CARNOT CYCLE

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CARNOT CYCLE
I am teaching Engineering Thermodynamics using
the textbook by Cengel and Boles. This set of
slides overlap somewhat with Chapter 6. But here
I assume that we have established the concept of
entropy, and use the concept to analyze the
Carnot cycle in the same way as we analyze any
other thermodynamic process. An isolated system
conserves energy and generates entropy. I did
add a few slides to show how Carnot motivated his
idea of entropy using the analogy of waterfall.
I used the Dover edition of his book. I went
through these slides in one 90-minute lecture.

Zhigang Suo, Harvard
University
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• Thermodynamics relates heat and motion
• thermo heat
• dynamics motion

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Stirling engine
Please watch this video
https//www.youtube.com/watch?vwGRmcvxB_dklistP
LZbRNoceG6UmydboILKclQv7Seqy4waCEindex22
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Carnots questionHow much work can be produced
from a given quantity of heat?
whether the motive power of heat is unbounded,
whether the possible improvements in
steam-engines have an assignable limit, a limit
which the nature of things will not allow to be
passed by any means whatever...
Modern translations Motive power work Motive
power of heat work produced by heat Limit
Carnot limit, Carnot efficiency
Carnot, Reflections on the Motive Power of Fire
(1824)
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Device runs in cycleSo they can run steadily
over many, many cycles
Heat, Q
Work, W
Device
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Isolated systemWhen confused, isolate.
Isolated system IS
Isolated system conserves mass over
time Isolated system conserves energy over
time Isolated system generates entropy over
time Define more words
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Reservoir of energy. Reservoir of entropyA
(purely) thermal system with a fixed temperature
QR
reservoir of energy and entropy Fixed TR Changing
UR, SR
The reservoir has a fixed temperature The
reservoir receives energy by heat Conservation of
energy The reservoir increases entropy
(Reversible process. Clausius-Gibbs equation)
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Thermodynamics permits heaterA device runs in
cycle to convert work to heat
Isolated system
Reservoir of energy, TR
Heat, Q
Heat, Q
Device
Work, W
Weight goes down.
Device runs in cycle Isolated system conserves
energy Isolated system generates entropy
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Thermodynamics forbids perpetual motion of the
second kinda device runs in cycle to produce
work by receiving heat from a single reservoir
Isolated system
Reservoir of energy, TR
Heat, Q
Weight goes up
Heat, Q
Device
Work, W
Device runs in cycle Isolated system conserves
energy Isolated system generates entropy
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Carnots remarks

• Wherever there exists a difference of
  temperature, motive power can be produced.
• To maximize motive power, contact (between
  bodies of different temperatures) should be
  avoided as much as possible

High-temperature source, TH
Q
Low-temperature sink, TL
Thermal contact of reservoirs of different
temperatures generates entropy, and does no work.
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Two reservoirs
For an engine running in cycle to convert heat to
work, a single reservoir will not do we need
reservoirs of different temperatures.
Isolated system of 4 parts
High-temperature source, TH
Engine
Wout
Low-temperature sink, TL
Isolated system conserves energy
isolated system generates entropy
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Carnot cycle
Clapeyron (1834)
Carnot (1824)
Gibbs (1873)
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Steam power plant
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Thermal efficiency
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Carnot efficiency
Isolated system
Isolated system conserves energy Isolated
system generates entropy All reversible
engines running in cycle between reservoirs of
two fixed temperatures TH and TL have the same
thermal efficiency (Carnot efficiency) All
real engines are irreversible. For an
irreversible (i.e. real) engine running in cycle
between reservoirs of two fixed temperatures TH
and TL, the thermal efficiency is below the
Carnot efficiency
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All real processes are irreversible So many ways
to generate entropy (i.e., to be irreversible)
Friction
Heat transfer through a temperature difference
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Carnot (1824) Two reservoirsReflections on the
Motive Power of Fire.
the re-establishing of equilibrium in the
caloric that is, its passage from a body in
which the temperature is more or less elevated,
to another in which it is lower. What happens in
fact in a steam-engine actually in motion? The
caloric developed in the furnace by the effect of
the combustion traverses the walls of the boiler,
produces steam, and in some way incorporates
itself with it. The latter carrying it away,
takes it first into the cylinder, where it
performs some function, and from thence into the
condenser, where it is liquefied by contact with
the cold water which it encounters there. Then,
as a final result, the cold water of the
condenser takes possession of the caloric
developed by the combustion... The steam is here
only a means of transporting the caloric. These
two bodies, to which we can give or from which we
can remove the heat without causing their
temperatures to vary, exercise the functions of
two unlimited reservoirs of caloric.
Modern translation Caloric entropy Reservoir of
caloric Thermal reservoir
Carnot (1796-1832)
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Carnot The steam is here only a means of
transporting the caloric.
High-temperature source, TH
High-temperature source, TH
Engine
Q
Low-temperature sink, TL
Low-temperature sink, TL
Thermal contact generates entropy
Reversible engine transports entropy
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Carnots analogy in his own words
The motive power of a waterfall depends on its
height and on the quantity of the liquid the
motive power of heat depends also on the quantity
of caloric used, and on what may be termed, on
what in fact we will call, the height of its
fall, that is to say, the difference of
temperature of the bodies between which the
exchange of caloric is made. In the waterfall the
motive power is exactly proportional to the
difference of level between the higher and lower
reservoirs. In the fall of caloric the motive
power undoubtedly increases with the difference
of temperature between the warm and the cold
bodies but we do not know whether it is
proportional to this difference. We do not know,
for example, whether the fall of caloric from 100
to 50 degrees furnishes more or less motive power
than the fall of this same caloric from 50 to
zero. It is a question which we propose to
examine hereafter.
Modern translations Motive power work Caloric
entropy
Carnot, Reflections on the Motive Power of Fire
(1824)
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Carnots analogy in pictures
high-height source
Wout
Low-height sink
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Carnots analogy in modern terms
Fall of caloric (entropy)
Fall of water
TH
zH
1
2
1
2
TL
zL
3
4
3
4
S2
m2g
S1
m1g
Fall of water Fall of caloric (entropy)
Reservoirs Two reservoirs of water Two reservoirs of caloric (entropy)
Height of fall zH - zL TH - TL
What is falling? Quantity of water, (m2g m1g) Quantity of entropy, (S2 S1)
Work produced by the fall (zH zL)(m2g m1g) (TH TL)(S2 S1)
1?2 Gain water from source Gain entropy from source
2?3 Drop elevation at constant quantity of water m2g Drop temperature at constant entropy S2
3?4 Lose water to sink Lose entropy to sink
4?1 Raise elevation at constant quantity of water m1g Raise temperature at constant entropy S1
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Carnot efficiencyreversible engine running
between two reservoirs of fixed temperatures TH
and TL
Carnot efficiency Low-temperature reservoir is
the atmosphere High-temperature reservoir is
limited by materials (Melting point of iron is
1811 K. Metals creep at temperatures much below
the melting point.) Carnot efficiency in numbers
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https//flowcharts.llnl.gov/
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What you need to know about energy, The National
Academies.
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Wasted energy
Yang, Stabler, Journal of Electronic Materials.
38, 1245 (2009)
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Refrigerator
Isolated system
Isolated system conserves energy Isolated
system generates entropy Carnot limit
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Isolated system
Heat pump
Isolated system conserves energy Isolated
system generates entropy Carnot limit
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Summary

• Thermodynamics permits heater (a device running
  in cycle to convert work to heat).
• Thermodynamics forbids perpetual motion of the
  second kind (a device running in cycle to produce
  work by receiving heat from a single reservoir of
  a fixed temperature).
• Carnot cycle A reversible cycle consisting of
  isothermal processes at two temperatures TH and
  TL, and two isentropic processes.
• All reversible engines running in cycle between
  reservoirs of two fixed temperatures TH and TL
  have the same thermal efficiency (Carnot
  efficiency)
• All real engines are irreversible. For an
  irreversible (i.e. real) engine running in cycle
  between reservoirs of two fixed temperatures TH
  and TL, the thermal efficiency is below the
  Carnot efficiency (Carnot limit)
• Carnot cycle also limits the coefficients of
  performance of refrigerators and heat pumps.