chapter 9 the second law of thermodynamic

8/16/2019 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

Pham Hong Quang Faculty of Fundamental Sciences 2

9.1 Heat Engines and the Second


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


+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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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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#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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! 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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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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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


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


"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


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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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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&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


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


! 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


&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.

94TheCarnotEngne


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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.

94TheCarnotEngne


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&arnot

&yc#e

94TheCarnotEngne


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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.

94TheCarnotEngne


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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.

94TheCarnotEngne


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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.

94TheCarnotEngne


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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.

94TheCarnotEngne


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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 = = − = −

94TheCarnotEngne


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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


&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


&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


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


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


∆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


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

95E t


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9.5 Entropy


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

95E t


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9.5 Entropy


) 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

95E t


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9.5 Entropy


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


/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*

chapter 9 the second law of thermodynamic

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