Acknowledgments
TheillustrationsprovidedbyseveralpastandcurrentgraduatestudentsofProf.Dinceraregratefully acknowledged,includingCananAcar,SeyedaliAghahosseini,EhsanBaniasadi,CamiloCassallas,SayantanGosh, HasanOzcan,MusharafRabbani,TahirRatlamwala,RonRoberts,andRafayShamim.
Inaddition,YusufBicer’shelpinmaterializingtheliteraturereviewfor Chapter8 isacknowledged. Lastbutnotleast,wewarmlythankourwives,GulsenDincerandIulianaMariaZamfirescu,andourchildren Meliha,Miray,IbrahimEren,Zeynep,andIbrahimEmirDincer,andIoana,Cosmin,andPaulinaZamfirescu.They havebeenagreatsourceofsupportandmotivation.
IbrahimDincerandCalinZamfirescu
January2016
1.1INTRODUCTION
Hydrogenbecomesincreasinglyimportanttosociety,asitisconsideredoneofthekeysolutionstosustainability. Sincetheglobalpopulationanditsdemandforservices,materials,transportation,commodities,etc.,arerapidly increasing,manyconcernsariserelatedtothesupplyofenergyandtheenvironmentalimpactrelatedtoitsconversion/transformation,distributionanduse.Thence,thereisaclearmotivationworldwidetodevelopcleanerprocesses andmoreefficientproductionmethodsinallsectors,whichwillbecomeabletosupplementandreplacetheconventionalpowergenerationandproductionmethodsbyincorporatinghydrogenandsustainableenergies,including renewablesandnuclear.
Hydrogencanbeproducedfromawealthofmaterialsexistentinabundanceonearthandeasilyaccessible.Wateris themostabundantsourceofhydrogen.Biomass,anthropogenicwastesandevenfossilfuels,whenprocessedthrough cleanmethods,representsourcesforsustainablehydrogenproduction.Asreviewedin DincerandZamfirescu(2012), fivegeneralmethodscanbeidentifiedforhydrogenproduction,namely:electrochemical,photochemical,biochemical, thermochemicalandradiochemical.Inaddition,hybridmethodsmaybepossiblesuchasphoto-electrochemical, photo-biochemical,etc.
Developing,designing,optimizing,andassessingthemethodsforhydrogenproduction,includinghydrogenstorageanddistribution,requiresaninterdisciplinaryeffort.Thermodynamicsasatoolanditsapplicationstoelectrochemical,thermochemical,photochemical,biochemicalprocesses,andcatalysisaretreatedasthemasterpiecefor systemdesign,analysis,assessment,andoptimizationinviewofmakinghydrogenproductionmoreefficient,more cost-effective,moreenvironmentallybenignandmoresustainable.
Inthischapter,fundamentalaspectsrelatedtohydrogenproductionarereviewedwithafocusonthermodynamics. Ofparticularattentionisthermodynamicsapplicationinthestudyofchemicalreactions,especiallythoserelevantto hydrogenproduction.Somegeneralaspectschemicalthermodynamicsareintroducedandcomplementedwithkey methodsonchemicalkinetics.Ofparticularinterestistheuseoftheconceptofexergyandchemicalexergyforprocess assessmentinaccordancewiththesecondlawofthermodynamics(SLT)andbyaccountingfortheinfluenceofthe surroundingsenvironment.Thechapterisexpandedwiththeenhanceduseofexergoeconomic,exergoenvironmental andexergosustainabilityassessments.
1.2PHYSICALQUANTITIESANDUNITSYSTEMS
Thescientificmethodinnaturalscienc esappealstoempiricalevidencesinordertoconstructandvalidatemodels topredictandunderstandnature’sphenomena.Therefore,oneneedstorelatetoquantitiesthataremeasurableby instruments,whichareknownas “physicalquantities. ” Physicalquantitiesareoftwotypes,namely:
• Extensivequantity:whichbydefinitionisthesumofquantitiesinallsystemconstituents(e.g.,mass,volume, electriccharge,energy)
• Intensivequantity:whichisindependentoftheextentofthesystem(e.g.,temperature,pressure,specificvolume)
Sevenphysicalquantities denotedasfundamentalquantities havebeenchosentorepresenttheInternationalSystemofUnits(ISU)accordingto ISU(2006).Thesearelength,mass,time,electriccurrent,thermodynamictemperature, amountofsubstance(molar)andluminousintensity(measuredincandela).Thestandarddefinitionofthesequantitiesis givenin Table1.1.Notethatallotherphysicalquantitiescanbederivedfromthefundamentalonesbasedonconstituencyrelationships.
Eachofthephysicalquantitytypeshasanassociatedunit,formingthustheISU. Table1.2 givesthedefinitionsofthe fundamentalunitsofmeasureaccordingtoISUformulations.Adoptionofasystemofunitsisanimportantstepinthe analyses.Therearetwomainsystemsofunits:theISU,whichisusuallyreferredtoasSIunits,andtheEnglishSystemof Units(sometimesreferredasImperial).TheSIunitsareusedmostwidelythroughouttheworld,althoughtheEnglish SystemistraditionalintheUnitedStates.SIunitsareprimarilyemployedthroughoutthisbook;however,relevantunit
TABLE1.1 DefinitionsandStandardSymbolsfortheFundamentalPhysicalQuantities
Quantity SymbolQuantitydefinition
Length l Geometricdistancebetweentwopointsinspace
Mass m Quantitativemeasurementofinertiathatistheresistancetoacceleration
Time t Ameasurableperiodoftheprogressofobservableornonobservableevents
Electriccurrent I Rateofflowofelectriccharge
Thermodynamic temperature T Ameasureofkineticenergystoredinasubstancethathasaminimumofzero(nokinetic “internal”)energy
Amountofsubstance n Thenumberofunambiguouslyspecifiedentitiesofasubstancesuchaselectrons,atoms,molecules,etc.
Luminousintensity Iv Luminousfluxofalightsourceperdirectionandsolidangle,forastandardmodelofhuman-eye sensitivity
From:ISU,2006.TheInternationalSystemofUnits(SI),eighthed.
TABLE1.2 DefinitionoftheFundamentalUnitsAccordingtoInternationalSystemofUnits
Quantity Dimensional symbolUnitSymbolMeasurementunitdefinition
Length L MetermThelengthofthepathtraveledbylightinavacuumduringatimeinterval of1/299,792,458ofasecond
Mass M
KilogramkgTheweightoftheInternationalPrototypeofthekilogrammadeinplatinum-iridiumalloy Time T SecondsThedurationof9,192,631,770periodsoftheradiationcorrespondingtothetransition betweenthetwohyperfinelevelsofthegroundstateofthecesium133atom
ElectriccurrentI AmpereATheconstantcurrentwhich,ifmaintainedintwostraightparallelconductorsofinfinite length,ofnegligiblecircularcross-section,andplaced1mapartinavacuum,would producebetweentheseconductorsaforceequalto2 10 7 N/moflength
Thermodynamic temperature Θ
Amountof substance
Luminous intensity
KelvinKThefraction1/273.16ofthethermodynamictemperatureofthetriplepointofwater (havingtheisotopiccompositiondefinedexactlybythefollowingamountofsubstance ratios:0.00015576moleof 2Hpermoleof 1H,0.0003799moleof 17Opermoleof 16O,and 0.0020052moleof 18Opermoleof 16O)
N MolemolTheamountofsubstanceofasystemthatcontainsasmanyelementaryentitiesasthereare atomsin0.012kgofcarbon12
J CandelacdTheluminousintensity,inagivendirection,ofasourcethatemitsmonochromatic radiationoffrequency540THzandthathasaradiantintensityinthatdirectionof1/683W persteradian
From:ISU,2006.TheInternationalSystemofUnits(SI),eighthed.
conversionsandrelationshipsbetweentheSIandEnglishunitsystemsforfundamentalpropertiesandquantitiesare listedin AppendixA.
Anyotherphysicalquantitybesidesthosegivenin Table1.1 canbederivedfromthefundamentalquantitiesusing constitutiverelationships.Theunitsofmeasureofanyderivedphysicalquantitycanbedeterminedbasedontheunits offundamentalquantitiesandtheconstitutiverelationshipsaccordingtothedimensionalanalysismethod.Inthis respect,thedimensionalsymbolsforthefundamentalquantitymustbeusedtoexpressthedimensionforthederived quantities.Thelistofdimensionsymbolsforthefundamentalphysicalquantitiesisgivenin Table1.2.
Now,wewillreviewthemainderivedphysicalquantitieswhicharethemostrelevantwithinthisbook.First,the thermodynamicpropertiespressure,specificvolumeandtemperatureareintroduced,andtheirinterconnectionsand interpretationsareprovided.Asknown,thethermodynamicstateofasystemisgenerallyspecifiedwhenitspressure, temperatureandspecificvolumeareknown.
Tobegin,letusintroducethespecificvolume,definedastheratiobetweenthevolumeandthemassofasystem. Here,massisafundamentalquantitybutvolumeisnot.Thence,thenotionofvolumemustbefirstdefined.Volumeis aphysicalquantity,representingathree-dimensionalextentofasystem.Thisisanextensiveproperty,havingthe dimensionequaltolengthtothepower3,noted L3.Thecommonsymbolforvolumeis V,thereforeonewrites
Here,thenotationbetweenbracketsistheunitofvolume,namelycubicmeter.Thespecificvolumeisthusdefined asfollows
¼ V m m3 =kg
Indimensionalanalysisnotation,onewritesthatthedimensionofthespecificvolumeisgivenby L3M 1,where L is thedimensionforlengthand M isthedimensionformass.Specificvolumeisinfactthereciprocalofdensity, ρ ¼ v 1 . Furthermore,onenotesthatspecificvolumecanbeexpressedwithrespecttotheamountofsubstanceinmoles (molar-specificvolume)bythefollowingequation
Here,thedimensionofthemolar-specificvolumeis,therefore, L3N 1.Pressureisdefinedastheforce(action)per unitofsurfacearea.Sinceboththeforceandsurfacearenotfundamentalphysicalquantities,definitionrelationships
mustfirstbeintroducedforthose.Area,denotedwithsymbol A,representsthetwo-dimensionalextentofasystem, havingthusthedimension L2 andtheunitm2.
Forcerepresentsameasureofactionorinteractionbetweensystems.Forcesdoexistinanyregionastheymanifest theirpresenceintheformofforcefields(e.g.,electromagneticorgravitationalfields).Theforceactingbetweentwo systemscanproduceacceleration,meaningachangeofvelocity.Ifanobjectchangesitsvelocity,thenitnecessarily behavessobecauseitisundertheactionofanetforce.Herewedefinevelocityasavector(havingthusdirectionand magnitude)andrepresentingthespeedofasystemtowardadefinedtarget.Sincespeedisdefinedasthedisplacement perunitoftime,onenotesthatthedimensionforvelocityis LT 1 withtheunitofSI(ISU)m/s,andthedefinition relationshipfollows
Theaccelerationmagnitudeisthederivativeofspeedwithrespecttotimeandwhencewillhavethedimensionof LT 2 andtheSIunitofm/s2;thedefinitionaccelerationiswrittenas
Forceisavectorquantityhavingthesamedirectionastheaccelerationthatitproduces.Forceisdefinedastheproductofmassandacceleration.Thatis,ifasystemofmass m isacceleratedwiththeacceleration a,thenanetforceacts uponitasfollows
Thedimensionforforceis MLT 2,meaningthatforceismeasuredinSIinkgm/s2,aunitthatisshorthandedas Newton(symbolN);thence1N ¼ 1kgm/s2.InBritishSystemofUnits,forceismeasuredinpound-forcedenotedas lbf.Pressureisdefinednowastheratiobetweenaforceandthenormalareaofthesurfaceoverwhichforceisexerted uniformly(heretheterm “normal” standsforadirectionperpendicularonforcevectordirection).Therefore,one writes
Notethatalthoughforceisavector,pressureisdefinedasascalar.Furthermore,pressureisanintensivequantity.The dimensionofpressureisequaltothedimensionofforcedividedbythedimensionofarea,thatis, ML 1T 2,having theSIunitofkg/s2m,whichisthesameasN/m2 andshorthandedasPa(Pascal).Onesaysthat1Pascalrepresents theforceof1N(Newton)exertedon1m2 surface.Pressureisaveryimportantparameterforthethermodynamics ofgasesandliquids.
Theatmospherethatsurroundstheearthactsasareservoiroflow-pressureair.Itsweightexertsapressurethat varieswithtemperature,humidity,andaltitude.Atmosphericpressurealsovariestemporarilyatagivengeographic location,duetothemovementofweatherpatterns.Thestandardvalueoftheatmosphericpressure(orthepressureof standardatmosphere)is101,325Paor760mmHg.
Theatmosphericpressureistypicallymeasuredwithaninstrumentcalledbarometer;fromhereitcomesthename of barometricpressure.Whilethechangesinbarometricpressureareusuallyasminoras <12.5mmofmercury,they needtobetakenintoaccountonlywhenprecisemeasurementsarerequired.
Gaugepressure isanypressureforwhichthebaseformeasurementistheatmosphericpressure.Thegaugepressure isexpressedaskPagauge.Atmosphericpressureservesasareferencelevelforothertypesofpressuremeasurements, forexample,gaugepressure.Asshownin Fig.1.1,thegaugepressureiseitherpositiveornegative,dependingonits levelaboveorbelowatmosphericlevel.Atthelevelofatmosphericpressure,thegaugepressurebecomeszero.
Adifferentreferencelevelisutilizedtoobtainavalueforabsolutepressure.Theabsolutepressurecanbeanypressureforwhichthebaseformeasurementisacompletevacuum,expressedinkPa(absolute).Absolutepressureiscomposedofthesumofthegaugepressure(positiveornegative)andtheatmosphericpressureasfollows
Forexample,toobtaintheabsolutepressure,wesimplyaddthevalueofatmosphericpressure.Absolutepressureis themostcommontypeusedinthermodynamiccalculations,despitehavingthepressuredifferencebetweentheabsolutepressureandtheatmosphericpressureexistinginthegaugebeingwhatisreadbymostpressuregaugesand indicators.
Avacuumisapressurelowerthanatmosphericandoccursonlyinclosedsystems,exceptinouterspace.Itisalso called negativegaugepressure.Avacuumisusuallydividedintofourlevels:(i)lowvacuum,representingpressures above133Pa( 1Torr)absolute;(ii)mediumvacuum,varyingbetween1and10 3 0.1333to133Paabsolute;(iii)high vacuum,rangingbetween10 3 and10 6 Torrabsolute(1Torr ¼ 133.3Pa);and(iv)veryhighvacuum,representing absolutepressurebelow10 6 Torr.The idealvacuum ischaracterizedbythelackofanyformofmatter.Notethat inphysics, matter isdefinedasparticleswithrestmass.
Asknown,theparticlespossessingrestmassinclude quarks and leptons,whichareabletocombineandform protons, neutrons and electrons.Amongthem,protonsandneutronscombinetoformnuclei,havingapositiveelectriccharge. Nucleicombinewithelectronsofnegativeelectricchargetoformatoms.Therefore,atomsbecomeneutralwithrespect totheelectriccharge.Intotal,thereare116knownkindsofatomscorrespondingto116chemicalelementsfromthe periodictableofelements.
Besidesmatter,intheuniverseforcefieldsmanifestofwhichofparticularimportanceistheelectromagneticfield. Theelectromagneticfieldissaidtopropagateviaphotonsmovingatthespeedoflight.Photonshavemass,butno rest;whichmeansthatphotonshavenorestmass.Beingmatterwithnorest,photonsdopropagateinspaceregions characterizedbyabsolutevacuum.Gravitationalfieldsalsopropagatethroughvacuum.
Itisgenerallyunderstoodthatbulkmatter(ormatterwithrestmass)andfields(photons,gravity,etc.)constitutethe substanceoftheuniverse.Sincethethermodynamictemperaturecharacterizesthekineticenergystoredinsubstance, itmeansthatthisphysicalquantityisnotrestrictedtobulkmatter,butalsomayrefertoforcefields(whichdonothave thepropertyofrestmass).Infurtherchaptersofthisbook,aninterpretationofthetemperatureofelectromagnetic radiation(blackbody,nonblackbody,monochromatic)willbegiven.Oneessentialaspectrelatedtothermodynamic temperaturecomesfromthefactthatthekineticenergyatthemicroscale(wheremanyparticlesmanifest)cannotbe entirelyretrievedatthemacroscaleduetoprobabilisticreasons,asdiscussedinthenextsectionofthischapterwhere ideal-gastheoryisintroduced.Theideal-gastheoryexplainsatabasiclevelthecorrelationbetweenpressure,temperatureandspecificvolumeofanidealgas.
Theforceactionresultingonadisplacementofmatterisquantifiedbyaphysicalquantityreferredtoaswork(also called “theworkofaforce”).Considerasituationasin Fig.1.2 whereaforceactsonasystemobliquelyatangle α and producesadisplacement l.Thenthedotproductofforceanddisplacementrepresenttheworkoftheforce.Provided thattheforceanddisplacementhavethesamedirection(α ¼ 0),theworkbecomes W ¼ Fl
FIG.1.2 Illustrationoftheconceptofwork.
FIG.1.1 Illustrationofrelationshipsamongpressures.
Beingdefinedasadotproduct,workisascalar.Itissaidthatworkrepresentstheamountofenergyspenttoperformadisplacementaction.Ifthereisnodisplacement,thenthereisnowork.Ifthereisnoforce,thenthereisnowork produced. Fig.1.2 showstheworkofgravity,displacingasysteminthegravitationalfieldwiththedistance z.Thence, forceanddisplacementarebothvertical, W¼mgz, g ¼ 9.81m/s2.Generally,themagnitudeofworkisgivenby W ¼ Fl cos α ðÞ (1.2)
Here,theworkhasdimensionofforcemultipliedbylength,whichis ML2T 2 withtheunitkgm2/s2 orNm (Newton-meter);thisunitisknownasJoule,J,where1J ¼ 1Nm.Thecapacityofasystemtodowork(orreceivework) definesthephysicalquantityknownasenergy.Energyhasthesamedimensionandunitaswork.Arigorousdefinition ofenergyrequirestheintroductionofthenotionofthermodynamicsystem.
Bydefinition,a thermodynamicsystem ispartoftheuniverse,delimitedbyarealorimaginaryboundarythatseparatesthesystemfromtherestoftheuniverse,whereastherestoftheuniverseisdenotedasthe surroundings.Ifa thermodynamicsystemexchangesenergybutnotmatterwithitssurroundings,itissaidtobea closedthermodynamic system or controlmass;seetherepresentationfrom Fig.1.3a.Ontheotherhand,an opensystem or controlvolume isa thermodynamicsystemthat,asrepresentedin Fig.1.3b,caninteractwithitssurroundingsbothbymassandenergy transfer.Aclosedthermodynamicsystemthatdoesnotexchangeenergyinanyformwithitssurroundingsisdenoted asanisolatedsystem. Fig.1.4 showsanisolatedthermodynamicsystem.
Energycanbeexchangedbyaclosedsystemwithitssurroundinginonlytwoforms:byworktransferorbyheat transfer.Thesymbolforenergyis E andanyenergychangeofasystemisdenotedwith ΔE.Ifaclosedthermodynamic systemhasadeformableboundarythatisaperfectthermalinsulator,thenthesystemiscapableofexchangingwork withitssurroundingsinanadiabaticmanner.Thesystemisadiabatic.Therefore,thechangeofenergyequalsthework transferunderadiabaticconditionsasfollows
FIG.1.3 Illustratingtheconceptsofthermodynamicsystemsas(a)closedand(b)open.
Impermeable and insulated wall (no mass exchange)
Surroundings No energy exchange by heat
Insulated system
Surroundings No energy exchange by work System boundary
Ifasystemhasarigidboundary,butispermeabletoheattransferanddoesnotexchangeworkwithitssurroundings,thentheonlywaytotransferenergyissaidtobebyheat.Anychangeofsystemenergyequalsaheattransfer, denotedwithsymbol Q;therefore,onenotes
ΔE ¼ Q, ðso-called:heattransferÞ
Inorderforatransferofenergybyheattobepossible,atemperaturedifferencemustexistbetweenthesystemand itssurrounding.Therefore,heatrepresentsenergytransferredduetoatemperaturedifference;however,oneremarks thatalthoughatemperaturedifferencemayexistbetweenaninsulatedsystemanditssurroundings,therewillnotbe heattransferduetotheperfectinsulationpropertyofthesystemboundary.
Internalenergy representsasummationofallmicroscopicformsofenergyincludingvibrational,chemical,electrical, magnetic,surface,andthermal.Internalenergyisanextensivequantity.Bydefinition,anextensivethermodynamic quantitydependsontheamountofmatter.Wheninternalenergy U isdividedbythemassofthecontrolvolume m, thenanintensivepropertyisobtained u ¼ U/m,thespecificinternalenergy.Intensivepropertiesareindependentof theamountofmatter(e.g.,intensivepropertiesarepressure,temperature,specificvolume,etc.).Usingthespecific internalenergy,thefollowingexpressionforasystem’sinternalenergyisobtainedforaclosedsystem
ΔU ¼ mu2 u1 ðÞ
Formanythermodynamicprocessesinclosedsystems,theonlysignificantenergychangesareofinternalenergy,and thesignificantworkdonebythesystemintheabsenceoffrictionistheworkofpressure-volumeexpansion,suchasina piston-cylindermechanism.Otherimportantenergychangesareoccurringduetoliquid-vapor-phasechange.Thevapor qualitychangesduringphase-changeprocessessuchasboiling,condensation,absorptionordesorption.Thence,thespecificinternalenergyofthetwo-phaseliquid-vapormixture-changesaccordingtothechange △x invaporquality.Ingeneral,thespecificinternalenergyofamixtureofliquidandvaporatequilibriumcanbewrittenasfollows
where u 0 isthespecificinternalenergyofthesaturatedliquid,andwhereas u 00 isthespecificinternalenergy ofsaturatedvapor. Enthalpy isanotherstatefunction.Specificenthalpy,usuallyexpressedinkJ/kg,isdefinedbased oninternalenergy,pressureandspecificvolume.Accordingtoitsdefinition,thespecificenthalpyisgivenby
Entropy isanotherimportantstatefunctiondefinedbyratiooftheinfinitezimalheataddedtoasubstancetothe absolutetemperatureatwhichitwasadded,andisameasureofthemoleculardisorderofasubstanceatagivenstate. Entropyquantifiesthemolecular(microscale)randommotionwithinathermodynamicsystemandisrelatedtothe thermodynamicprobability (p)ofpossiblemicroscopicstatesasindicatedbyBoltzmannequation S ¼ kB ln p.Entropyis anextensiveproperty,whereasspecificenthalpy(s)isanintensiveproperty.
Itisknownthatallsubstancescan “hold” acertainamountofheat;thatpropertyistheirthermalcapacity.Whena liquidisheated,thetemperatureoftheliquidrisestotheboilingpoint.Thisisthehighesttemperaturethattheliquid canreachatthemeasuredpressure.Theheatabsorbedbytheliquidinraisingthetemperaturetotheboilingpointis called sensibleheat.Thethermodynamicquantityknownas specificheat isaparameterthatcanquantifythestatechange
FIG.1.4 Representationofaninsulatedthermodynamicsystem.
ofasystemthatperformsaprocesswithsensibleheatexchange.Specificheatisdefinedbasedoninternalenergyor enthalpy,dependingonthenatureofthethermodynamicprocess.Thespecificheatatconstantvolumeisequaltothe changeininternalenergywithtemperatureatconstantvolumeasdefinedbelow
The specificheatatconstantpressureCp representstheamountofheatrequiredtoincreasethetemperatureofasystem evolvingatconstantpressurewith1K.Thespecificheatisthechangeofenthalpywithtemperatureatconstantpressuredefinedaccordingto
Forexample,thespecificheatatconstantpressureandthespecificheatatconstantvolumeofanyincompressiblesubstance(e.g.,solidandliquid) areequal.Theheatrequiredforconvertingliquidtovaporatthesametemperatureandpressureiscalled latentheat .Thisisthechangeinenthalpyduringastatechange(theamountofheat absorbedorrejectedatconstanttemperatureatanypressu re,orthedifferenceinenthalpiesofapurecondensable fluidbetweenitsdrysaturatedstateanditssaturated-liquidstateatthesamepressure).
Fusionisassociatedwiththemeltingandfreezingofamaterial.Formostpuresubstances,thereisaspecificmelting/freezingtemperature,relativelyindependentofthepressure.Forexample,icebeginstomeltat0°C.Theamount ofheatrequiredtomelt1kgoficeat0°Cto1kgofwaterat0°Ciscalledthelatentheatoffusionofwater,andequals 334.92kJ/kg.Theremovalofthesameamountofheatfrom1kgofwaterat0°Cchangesliquidwaterbacktoice.
Anumberoffundamentalphysicalconstantsareveryrelevantforthermodynamics;examplesaretheuniversalgas constant,Boltzmannconstant,Faradayconstantandelementaryelectriccharge.Inaddition,somestandardparameters,suchasstandardatmosphericpressureandtemperature,standardmolarvolumeandsolarconstantarevery importantforthermodynamicanalysis. Table1.3 presentsfundamentalphysicalconstantsandstandardparameters. Thetableliststheconstantname,itssymbol,thevalueandunitsandabriefdefinition.
TABLE1.3 FundamentalConstantsandStandardParameters
Constant/ parameter Value
Speedoflightin vacuum
c ¼ 299,792,458m=s
Elementarycharge e ¼ 1 60218 10 19 C
Faraday’sconstant F ¼ 96,485C=mol
Gravitational acceleration g ¼ 9 80665m=s2
Planck’sconstant h ¼ 6 626 10 37 kJs
Boltzmann constant kB ¼ 1 3806 10 23 J=K. kB ¼ R=NA
Numberof Avogadro NA ¼ 6 023 1026 molecules=kmol
Standard atmospheric pressure P0 ¼ 101 325kPa
Universalgas constant R ¼ 8 314J=mol K R ¼ Pv=T
Stefan-Boltzmann constant
σ ¼ 5 670373 10 8 W=m2 K4
Definition
Maximumspeedatwhichmatterandinformationcanbetransportedinthe knowncosmos
Electricalchargecarriedbyasingleproton
Electricchargeofonemoleofelectrons
Gravitationalforce(G)perunitofmassas g ¼ G=m
Magnitudeofenergyofaquanta(particle)thatexpressestheproportionalitybetween frequencyofaphotonanditsenergyaccordingto E ¼ h ν
Ameasureofkineticenergyofonemoleculeofidealgas
Ratioofconstituententitiesofabulksubstancetotheamountofsubstance. NA ¼ N =n
Pressureoftheterrestrialatmosphereatsealevelinstandardconditions
Ameasureofkineticenergyofonemoleofanidealgasatmolecularlevel
AconstantinStefan-Boltzmannlawexpressingtheproportionalitybetweenforthpower oftemperatureandblackbody’semissivepower
1.3IDEAL-GASTHEORY
Ideal-gastheoryisveryimportantforanalysisofprocessesbecauseinmostofthepracticalsituationsgasesbehaveas rarefiedmatter(theinteractionbetweengasmoleculescanbeneglected).Anidealgascanbedescribedintermsofthree parameters:thevolumethatitoccupies,thepressurethatitexertsonboundaries,anditstemperature.Accordingtothe definition,idealgasrepresentsaspecialstateofmatterthatcanbedelimitedbyasystemboundary.Idealgasisformedby anumber N offreelymovingmoleculesoratomswithperfectelasticbehavioratcollisionsamongeachotherandwiththe systemboundary.Itisassumedthat:
• Allparticleshaverestmass(m > 0;theparticlesarenotphotons)
• Thenumberofparticleswithrespecttothesystemvolumeissmall
• Thetotalvolumeofparticlesisnegligiblewithrespecttosystemvolume
• Thecollisionsofparticleswitheachotheraremuchlessprobablethanthecollisionswiththesystemboundary
Thepracticaladvantageoftreatingrealgasesasidealisthatasimpleequationofstatewithonlyoneconstantcanbe appliedinthefollowingform
where P isthepressureinPa, V isthegasvolumeinm3, m ismassofgasinkg, T isgastemperatureinK, R isknownas gasconstantandisgiveninJ/kgK, v ismass-specificvolumeinm3/kg, ismolar-specificvolumeinm3/kmol, R is theuniversalgasconstantof8.134J/molK(Table1.3).Observethatthegasconstantisspecifictoeachparticulargas anddependsontheuniversalgasconstantandthemolecularmass(M)ofthegasaccordingto
NotethatEq. (1.7) isnamed “ thethermalequationofstate ” oftheidealgasbecauseitexpressestherelationship betweenpressure,specificvolumeandtemperature.Itispossibletoexpresstheideal-gasequationintermsofinternalenergy,specificvolumeandtemperature.Inthiscase, theequationofstateiscalledcaloricequationofstate.In particular,foridealgasonly,theinternalenergydependsontemperatureonly.Thecaloricequationofstatefora monoatomicidealgasis u ¼ 1:5 R T ,where u isthemolar-specificinternalenergy.Since h ¼ u + Pv,itfollowsthatthe enthalpyofmonoatomicidealgasisgivenby h ¼ 2 5 R T .BasedonthespecificheatsdefinitionsfromEqs. (1.5) and (1.6) ,thewell-knownRobertMeyerequationforidealgascanbederived
Notethat,specificheatsforidealmonoatomicgasare Cv ¼ 1 5 R and Cp ¼ 2 5 R.Thence,theratioofspecificheatat constantpressureandconstantvolume,knownasthe adiabaticexponent,namely
hasthefollowingvaluesforidealgas:monoatomicgas5/3 ¼ 1.67,whereasfordiatomicgasitis7/5 ¼ 1.4. Therearesomespecialcasesifoneof P, v and T isconstant.Atafixedtemperature,thevolumeofagivenquantityof idealgasvariesinverselywiththepressureexertedonit(thisisknownasBoyle’slaw),describinggascompressionor expansionasfollows
wherethesubscriptsrefertotheinitialandfinalstates.Thisequationisemployedbyanalystsinavarietyofsituations: whenselectinganaircompressor,forcalculatingtheconsumptionofcompressedairinreciprocatingaircylinders,and fordeterminingthelengthoftimerequiredforstoringair,forselectingairmotors(orexpanders)anddeterminingtheir airconsumptionetc.Iftheprocessisatconstantpressureoratconstantvolume,thenCharleslawsapply
TABLE1.4 SimpleThermodynamicProcessesandCorrespondingEquationsforIdeal-GasModel
Ifthenumberofmolesofidealgasdoesnotchangeinanenclosedvolume,thenthecombinedidealequationof stateis
Ifthereisnoheatexchangewiththeexterior dq ¼ 0 ðÞ,thentheprocessiscalledadiabatic.Also,ifaprocessisneither adiabaticnorisothermal,itcouldbemodeledaspolytropic. Table1.4 givestheprincipalfeaturesofsimpleprocesses foridealgas. Fig.1.5 showsrepresentationin P v diagramforfoursimpleprocesseswithidealair,modeledasideal gas,byusingtheEngineeringEquationSolver(EES)software.
Theentropychangeofanidealgaswithconstantspecificheatsisgivenbythefollowingequations,dependingon thetypeofprocess(atconstantpressureorconstantvolume)
Theshapeofthethermodynamicsystemcanbearbitrary,butforsimplicity,weassumehereacubicalvolumeas indicatedin Fig.1.6.Theaverageparticlevelocityisdenotedwith andthecubeedgeis l;itfollowsthatthetime
FIG.1.5 Ideal-gasprocessesrepresentedon P v diagram.
FIG.1.6 Athermodynamicsystemformedbytheidealgasenclosedinacubeboundary.
betweentwocollisions,whichisapproximatedwiththetimeneededfortheparticletotravelbetweentwoopposite wallsis
Basedonmomentumconservationlaw,theforceexertedbyoneparticleonthewall,duringcollision,is
OnealsoassumesthatthereisauniformdistributionofparticlecollisionsforthethreeCartesiandirections;thusonly 1/3ofparticlesexertforceonawall;thereforethepressureexpressionisdeterminedbydividedtheforce givenby Eq. (1.14) withwallarea A
where V ¼ lA isthevolumeofthermodynamicsystemand A isthesurfaceareaoftheface,and
whichisthegasdensity(totalmassofparticlesdividedtothevolumeoftheenclosure).Thekineticenergyofasingle gasparticlecanbeexpressedbasedontheaverageparticlevelocity;inthisrespect,Eq. (1.15) issolvedfor 2 andit resultsin
The degreeoffreedom ofmonoatomicgasmoleculesisDOF ¼ 3,becausethereareonlythreepossibletranslationmovementsalongCartesianaxes.Accordingtoitsthermodynamicdefinition, temperature (T)isameasureof theaveragekineticenergyofmoleculesperdegreeoffreedom.Thequantitativerelationshipbetweentemperature andkineticenergyofonesinglemoleculeis
where kB isBoltzmannconstant,definedin Table1.2.SolvingEq. (1.17) for T itresultsthethermodynamicexpression fortemperatureasfollows
KineticenergyexpressionfromEq. (1.16) canbeintroducedinEq. (1.18) andthefollowingitisobtained
TABLE1.5 AmagatandDaltonmodelsforidealgasmixturesModels
Definition Daltonmodel Amagatmodel
Assumptions
Equationsforthecomponents
Equationforthemixture
TABLE1.6 RelevantParametersofMixturesofIdeal-Gas
Parameter
Equation(s)
Totalmassofamixtureof N components mtot ¼ Xmi
Totalnumberofmolesofamixtureof N components
Massfractionforeachcomponent
Molefractionforeachcomponent
tot ¼ Xni
¼ ni ntot ¼ Pi Ptot Daltonmodel ¼ Vi Vtot Amagatmodel
Molecularweightofthemixture Mmix ¼ mtot ntot ¼ X ni Mi ðÞ ntot ¼ X yi Mi ðÞ
Internalenergyofthemixture
Umix ¼ X ni Ui ðÞ
Enthalpyofthemixture Hmix ¼ X ni Hi ðÞ
Entropyofthemixture
Entropydifferenceforthemixture
Smix ¼ X ni Si ðÞ
S2 S1 ¼ R X ni ln yi ðÞ
where v isthe molar-specificvolume and n istheamountofsubstance(numberofmoles).Therefore,thefollowingthermodynamicdefinitionoftemperatureisobtained,whichisequivalentwiththatgiveninEq. (1.18)
where R the universalgasconstant givenin Table1.2 asfollows
Inmanypracticalsituations,mixturesofrealgasescanbeapproximatedasmixturesofidealgases.Therearetwo ideal-gasmodelsforgasmixtures:theDaltonmodelandAmagatmodel.Forbothmodels,itisassumedthateachgasis unaffectedbythepresenceofothergases.TheDaltonmodelassumesthatthemixtureisatconstanttemperatureand volume,whereastheAmagatvolumeconsidersthecasewhentemperatureandpressureareconstant.
Table1.5 comparesmodelsofAmagatandDaltonforideal-gasmixtures.Theequationsrelatingthethermodynamicparametersofthecomponentgaseswiththeparametersofthemixturearegivenin Table1.6
1.4EQUATIONSOFSTATE
Equationsofstatedescribethethermodynamicbehaviorofbulkmatter(whichisformedbygroupsofatoms,moleculesandclustersofthem)generallyintermsoftemperature,pressureandspecificvolume.Otherstatevariablessuch asspecificinternalenergy,specificentropyandspecificvolumecanbealsousedtoformulateequationsofstate.There arefour formsofaggregation ofsubstances,denotedalsoasphasesorstates,namely solid, liquid, gas,and plasma.Eachof thepropertiesofasubstanceinagivenstatehasonlyonedefinitevalue,regardlessofhowthesubstancereachesthe state.Temperatureandspecificvolumerepresentasetofthermodynamicpropertiesthatdefinescompletelythethermodynamicstateandthestateofaggregationofasubstance.
Thethermodynamicstateofasystemcanbemodifiedviavariousinteractions,amongwhichheattransferisone. Heatcanbeaddedorremovedfromasystem.Whensufficientheatisaddedorremovedatacertaincondition,most substancesundergoastatechange.Forpuresubstances,thetemperatureremainsconstantuntilthestatechangeis complete.Thestatetransitioncantransformfromsolidtoliquid,liquidtovapor,orviceversa.
Fig.1.7 showsthephasediagramofwater,calculatedusingEES(see EES,2013),whichisatypicalexampleoftemperaturenonvariationduringlatentheatexchangeasinmeltingandboiling.Icereachesitsmeltingpointat273.15K. Duringthemeltingprocess,anice-watermixtureisformed.Duetophasechange,thetemperatureremainsconstant (see Fig.1.7),althoughheatiscontinuouslyadded.Attheendofthemeltingprocess,allwaterisinaliquidstateof aggregation.Waterisfurtherheatedanditstemperatureincreasesuntilitreachestheboilingpointat373.15K.Additionalheatingproducesboiling,whichevolvesatconstanttemperature,whileawater+steammixtureisformed.The boilingprocessiscompletedwhenallliquidwateristransformedinsteam.Furtherheatingleadstotemperature increaseandgenerationofsuperheatedsteam.
Arepresentationofsolid,liquid,andvaporphasesofapuresubstanceisqualitativelyexhibitedalsoona temperature-volume(T-v)diagramin Fig.1.8.Inthisdiagram, “T” isthetriplepointofthepuresubstance.Thetriple pointrepresentsthatthermodynamicstatewheresolid,liquidandvaporcancoexist.Forexample,thetriplepointof wateroccursat273.16K,6.117mbar,andspecificvolumeis1.091dm3/kgforice,1dm3/kgforliquidwater,and 206m3/kgforvapor.Belowthetriple-pointisobar,thereisnoliquidphase.Asublimationordesublimationprocess occurs,whichrepresentsphasetransitionbetweensolidandvapor.
FIG.1.7 Representationofphasediagramofwater.
FIG.1.8 Illustrationofthetemperature-volumediagramfeaturesforapuresubstance.
Betweentriple-pointisobarandcritical-pointisobar,threephasesdoexist:solid,liquid,andvapor.Inaddition, therearedefinedthermodynamicregionsofsubcooledliquid,two-phaseandsuperheatedvapor.Subcooledliquid regionsexistbetweenthecriticalisobarandliquidsaturationline(see Fig.1.8).Thetwo-phaseregionisdelimited bytheliquidsaturationlineattheleft,vaporsaturationlineattherightandtriple-pointisobaratthebottom.Superheatedvaporexistsabovethevaporsaturationlineandbelowthecriticalisobar.Attemperatureshigherthanthetemperatureofcriticalpointandabovethecriticalisobar,thereisathermodynamicregiondenotedas supercriticalfluid region wherethesubstanceisneitherliquidnorgas,buthassomecommonpropertieswithgasesandliquid;supercriticalfluidswillbediscussedindetailinotherchaptersofthisbook.
Thespecificvolumealongtheboilingpalliercanbeexpressedbasedonvaporquality,whichisdefinedbased
thespecificvolumesofmixture,saturatedliquidandsaturatedvapor,respectively,accordingto
Onthediagramfrom Fig.1.8,theconstantvaporqualitylinesaresuggestedandstatepointsA–Iareindicated. Thesestatepointsarerepresentativeforvariousprocessesasfollows:
• A-B-C-D:Representsaconstant-pressureprocess
• A-B:Representstheprocesswherethesubstanceinliquidphaseisheatedfromtheinitialtemperaturetothe saturationtemperature(liquid)atconstantpressure;atpointB,afullysaturatedliquidwithaquality x ¼ 0is hasformed
• B-C:Representsaconstant-temperatureboilingprocessinwhichthereisphasechangefromasaturatedliquidtoa saturatedvapor;asthisprocessproceeds,thevaporqualityvariesfrom0%to100%;withinthiszone,thesubstance isamixtureofliquidandvapor;atpointC,wehaveacompletelysaturatedvaporandthequalityis100%.
• C-D:Representstheconstant-pressureprocessinwhichthesaturatedvaporissuperheatedwithincreasing temperature
• E-F-G:Representsaconstant-pressureheatingprocessevolvingatcriticalpressure.PointFiscalledthecriticalpoint wherethesaturated-liquidandsaturated-vaporstatesareidentical;thethermodynamicpropertiesatthispointare calledcriticalthermodynamicproperties,forexample,criticaltemperature,criticalpressureandcriticalspecific volume.StateGrepresentsathermodynamicstatepointalongthecriticalpointisobar,atatemperaturehigherthan thecriticaltemperature
• H-I:Representsaconstant-pressureheatingprocessinwhichthereisnochangefromonephasetoanother(because thepressureissetatasuper-criticalvalue.);however,thereisacontinuouschangeindensityduringthisprocess
Anotherimportantstatediagramisthepressureversusvolumediagramforpuresubstances.Thepressureversus specificvolumediagramofpurewaterispresentedin Fig.1.9,whichhasbeenconstructedusingtheEESsoftware.This plotindicatesthesaturationlineswhereliquidandvaporreachthesaturationtemperatureatagivenpressure.
Critical point isotherm at 647.15 K
FIG.1.9 Thepressure-volumediagramforpurewater.
FIG.1.10 Pressureversustemperaturediagramofwater. DatafromHaynes,W.M.,Lide,D.R.,2012.CRCHandbookofChemistryandPhysics,92nd Ed.Internetversion.CRCPress,NewYork.
Onemayobservethatthespecificvolumeofsaturatedvaporsis 1000timeshigherthanthevolumeofliquidfora processevolvingalongthenormalboilingpointisotherm.Thenormalboilingpointisothermcorrespondstoatemperatureof373.15K(and1atmpressure).
The pressureversustemperaturediagram isalsoanimportanttoolthatshowsphasetransitionsofanysubstance. Fig.1.10 qualitativelyshowsthe P-T diagramofapuresubstance.Therearefourregionsdelimitedinthediagrams: solid,vapor,liquid,andsupercriticalfluid.Thephasetransitionlinesaresublimation,solidification,boiling,critical isotherm,andcriticalisobar;thelasttwolinesarerepresentedonlyforsupercriticalregion(atpressureandtemperaturehigherthancritical).
Theideal-gasequationofstate (P = nRT) isnotapplicableattheliquid-vaportransitionregion,liquidandsolid region.Therefore,moreaccuratemodelsarerequiredtopredictthebehaviorofrealsubstancesforalargerextentofthe thermodynamicparameters.Theidealgasisapplicableonlyforrarefiedgases(lowpressuresandhightemperature, farfromtheliquid-vaporsaturationline).
Inthisrespect,the compressibilityfactor (Z)isintroducedtomeasurethedeviationofarealsubstancefromtheidealgasequationofstate.Thecompressibilityfactorisdefinedbythefollowingrelation
wherespecificvolumeisexpressedonmassbasis.
Theorderofmagnitudeisabout0.2formanyfluids.Foraccuratethermodynamiccalculations,compressibility chartscanbeused,whichexpresscompressibilityfactorasafunctionofpressureandtemperature.Inthisway,an equationofstateisobtainedbasedoncompressibilityfactorbythefollowing
wherethecompressibilityfactorisafunctionofpressureandtemperature.
Accordingtotheso-called principleofcorrespondingstates,compressibilityfactorhasaquantitativesimilarityforallgases whenitisplottedagainstreducedpressureandreducedtemperature.Thereducedpressureisdefinedbytheactualpressuredividedbythepressureofthecriticalpoint
wheresubscriptcreferstocriticalpropertiesandsubscriptrtoreducedproperties.Analogously,thereducedtemperatureisdefinedby
FIG.1.11 Generalizedcompressibilitychartaveragedforwater,oxygen,nitrogen,carbondioxide,carbonmonoxide,methane,ethane,propane, n-butane,isopentane,cyclohexane, n-heptane.
TABLE1.7 DescriptionoftheVanderWaalsEquationofState
Item
Reducedpressure,temperature,andspecificvolume
Thermalequationofstate
Caloricequationofstate
Thecompressibilitychartsshowingthedependenceofthecompressibilityfactoronreducedpressureandtemperaturecanbeobtainedfromaccurate P, v, T dataforfluids.Thesedataareobtainedprimarilybasedonmeasurements. Accurateequationsofstateexistformanyfluids;theseequationsarenormallyfittedtotheexperimentaldatatomaximizethepredictionaccuracy.Ageneralizedcompressibilitychart Z ¼ fPr , Tr ðÞ ispresentedin Fig.1.11.Asseeninthe figure,atalltemperatures, Z tendsto1as Pr tendsto0.Thismeansthatthebehavioroftheactualgasclosely approachesideal-gasbehaviorasthepressureapproacheszero.
Intheliterature,therearealsoseveralequationsofstateforaccuratelyrepresentingthe P-v-T behaviorofagasover theentiresuperheatedvaporregion,forexample,theBenedict –Webb–Rubinequation,thevanderWaalsequation, andtheRedlichandKwongequation;However,someoftheseequationsofstatearecomplicated,duetothenumberof empiricalconstantstheycontain,andaremoreconvenientlyusedwithcomputersoftwaretoobtainresults.Themost basicequationofstateisthatof VanderWaals,whichiscapabletopredictthevaporandliquidsaturationlineanda qualitativelycorrectfluidbehaviorinthevicinityofthecriticalpoint.Thisequationisdescribedasgivenin Table1.7.
1.5THELAWSOFTHERMODYNAMICS
Therearethreelawsofthermodynamics.The zerothlawofthermodynamics isastatementaboutthermodynamicequilibriumexpressedasfollows: “iftwothermodynamicsystemsareinthermalequilibriumwithathird,theyarealsoin thermalequilibriumwitheachother.” Asystematinternalequilibriumhasauniformpressure,temperatureand chemicalpotentialthroughoutitsvolume.
Notethattwothermodynamicsystemsaresaidtobein thermalequilibrium iftheycannotexchangeheat,orinother words,theyhavethesametemperature.Twothermodynamicsystemsarein mechanicalequilibrium iftheycannot exchangeenergyintheformofwork.Twothermodynamicsystemsarein chemicalequilibrium iftheyarenotable
Total energy entering the system
Total energy leaving the system Change in total energy of the system
Illustratingthefirstlawofthermodynamicsforaclosedsystem.
tochangetheirchemicalcomposition.Aninsulatedthermodynamicsystemissaidtobein thermodynamicequilibrium whennomass,heat,work,chemicalenergy,etc.,areexchangedbetweenanypartswithinthesystem.
The firstlawofthermodynamics (FLT)postulatestheenergyconservationprinciple: “energycanbeneithercreatednor destroyed.” TheFLTcanbephrasedas “ youcan ’tgetsomethingfromnothing.” Ifonedenotes E theenergy(inKJ)and ΔEsys thechangeofenergyofthesystem,thentheFLTforaclosedsystemundergoinganykindofprocessiswrittenin themannerillustratedin Fig.1.12.TherearethreemathematicalformsforFLT,namelyonanamountbasisonrate basisandonmassspecificbasis.Thesemathematicalformulationsarewrittenaccordingtothefollowingthree equations:
Energycanbetransferredtoorfromathermodynamicsysteminthreebasicforms,namelyaswork,heatand throughenergyassociatedwithmass-crossingthesystemboundary.Inclassicalthermodynamics,thereis,however, asignconventionforworkandheattransfer,whichisthefollowing:
• Theheatispositivewhengiventothesystem,thatis, Q ¼ XQin XQout ispositivewhenthereisnetheat providedtothesystem
• Thenetoutputwork, W ¼ XWout XWin ,ispositivewhenworkisgeneratedbythesystem
Usingthesignconvention,theFLTforclosedsystemsbecomes
where e isthespecifictotalenergyofthesystemcomprisinginternalenergy,kineticenergyandpotentialenergy,and expressedasfollows
TheFLTcanbeexpressedindifferentialform.ForaclosedsystemhereistheexpressionofFLTindifferentialform
Ifitisassumedthatthereisnokineticandpotentialenergychange,theFLTforclosedsystembecomes
Ifthesystemisacontrolvolume,thentheenergytermwillcomprisetheadditionaltermofflowwork.Inthiscase, thetotalspecificenergyofaflowingmatteris
Usingenthalpyformulation,theFLTforacontrolvolumethathasneithervelocitynorelevationbecomes
FIG.1.12
TheFLTforcontrolvolume,usingthesignconventionforheatandworkisformulatedmathematically,inrateform, inthefollowingway
Because u ¼ uT , v ðÞ and h ¼ hT , P ðÞ,thefollowingtworelationshipscanbeobtainedfromFLT
Fromtheabovetwoexpressions,thepressureandspecificvolumecanbeobtainedfromthespecificinternalenergy andspecificenthalpy,respectivelyasfollows
Thefirstlawofthermodynamicsispracticallycomplementedbythesecondlawofthermodynamics(SLT)whichprovidesameanstopredictthedirectionofanyprocessintime,toestablishconditionsofequilibrium,todeterminethemaximumattainableperformanceofmachinesandprocesses,toassessquantitativelytheirreversibilitiesanddeterminetheir magnitudeforthepurposeofidentifyingwaysofimprovementofprocessesandengineeredsystems.TheSLTisrelatedto theconceptsofreversibilityandirreversibility.Onesaysthatathermodynamicprocessisreversibleifduringatransformationboththethermodynamicsystemanditssurroundingscanbereturnedtotheirinitialstates.Reversibleprocessesare ofthreekindsasfollows:
• externallyreversible:withnoassociatedirreversibilitiesoutsidethesystemboundary
• internallyreversible:withnoirreversibilitieswithintheboundaryofthesystemduringtheprocess
• totallyreversible:withnoirreversibilitieswithinthesystemandsurroundings
TherearetwoclassicalstatementsofSLT,whichstatethatheatcannotbecompletelyconvertedintoworkalthough theoppositeispossible:
• TheKelvin–Plankstatement:Itisimpossibletoconstructadevice,operatinginacycle(e.g.,heatengine),that accomplishesonlytheextractionofheatenergyfromsomesourceanditscompleteconversiontowork.Thissimply showstheimpossibilityofhavingaheatenginewithathermalefficiencyof100%.
• TheClausiusstatement :Itisimpossibletoconstructadevice,operatinginacycle(e.g.,refrigeratorandheatpump), thattransfersheatfromthelow-temperatureside(cooler)tothehigh-temperatureside(hotter).Thissimplyshows theimposibilityofhavingaheatpumporrefrigeratorworkingspontaneously.TheClausiusinequalityprovidesa mathematicalstatementoftheSLT,namely:
wherethecircularintegralindicatesthattheprocessmustbecyclical.
Atthelimitwhentheinequalitybecomeszero,thentheprocessesarereversible(idealsituation).AusefulmathematicalartificeistoattributetotheintegralfromEq. (1.30) anewphysicalquantity.Anyrealprocessmusthavegenerated entropy.Thefollowingcasesmaythusoccur:
(i) Sgen > 0,real,irreversibleprocess; (ii) Sgen ¼ 0,ideal,reversibleprocess; (iii) Sgen < 0,impossibleprocess.
Generatedentropyofasystemduringaprocessisasuperpositionofentropychangeofthethermodynamicsystem andtheentropychangeofthesurroundings.Thiswilldefineentropygeneratedbythesystem Sgen
Sinceforareversibleprocess Sgen ¼ 0,itresultsthatentropychangeofthesystemistheoppositeoftheentropy changeofthesurroundings
Althoughthechangeinentropyofthesystemanditssurroundingsmayindividuallyincrease,decreaseorremain constant,thetotalentropychange(thesumofentropychangeofthesystemandthesurroundingsorthetotalentropy generation)cannotbelessthanzeroforanyprocess.Notethatentropychangealongaprocess1–2resultsfromthe integrationofthefollowingequation
hence
TheSLTisausefultoolinpredictingthelimitsofasystemtoproduceworkwhilegeneratingirreversibilitiesto variousimperfectionsofenergyconversionortransportprocesses.Themostfundamentaldevicewithcyclicaloperationwithwhichthermodynamicoperatesistheheatengine;ortheotherimportantdeviceisaheatpump.These devicesoperatebetweenaheatsourceandaheatsink.Aheatsinkrepresentsthethermalreservoircapableofabsorbingheatfromothersystems.Aheatsourcerepresentsathermalreservoircapableofprovidingthermalenergytoother systems.Aheatengineoperatescyclicallybytransferringheatfromaheatsourcetoaheatsink.Whilereceivingmore heatfromthesource(QH)andrejectinglesstothesink(QC),aheatenginecangeneratework(W).AsstatedbytheFLT, energyisconserved,thus QH ¼ QC + W .
Atypical “blackbox” representationofaheatengineispresentedin Fig.1.13a.AccordingtotheSLT,thework generatedmustbestrictlysmallerthantheheatinput, W < QH .Thethermalefficiencyofaheatengine alsoknown asenergyefficiency isdefinedasthenetworkgeneratedbythetotalheatinput.Usingnotationsfrom Fig.1.13a, energyefficiencyofaheatengineisexpressed(bydefinition)with
Ifathermodynamiccycleoperatesasarefrigeratororheatpump,thenitsperformancecanbeassessedbythe coefficientofperformance (COP)definedasusefulheatgeneratedperworkconsumed.Asobservedin Fig.1.13b,theenergy balanceequation(EBE)foraheatpumpiswrittenas QC + W ¼ QH .AccordingtoSLT, QH W (thismeansthatwork canbeintegrallyconvertedintoheat).Basedonitsdefinition,theCOPis
TheCarnotcycleisafundamentalmodelinthermodynamics,representingaheatengine(orheatpump)thatoperatesbetweenaheatsourceandaheatsink,bothofthembeingatconstanttemperature.Thiscycleisaconceptual
FIG.1.13 Conceptualrepresentationofa(a)heatengineand(b)heatpump.
(theoretical)cycleandwasproposedbySadiCarnotin1824.Thecyclecomprisesfullyreversibleprocesses,namely twoadiabaticandtwoisothermalprocesses.TheefficiencyoftheCarnotcycleisindependentofworkingfluid, whichperformstheprocessescyclically.BasedonthedefinitionoftheCarnotcycle,itresultsthat
and s4 ¼ s1 (forheatengine).Theheattransferredatthesourceandsinkare
and QL ¼ TL s2 s1 ðÞ,respectively.Therefore,theenergyefficiencyofareversibleCarnotheatengineisdefinedas
sotheCOPofthereversibleCarnotheatpumpbecomes
thustheCOPofthereversibleCarnotrefrigeratorbecomes
usingthetemperaturescaleas(QH/QL)rev ¼ (TH/TL).
Insummary,theabovegivenCarnotefficiencyandCarnotCOPsareusefulcriteriatoassesspracticalheatengines, refrigerators,heatpumpsorotherenergyconversionsystemswithrespecttotheidealizedcaseofreversibledevices. Accordingly,energyefficiency(η)andtheCOPofareversiblethermodynamiccycle(Carnot)isthehighestpossible andanyactual(irreversible)cyclehassmallerefficiency η
Exergyrepresentsthemaximumworkthatcanbeproducedbyathermodynamicsystemwhenitcomesintoequilibriumwithitssurroundingenvironment.Thisstatementassumesthatataninitialstate,thereisathermodynamic systemthatisnotinequilibriumwiththeenvironment.Inaddition,itisassumedthat,atleastpotentially,mechanisms ofenergy(andmass)transferbetweenthesystemandtheenvironmentmustexist,suchthateventuallythesystemcan evolvesuchequilibriumconditionwilleventuallyoccur.
Duringtheassumedprocess,systemmustexchangeworkwiththeenvironment.Bydefinition,exergyassumesthe existenceofareferenceenvironment.Thesystemundertheanalysiswillinteractonlywiththatenvironment.Exergy analysisisamethodappertainingtoengineeringthermodynamicsandcanbeusedtodeterminethealleviationof manmadeandnaturalsystemsfromtheidealcase.Here,byanidealsystem,oneunderstandsareversiblesystem.
Inmanypracticalproblems,thereferenceenvironmentisassumedtobetheearth ’satmosphere,characterizedbyits averagetemperatureandpressure.Oftenstandardpressureandtemperatureareusedforthereferenceenvironment: P0 ¼ 101 325kPa, T0 ¼ 298 15K.
Insomeclassesoftheproblemswhenreactingsystemsarepresent,thechemicalpotentialofthereferenceenvironmentmustbespecified.Insuchcases,thermodynamicequilibriumwillrefertoalltypesofinteractions,including chemicalreactions.Onecansaythatasystemisinthermodynamicequilibriumwiththeenvironmentifitshares thesametemperature(thermalequilibrium),thesamepressure(mechanicalequilibrium)andthesamechemical potential.Therefore,exergyincludesatleasttwocomponents,onebeingthermomechanicalandonechemical.
Exergycannotbeconserved.Anyrealprocessdestroysexergyas,similarly,itgeneratesentropy.Exergyis destroyedandentropyisgeneratedduetoirreversibilities.Accordingto DincerandRosen(2012),theexergyofa closed(nonflow)thermodynamicsystemcomprisesfourterms,namelyphysical(orthermomechanical),chemical, kinetic,andpotential.Inbrief,totalexergyofanonflowsystemis
Theexergyofaflowingstreamofmatter Exf representsthesumofthenonflowexergyandtheexergyassociated withtheflowworkofthestream P P0 ðÞ V ,therefore
Thephysicalexergyforanonflowsystemisdefinedby
