus on entropy and
the second law of thermodynamics
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PHY 113 A Fall 2012 -- Lecture 32
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Thermodynamic cycles for designing ideal engines
and heat pumps
http://auto.howstuffworks.com/engine1.htm
Engine process:
P (1.013 x 105) Pa
Pf
Work of engine :
B
C
Heat input to system : Q  Qin  Qout
Efficiency :
A
Pi
Vi
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Weng  W
D

Weng
Qin
Vf
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Examples process by an ideal gas:
P (1.013 x 105) Pa
Pf
B
C
AB
Q
W
A
Pi
D
DEint
BC
γPf (V f  Vi )
 V f ( Pf  Pi )
-γPi (V f  Vi )
γ -1
γ -1
γ -1
γ -1
0
-Pf(Vf-Vi)
0
Pi(Vf-Vi)
Vi ( Pf  Pi )
Pf (V f  Vi )
 V f ( Pf  Pi )
-Pi (V f  Vi )
γ -1
γ -1
γ -1
γ -1
Vf

Weng
Qin

P

f
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DA
Vi ( Pf  Pi )
Efficiency :
Vi
CD
PHY 113 A Fall 2012 -- Lecture 32
 Pi V f  Vi 
QAB  QBC
4
Example from homework

Efficiency :
Weng
Qin

P

 Pi V f  Vi 
f
QAB  QBC
Also :  W  Weng  Q  Qin  Qout

Qin  Qout
  1
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PHY 113 A Fall 2012 -- Lecture 32
Qin
 1
Qout
Qin
QCD  QDA
QAB  QBC
5
Most efficient thermodynamic cycle -- Carnot
Sadi Carnot 1796-1832
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PHY 113 A Fall 2012 -- Lecture 32
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Carnot cycle:
AB
BC
CD
DA
Isothermal at Th
Adiabatic
Isothermal at Tc
Adiabatic
Efficiency of Carnot cycle

Qin  Qout
Qin
 1
Qout
Qin
Tc
ε  1
Th
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iclicker exercise:
We discussed the efficiency of an engine as

Qin  Qout
Qin
 1
Qout
Qin
Is this result
A. Special to the Carnot cycle
B. General to all ideal thermodynamic cycles
iclicker exercise:
We discussed the efficiency of an engine running
with hot and cold reservoirs as
T
  1 c
Th
Is this result
A. Special to the Carnot cycle
B. General to all ideal thermodynamic cycles
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Note that for a Carnot cycle :
Qout
Qin

WAB
WCD
nRTc ln(VC / VD )

nRTh ln(VB / VA )
For adiabatic process
ThVB 1  TcVC 1
ThVA 1  TcVD 1
 VC / VD  VB / VA

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Qout
Qin

Tc
Th
PHY 113 A Fall 2012 -- Lecture 32
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iclicker exercise:
Why should we care about the Carnot
cycle?
A. We shouldn’t
B. It approximately models some
heating and cooling technologies
C. It provides insight into another
thermodynamic variable -- entropy
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The Otto cycle
Theoretical efficiency :
 V2 
  1   
 V1 
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PHY 113 A Fall 2012 -- Lecture 32
 1
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The Diesel cycle
Theoretical efficiency :
1  TD  TA 

  1  
  TC  TB 
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Engine vs heating/cooling designs
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