Download - Chapter 9 the Second Law of Thermodynamic
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Fundamental Physics
Chapter 9
PETROVIETNAM UNIVERSITY
FACULTY OF FUNDAMENTAL SCENCES
Hanoi, August 2012
Pham Hong QuangE-mail: [email protected]
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Law of Thermodynamics
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9.1 Heat Engines and the Second
Law of Thermodynamics
9.2 Heat Pumps and Refrigerators
9. Re!ersi"#e and $rre!ersi"#e Processes
9.% The &arnot Engine9.' Entropy
9.( Entropy &hanges in $rre!ersi"#e
Processes
9.) Entropy on a *icroscopic Sca#e
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Law of Thermodynam cs
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+irst Law of Thermodynamics ,
Re!iew The frst law is a statement o Conservation o
Energy.
The frst law states that a change in internalenergy in a system can occur as a result o
energy transer by heat, by work, or by both.
The frst law makes no distinction between
processes that occur spontaneously and those
that do not.
Only certain types o energy-conversion and
energy-transer processes actually take place
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Law of Thermodynamics
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Establishes which processes do and which do notoccurome processes can occur only in one directionaccording to the frst law.
This directionality is governed by the second law. These types o processes are irreversible.
!n irreversible process is one that occursnaturally in one direction only."o irreversible process has been observed to runbackwards.
The Second Law of
Thermodynamics
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Law of Thermodynamics
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#illiam Thomson, $ord
%elvin&'() * &+ritish physicist andmathematician
/irst to propose the useo an absolute scale otemperature0is work inthermodynamics led tothe idea that energycannot passspontaneously rom acolder ob1ect to a hotter
ob1ect.
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Law of Thermodynamics
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! heat engine is a devicethat takes in energy by heatand, operating in a cyclicprocess, e2pels a raction o
that energy by means owork.! heat engine carries someworking substance through acyclical process.
The working substanceabsorbs energy by heat roma high temperature energyreservoir 3Qh4.
#ork is done by the engine
3W eng4.
Heat Engine
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Law of Thermodynamics
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ince it is a cyclical process, 5Eint 6
7ts initial and fnal internal energies are
the same.
Therefore- W eng Qnet /Qh/ 0 /Qc/
The net work done by a heat engine e8uals
the net energy transerred to it.
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Law of Thermodynamics
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Thermal e9ciency is defned as the ratio othe net work done by the engine during onecycle to the energy input at the higher
temperature.
#e can think o the e9ciency as the ratio o
what you gain to what you give.7n practice, all heat engines e2pel only araction o the input energy by mechanicalwork.
Thereore, their e9ciency is always less than&:.
eng 1h c c
h h h
W Q Q QeQ Q Q
−≡ = = −
Therma# Eciency of a Heat
Engine
91H tE dth S d
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9.1 Heat Engnes and the SecondLaw of Thermodynamics
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Second Law 3e#!in0P#anc4+orm
It is impossible to construct a heat engine
that, operating in a cycle, produces no
efect other than the input o energy byheat rom a reservoir and the perormance
o an equal amount o work.
#eng can never be e8ual to ;
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9.1 Heat Engnes and the SecondLaw of Thermodynamics
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"o energy is e2pelled to thecold reservoir.7t takes in some amount oenergy and does an e8ualamount o work.e 6 &:It is impossible toconstruct such anengine.
Perfect Heat Engine
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92H tP dR f t
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9.2 Heat Pumps and Refrgerators
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Second Law 0 ausius statement for
refrigeratorIt is not possible orheat to ow rom acolder body to a
warmer body withoutany work havingbeen done toaccomplish this ow.
Energy will not owspontaneously rom alow temperatureob!ect to a higher
temperature ob!ect.
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9.2 Heat Pumps and Refrigerators
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The e?ectiveness o a heat pump is describedby a number called the coecient ofperformance [email protected] to thermal e9ciency or a heat engine
7t is the ratio o what you gain 3energytranserred to or rom a reservoir4 to whatyou give 3work input4.
7n coo#ing mode, you AgainB energy removed
rom a cold temperature reservoir.
! good rerigerator should have a high CO@. Typical values are or D
&oecient of Performance
COP c Qenergy transferred at low temp
work done on the pump W = =
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9.2 Heat Pumps and Refrigerators
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&5P- Heating *ode
7n heating mode, the CO@ is the ratio othe heat transerred in to the work re8uired.
Qh is typically higher than W
alues o CO@ are generally about )/or outside temperature about (F /
The use o heat pumps that e2tract energyrom the air is most satisactory inmoderate climates.
COP =
hQenergy transferred at high temp
work done by heat pump W =
93R bl dI blP
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9.3 Reversble and Irreversble Processes
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Re!ersi"#e and $rre!ersi"#eProcesses " reversible process is one in which boththe system and its environment can bereturned to e#actly the states they were in
beore the process occurred. ! reversible process is one in which every pointalong some path is an e8uilibrium state.!n irreversible process does not meet these
re8uirements.!ll natural processes are known to beirreversible.Geversible processes are an idealiHation, butsome real processes are good appro2imations.
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9.3 Reversible and Irreversible Processes
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! real process that is a good appro2imation oa reversible one will occur very slowly.
The system is always very nearly in ane8uilibrium state.
! general characteristic o a reversibleprocess is that there are no dissipative e?ectsthat convert mechanical energy to internalenergy present.
"o riction or turbulence, or e2ample
94TheCarnotEngne
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9.4 The Carnot Engne
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&arnot Engine
! theoretical engine developed by adiCarnot! heat engine operating in an ideal,reversible cycle 3now called a Carnotcycle4 between two reservoirs is themost e9cient engine possible
This sets an upper limit on the
e9ciencies o all other engines.
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9.4 The Carnot Engne
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&arnot6s Theorem
$o real heat engine operating betweentwo energy reservoirs can be moree%cient than a &arnot engine
operating between the same tworeservoirs.
!ll real engines are less e9cient than aCarnot engine because they do not
operate through a reversible cycle. The e9ciency o a real engine is urtherreduced by riction, energy lossesthrough conduction, etc.
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9.4 The Carnot Engne
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&arnot
&yc#e
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9.4 The Carnot Engne
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A I B is anisothermale2pansion.
The gas is placed incontact with the hightemperaturereservoir, T h.
The gas absorbsheat ;Qh;.
The gas does workW AB in raising the
piston.
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9.4 The Carnot Engne
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B I C is an adiabatice2pansion.
The base o the
cylinder is replacedby a thermallynonconducting wall."o energy enters orleaves the system
by heat. The temperaturealls rom T h to T c.
The gas does workW BC.
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9.4 The Carnot Engne
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The gas is placed inthermal contactwith the cold
temperaturereservoir.C I D is anisothermalcompression.
The gas e2pelsenergy ;Qc|.
#ork W CD is done
on the gas.
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9.4 The Carnot Engne
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D I A is an adiabaticcompression.
The base is replaced bya thermallynonconducting wall.
o no heat ise2changed with thesurroundings.
The temperature o the
gas increases rom T c to T h.
The work done on thegas is W DA.
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9.4 The Carnot Engne
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The work done by the engine is
shown by the area enclosed bythe curve, W eng.
The net work is e8ual to ;Qh; * ;Qc;.∆Eint 6 or the entire cycle
Carnot showed that thee9ciency o the enginedepends on the temperatures othe reservoirs.
Temperatures must be in %elvins!ll Carnot engines operatingbetween the same twotemperatures will have the
same e9ciency.
1 1eng c c
h h h
W Q T e
Q Q T = = − = −
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9.4 The Carnot Engne
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E9ciency is i Th 6 TcE9ciency is &: only i Tc 6 %
uch reservoirs are not available
E9ciency is always less than &: The e9ciency increases as Tc is lowered andas Th is raised.7n most practical cases, Tc is near room
temperature, J % o generally Th is raised to increasee9ciency.
7otes 8"out &arnot
Eciency
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9.4 The Carnot Engine
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&arnot &yc#e in Re!erse
Theoretically, a Carnot-cycle heat
engine can run in reverse.
This would constitute the moste?ective heat pump available.
This would determine the ma2imum
possible CO@s or a given combination
o hot and cold reservoirs.
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9.4 The Carnot Engine
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&arnot Heat Pump &5Ps
7n heating modeK
7n cooling modeK
7n practice, the CO@ is limited tovalues below &
C
h h
h c
Q T COP
W T T = =
−
c c C
h c
Q T COP
W T T = =
−
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9.5 Entropy
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Entropy and
Heat The original ormulation o entropy dealt with thetranser o energy by heat in a reversible process.$et dQr be the amount o energy transerred by heat
when a system ollows a reversible path. The change in entropy, dS is
The change in entropy depends only on the
endpoints and is independent o the actual pathollowed.
The entropy change or an irreversible process canbe determined by calculating the change in entropy
or a reversible process that connects the sameinitial and fnal oints.
r dQdST
=
5
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9.5 Entropy
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dQr is measured along a reversible path, even i the
system may have ollowed an irreversible path./or a fnite process, T is generally not constantduring process.
The fnite change in entropy depends only on theproperties o the initial and fnal e8uilibrium states.
Thereore we are ree to choose a particularreversible path over which to evaluate theentropy rather than the actual path, as long as
the initial and fnal states are the same.
f f r
i i
dQS dST
∆ = =∫ ∫
Entropy and Heat-
&ont.
5
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9.5 Entropy
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∆S for a Re!ersi"#e &yc#e
∆S 6 or any reversiblecycle
7n general,
This integral symbolindicates the integral isover a closed path.
0r dQ
T =∫ L
95E
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9.5 Entropy
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To calculate the change in entropy in a realsystem, remember that entropy depends only on
the state o the system.#e fnd a reversible process which has the sameinitial and fnal e8uilibrium states and calculatethe change in entropy or this process>o not use Q, the actual energy transer in the
process.>istinguish this rom Qr , the amount oenergy that would have been transerred byheat along a reversible path.Qr is the correct value to use or ∆S.
Entropy &hanges in
$rre!ersi"#e Processes
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9.5 Entropy
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Entropy is a measure o disorder.'he entropy o the (niverseincreases in all real processes.
This is another statement o thesecond law o thermodynamics.
7t is e8uivalent to the %elvin-@lanck and Clausius statements.
Entropy and theSecond Law
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9.5 Entropy
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) in Therma#
&onduction The cold reservoir absorbs energy Q and its
entropy changes by QMT c.
!t the same time, the hot reservoir loses Q
and its entropy changes by -QMT h.
ince T h N T c , the increase in entropy in the
cold reservoir is greater than the decrease in
entropy in the hot reservoir. Thereore, ∆SU N
/or the system and the niverse
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9.5 Entropy
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Consider an adiabatic reee2pansion.
This process is irreversiblesince the gas would not
spontaneously crowd intohal the volume ater fllingthe entire volume .Q 6 but we need to fnd
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9.5 Entropy
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/or an isothermal process, thisbecomes
ince V f N V i , >S is positive
This indicates that both the entropyand the disorder o the gas increaseas a result o the irreversibleadiabatic e2pansion .
ln f
i
V S nr
V
∆ =
) in +ree Epansion- cont
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'hank you*