1st VS 2nd Laws of Thermodynamics

• Directionofaprocess• Qualitypointofview- Intermsof“Entropy”• Entropygenerationalwaysincreases- Ifnot,itviolates2nd lawofthermodynamics• AprocessincreaseEntropyhigh

à Irreversibilityhigh• AprocessincreaseEntropylow

à Irreversibilitylow• Hotà Cold(O);Coldà Hot(X)

• Energyconservation• Quantitypointofview- Intermsof“Energy”• Energycannotbe createdordestroyed,butitalwaysconserves- Ifnot,itviolates1st lawofthermodynamics• Energyinput– Energy output=Energystored• 100%outputw/oanyloss

ThefirstLaws ThesecondLaws

GENESYSLaboratory

1st law of Thermodynamics

Controlmass(ClosedSystem) Controlvolume(OpenedSystem)

W Q KE PU ED + D = + D + DD ( )mass boundaryW Q KE PEW Q KE PE

UHE E D

D

D + D + = + D +D D

D + D = + D + D

D

IfyoursystemisastationarysystemUW QD + D = D ( )mass boundaryW Q UE

HWE

QD + D + =

D

D

+ D

D

= D

D

Emass=PVMovingboundary(closedSystem)

GENESYSLaboratory

Some Remarks about Entropy1. Processescanoccurina certain directiononly,notinany direction.Aprocessmustproceedinthedirectionthatcomplieswiththeincreaseofentropyprinciple,thatis,Sgen≥0.2. Entropyisnon-conservedproperty,andthereisnosuchthingastheconservation

ofentropyprinciple.

3. Theperformanceofengineeringsystemsisdegradedbythepresenceofirreversibility,andentropygeneration isameasureofthemagnitudesoftheirreversibility'spresentduringthatprocess

GENESYSLaboratory

Week1.GasPowerCyclesI

GENESYSLaboratory

Objectives1. Evaluatetheperformanceofgaspowercyclesforwhichtheworkingfluidremainsagasthroughouttheentirecycle2. Developsimplifyingassumptionsapplicabletogaspowercycles3. Discussbothapproximateandexactanalysisofgaspowercycles4. Reviewtheoperationofreciprocatingengines5. SolveproblemsbasedontheOtto,Diesel,Stirling,andEricssoncycles6. SolveproblemsbasedontheBraytoncycle;theBraytoncyclewithregeneration;andtheBraytoncyclewithintercooling,reheating,andregeneration7. Analyzejet-propulsioncycles8. Identifysimplifyingassumptionsforsecond-lawanalysisofgaspowercycles9. Performsecond-lawanalysisofgaspowercyclesGENESYSLaboratory

Combustor And Cycle

Chemical Energy Thermal Energy Mechanical Energy

Fuel

Low Heat Value

Combustion Mechanical linkage

Heat Power Output

Temperature rise Pressure rise

Rotational torque

Rankine CycleStirling Cycle

Otto Cycle

Diesel Cycle

Brayton CycleJet-propulsion Cycle

Combustor ExternalCombustorInternalCombustor

StirlingEngineSteamEngineDieselEngine(Compression-ignition)GasolineEngine(Spark-ignition)GasTurbineJetEngine

GENESYSLaboratory

Basic Considerations in the Analysis of Power CyclesTheanalysisofmanycomplexprocessescanbereducedtoamanageablelevelbyutilizingsomeidealizations

Theidealizationsandsimplificationscommonlyemployedintheanalysisofpowercyclescanbesummarizedasfollows:1. Thecycledoesnotinvolveanyfriction.Therefore,theworkingfluiddoesnotexperienceanypressuredrop asitflowsinpipesordevicessuchasheatexchangers.2.Allexpansionandcompressionprocessestakeplaceinaquasi-equilibriummanner.3.Thepipesconnectingthevariouscomponentsofasystemarewellinsulated,andheattransferthroughthemisnegligible.4.Neglectingthechangesinkineticandpotentialenergiesoftheworkingfluidisanothercommonlyutilizedsimplificationintheanalysisofpowercycles.GENESYSLaboratory

The Carnot Cycle And Its Value in Engineering• TheCarnotcycleisthemostefficientcyclethatcanbeexecutedbetweenaheatsourceandasink• Itiscomposedoffourtotallyreversibleprocesses:Isothermalheataddition,Isentropicexpansion,Isothermalheatrejection,andIsentropiccompression• Itsthermalefficiency•Example9-1(showthatthethermalefficiencyofaCarnotcycleoperatingbetweenthetemperaturelimitsofTH andTL issolelyafunctionofthesetwotemperature)• TherealvalueoftheCarnotcyclecomesfromitbeingastandard againstwhichtheactualortheidealcyclescanbecompared P-vandT-sdiagramsofaCarnotcycle

H

L

TT

-=1Carnot th,h

GENESYSLaboratory

Air-Standard Assumptions

• Theworkingfluidisair,whichcontinuouslycirculatesinaclosedloopandalwaysbehavesasanidealgas• Alltheprocessesthatmakeupthecycleareinternallyreversible• Thecombustionprocessisreplacedbyaheat-additionprocessfromanexternalsource• Theexhaustprocessisreplacedbyaheat-rejectionprocessthatrestorestheworkingfluidtoitsinitialstate• Airhasconstantspecificheatswhosevaluesaredeterminedatroomtemperature(25oC)ß cold airstandardassumption

GENESYSLaboratory

Entropy Change of Ideal Gases

TvdP

Tdh

T

Pdv Tduds

-=

+=

dTcdhdTcdu

RTPv

p

v

===

v

p

dT dv ds c RT vdT dPc RT P

= +

= -

1

22

1

1

22

112

ln)(

ln)(

P PR

TdTTc

v vR

TdTTcss

p

v

-=

+=-

ò

ò

Thedifferentialentropychangeofanidealgas

Theentropychangeforaprocessobtainedbyintegrating

GENESYSLaboratory

Constant Specific Heats (Approximate Analysis)

2 22 1 avg

1 1

2 2,avg

1 1

, ln ln

ln ln (kJ/kg K)

v

p

T v s s c RT vT P c RT P

- = +

= - ×

2 22 1 avg

1 1

2 2,avg

1 1

, ln ln

ln ln (kJ/kmol K)

v u

p u

T v s s c RT vT P c RT P

- = +

= - ×

Entropychangescanalsobeexpressedonaunitmolebasis

Theentropychangerelationsforidealgasesundertheconstantspecificheatassumption

GENESYSLaboratory

Isentropic Processes of Ideal Gases (Approximate Analysis)

vcR

v vv

TT

v v

cR

TT

÷÷ø

öççè

æ=Þ-=

2

1

1

2

1

2

1

2 lnlnlnln

1, -=Þ=-= kcR

cckccR

vv

pvp

1

2 1

1 2const.

(ideal gas)k

s

T vT v

-

=

æ ö æ ö=ç ÷ ç ÷

è ø è ø1st isentropicrelation

2 22 1 avg

1 1

2 2,avg

1 1

, ln ln

ln ln

v

p

T v s s c RT vT P c RT P

- = +

= -

( )1

2 2

1 1const.

(ideal ga s)

kk

s

T PT P

-

=

æ ö æ ö=ç ÷ ç ÷

è ø è ø 2nd isentropicrelation2 1

1 2const.

(ideal gas) k

s

P vP v

=

æ ö æ ö=ç ÷ ç ÷

è ø è ø 3rd isentropicrelation1

1

constant

constant (ideal gas) constant

k

( -k)k

k

Tv

TPPv

- =

=

=

CompactformsGENESYSLaboratory

Variable Specific Heats (Exact Analysis)

K)(kJ/kg ln1

21212 ×--=-

P PRssss oo

Itisexpressedonaunit-molebasisTheentropychangerelationsforidealgasesunderthevariablespecificheatassumption

ò=T

p TdTTcs

0)(o

oo12

2

1)( ss

TdTTcp -=ò

K)(kJ/kmol ln1

21212 ×--=-

P PRssss u

oo

GENESYSLaboratory

Isentropic Processes of Ideal Gases (Exact Analysis I)

0ln1

21212 =--=-

P PRssss oo

)exp( RsPro

=

1

212 ln

P PRss += oo

÷øö

çèæ

÷øö

çèæ

=-

=

Rs

Rs

Rss

P P

o

o

oo

1

2

12

1

2

exp

expexp

Relativepressure1

2

const.1

2

r

r

s PP

P P

=÷÷ø

öççè

æ

=

2

1

1

2

1

2

2

22

1

11

PP

TT

vv

TvP

TvP

=®=

1

1

2

2

2

1

1

2

1

2

r

r

r

r

PT

PT

PP

TT

vv

==1

2

const1

2

r

r

s vv

vv

=÷÷ø

öççè

æ

=

Relativespecificvolumevr=T/Pr

• Strictlyvalidforisentropicprocessesofidealgasesonly• ThevaluesofPr andvr arelistedforairinTableA-17

GENESYSLaboratory

Isentropic Processes of Ideal Gases (Exact Analysis II)

• ThevaluesofPr andvr listedforairinTableA-17areusedforcalculatingthefinaltemperatureduringanisentropicprocess

GENESYSLaboratory