Chapter 19
Heat Engines
Heat Engines
Refrigerators
Carnot Cycle
Limits of Heat Efficiency
Qc
Tc
Tc
 and ec  1 
Qh Th
Th
Qc
Tc
COPC 

W
Th  Tc
Qh
Th
COPH 

W
Th  Tc
Heat Engines
 In a steam turbine of a
modern power plant,
expanding steam does
work by spinning the
turbine.
 The steam is then
condensed to liquid
water and pumped back
to the boiler to start the
process again.
 First heat is transferred to the water in the boiler to
create steam, and later heat is transferred out of the
water to an external cold reservoir, in the condenser.
 This steam generator is an example of a heat engine.
© 2013 Pearson Education, Inc.
Slide 19-33
Heat Engine
Energy Transfer Diagram
Eint = 0 for the entire cycle





A heat engine is a device that
takes in energy by heat and,
operating in a cyclic process, expels
a fraction of that energy by means
of work
A heat engine carries some working
substance through a cyclical process
The working substance absorbs
energy by heat from a high
temperature energy reservoir (Qh)
Work is done by the engine (Weng)
Energy is expelled as heat to a
lower temperature reservoir (Qc)
Energy-Transfer Diagrams
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Slide 19-26
Work into Heat
 Turning work into heat is
easy — just rub two
objects together!
 Shown is the energy
transfer diagram for this
process.
 The conversion of work into heat is 100% efficient, in
that all the energy supplied to the system as work is
ultimately transferred to the environment as heat.
© 2013 Pearson Education, Inc.
Slide 19-27
Heat into Work
 Transforming heat into work is not easy.
 To be practical, a device that transforms heat into work
must return to its initial state at the end of the process
and be ready for continued use.
 It is impossible to invent a
“perfect engine” that transforms
heat into work with 100%
efficiency and returns to its initial
state so that it can continue to
do work as long as there is fuel.
 The second law of
thermodynamics forbids a
“perfect engine.”
© 2013 Pearson Education, Inc.
Slide 19-28
Thermal Efficiency of a Heat Engine
Eint = 0 for the entire cycle
W eng  Q h  Q c
Thermal efficiency is defined as
the ratio of the net work done
by the engine during one cycle
to the energy input at the
higher temperature
e
W eng
Qh
Qh  Qc
Qc

1
Qh
Qh
What’s the efficiency of our engine?
e
W eng
Qh
Qh  Qc
Qc

1
Qh
Qh
Otto Cycle
The Otto cycle approximates the
processes occurring in an
internal combustion engine
If the air-fuel mixture is
assumed to be an ideal gas, then the
efficiency of the Otto cycle is
e  1
1
V1 V2 
 1

is the ratio of the molar specific heats
V1 / V2 is called the compression ratio
Typical values:
Compression ratio of 8
 = 1.4
e = 56%
Efficiencies of real engines are 15% to 20%
Mainly due to friction, energy transfer
by conduction, incomplete combustion
of the air-fuel mixture
The Brayton Cycle
 Many ideal-gas heat engines,
such as jet engines in aircraft,
use the Brayton Cycle, as
shown.
 The cycle involves adiabatic
compression (1-2), isobaric
heating during combustion
(2-3), adiabatic expansion
which does work (3-4), and
isobaric cooling (4-1).
 The efficiency is:
© 2013 Pearson Education, Inc.
Slide 19-58
Heat Engine: Lab
Heat Pumps and
Refrigerators

Heat engines can run in reverse
 This is not a natural direction of
energy transfer
 Must put some energy into a
device to do this
 Devices that do this are called
heat pumps or refrigerators
COPheating =
energy transferred at high temp Qh

work done by heat pump
W
COPcooling =
energy transferred at low temp QC

work done by heat pump
W
Refrigerators
 In a sense, a refrigerator
or air conditioner is the
opposite of a heat engine.
 In a heat engine, heat
energy flows from a hot
reservoir to a cool
reservoir, and work Wout
is produced.
 In a refrigerator, heat energy is somehow forced to flow
from a cool reservoir to a hot reservoir, but it requires
work Win to make this happen.
© 2013 Pearson Education, Inc.
Slide 19-41
https://www.youtube.com/watch?v=EIP3pSio7-M
© 2013 Pearson Education, Inc.
https://www.youtube.com/watch?v=wzqTWv8z
GlM
© 2013 Pearson Education, Inc.
Heat Pumps
Coefficient of Performance


The effectiveness of a heat pump is
described by a number called the
coefficient of performance (COP)
In heating mode, the COP is the ratio
of the heat transferred in to the work
required
energy transferred at high temp Qh
COP =

work done by heat pump
W
A heat pump, is essentially an air conditioner
installed backward. It extracts energy from colder
air outside and deposits it in a warmer room.
Suppose that the ratio of the actual energy
entering the room to the work done by the device’s
motor is 10.0% of the theoretical maximum ratio.
Determine the energy entering the room per joule
of work done by the motor, given that the inside
temperature is 20.0°C and the outside temperature
is –5.00°C.
energy transferred at high temp Qh
COPheating =

work done by heat pump
W
 Qh 
 0.100 

W
W

Carnot cycle
Qh
Qh
W
 Th 
293 K


 0.100

0.
100

  1.17


T

T
293
K

268
K
 h c
1.17 joules of energy enter the room by heat for each joule of work done.
Refrigerators
Refrigerators
• Understanding a refrigerator is a little harder
than understanding a heat engine.
• Heat is always transferred from a hotter
object to a colder object.
• The gas in a refrigerator can extract heat
QC from the cold reservoir only if the gas
temperature is lower than the cold-reservoir
temperature TC. Heat energy is then
transferred from the cold reservoir into the
colder gas.
• The gas in a refrigerator can exhaust heat
QH to the hot reservoir only if the gas
temperature is higher than the hot-reservoir
temperature TH. Heat energy is
then transferred from the warmer gas into
the hot reservoir.
Refrigerators
 Shown is the energytransfer diagram of a
refrigerator.
 All state variables
(pressure, temperature,
thermal energy, etc.)
return to their initial
values once every cycle.
 The heat exhausted per
cycle by a refrigerator is:
QH = QC +Win
© 2013 Pearson Education, Inc.
Slide 19-42
Refrigerators
 The purpose of a refrigerator is to remove heat from a
cold reservoir, and it requires work input to do this.
 We define the coefficient of performance K of a
refrigerator to be:
 If a “perfect refrigerator” could be built in which Win = 0,
then heat would move spontaneously from cold to hot.
 This is expressly forbidden by the second law of
thermodynamics:
© 2013 Pearson Education, Inc.
Slide 19-43
2nd Law:
Perfect Heat Engine
Can NOT exist!






No energy is expelled to
the cold reservoir
It takes in some amount
of energy and does an
equal amount of work
e = 100%
It is an impossible engine
No Free Lunch!
Limit of efficiency is a
Carnot Engine
2nd Law: Carnot’s Theorem

No real heat engine operating
between two energy reservoirs can
be more efficient than a Carnot
engine operating between the same
two reservoirs
 All real engines are less efficient
than a Carnot engine because
they do not operate through a
reversible cycle
 The efficiency of a real engine is
further reduced by friction, energy
losses through conduction, etc.
1796 – 1832
French engineer
The Limits of Efficiency
Everyone knows that heat can produce motion. That it
possesses vast motive power no one can doubt, in
these days when the steam engine is everywhere so well
known. . . . Notwithstanding the satisfactory condition to
which they have been brought today, their theory is very
little understood. The question has often been raised
whether the motive power of heat is unbounded, or
whether the possible improvements in steam engines
have an assignable limit.
Sadi Carnot
Carnot Cycle
The Limits of Efficiency
A perfectly reversible engine must use only two types of
processes:
1. Frictionless mechanical interactions with no
heat transfer (Q = 0)
2. Thermal interactions in which heat is transferred in
an isothermal process (ΔEth = 0).
Any engine that uses only these two types of processes is
called a Carnot engine.
A Carnot engine is a perfectly reversible engine; it has the
maximum possible thermal efficiency and, if operated as
a refrigerator, the maximum possible coefficient of
performance.
Reversible and Irreversible Processes
The reversible process is an idealization.
All real processes on Earth are irreversible.
Example of an approximate reversible
process:
 The gas is compressed isothermally
 The gas is in contact with an energy
reservoir
 Continually transfer just enough
energy to keep the temperature
constant

The change in entropy is equal to
zero for a reversible process and
increases for irreversible processes.
Section 22.3
Carnot Engine – Carnot Cycle
A heat engine operating in an ideal, reversible cycle (now called
a Carnot cycle) between two reservoirs is the most efficient
engine possible. This sets an upper limit on the efficiencies of all
other engines
Qc
Tc
Tc
 and ec  1 
Qh Th
Th
Temperatures must be in Kelvins
Ideal-Gas Refrigerators
 An ideal-gas refrigerator can
use a Brayton cycle in reverse.
 A gas is compressed
adiabatically to make it
extremely hot (4-3).
 Then heat is lost to the hot
reservoir (3-2).
 Then the gas expands
adiabatically (2-1) making it
extremely cold.
 Lastly, heat flows into the gas
from the cool reservoir (1-4).
© 2013 Pearson Education, Inc.
Slide 19-60
The Limits of Efficiency
If a perfectly reversible heat engine is used to operate a
perfectly reversible refrigerator, the two devices exactly
cancel each other.
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Slide 19-63
No Perfect Heat Engines
A perfect heat engine connected to a refrigerator would
violate the second law of thermodynamics.
© 2013 Pearson Education, Inc.
Slide 19-46
Limits of Heat Efficiency
Qc
Tc
Tc
 and ec  1 
Qh Th
Th
Qc
Tc
COPC 

W
Th  Tc
Qh
Th
COPH 

W
Th  Tc