大學(xué)物理雙語奧本漢姆ChapThermoGas

會計學(xué)1大學(xué)物理雙語奧本漢姆ChapThermoGasQuasi-steadyprocess(準(zhǔn)靜態(tài)過程)andwork:Anequilibriumstateofasystemcanbedescribedbyseveralparameters,suchasthepressurep,thevolumeV,andthetemperatureT.Intheparameterspace(thatisp-V-Tphasediagram),itisexpressedbyapoint.p1,V1p2,V2Vp

1

2Nowthesystemexperiencesaserieschangesfromstate1tostate2.Eachstateisanewequilibriumstate.17-1TheFirstLawofThermodynamics(407)第1頁/共45頁F=pSdldW=Fdl=pAdl=pdVTheworkdonebythegasasthecaseinFig.17-7ofP410:wheredVisthedifferentialchangeinvolumeofthegasowingtothemovementofthepiston.WhenthepistonismovedslowlyandchangethevolumeofgasfromVitoVf,thetotalworkdonebythegasis:òò==.fiVVpdVdWW第2頁/共45頁(1)Itistheshadedareaunderthep-Vprocesscurvebetweeninitialtofinalstate功是過程曲線下的面積(P411).(2)Theworkdonebythegasdependsontheprocess功與過程有關(guān),功是過程量.Descriptions:(3)Theworkdonebythegasispositivewhenitsvolumeexpands;otherwise,negative.pVO第3頁/共45頁Experimentally,itisfoundthatbothworkWandheatQ

aredependentonthenatureoftheprocess.However,asurprisingthingisthatthequantityQ-Wisthesameforallprocessesbetweentwostates

.Itdependsonlyontheinitialandfinalstates.Thefirstlawofthermodynamics(P407):第4頁/共45頁OnecaninferthatthequantityQ-Wmustrepresentachangeinsomeintrinsicpropertyofthesystem.ThisintrinsicpropertyiscalledtheinternalenergyU,whichisafunctionofstate,orastate-function

(內(nèi)能是狀態(tài)的單值函數(shù)(狀態(tài)量).SoTheFirstLawofThermodynamics.Foradifferentialprocess,itcanbewrittenas:Itisholdforanysystemandanyprocess!第5頁/共45頁“系統(tǒng)從外界吸收的熱量,一部分使系統(tǒng)的內(nèi)能增加,另一部分用于對外做功”.AboutthesignofW,Q,andU:workdoneby

thesystem

W>0systemabsorbsheat

Q>0system’senergyincreasing

U>0包括熱現(xiàn)象在內(nèi)的能量守恒定律TheinternalenergyUofasystemtendstoincreaseifenergyisaddedasheatQandtendstodecreaseifenergyislostasworkdonebythesystem.(第一類永動機不需能量輸入而能繼續(xù)做功的機器不存在）第6頁/共45頁Twowaystochangesystem’sinternalenergy:“EnergymaybetransferredintooroutofasystemaseitherworkWorheatQ.”RelationshipbetweenWandQ:1cal=4.18JThetransformationbetweenworkandheatisnotdirect,butonthesystem.Thedirectresultsisthattheinternalenergyofthesystemchanges.第7頁/共45頁——Thechangeoftheinternalenergyisbytheamountofwork.DE<0,iftheworkisdonebythesystem.>0,iftheworkisdoneonthesystem.17-2SomeSpecialCasesoftheFirstLawofThermodynamics(P409)1.Adiabaticprocess(絕熱過程)Itisonethatoccurssorapidlyoroccursinasystemwellisolatedthatnotransferofenergyasheatbetweenthesystemanditsenvironment.Q=0特征：Q=0第8頁/共45頁DU>0,systemabsorbsheatfromitsenvironment;<0,thenthesystemreleasesheat.dW=pdV=0,orW=0

2.Isochoric(constant-volume)processThevolumeofthesystemisheldconstant,noworkisdoneforthesystem.VpV=const.IIoIStateEquation:or,V=CdV=0特征：第9頁/共45頁Theheatabsorbedbygasisusedforincreasingitsinternalenergyanddoingwork(氣體吸收的熱量一部分用于增加內(nèi)能，另一部分用于對外作功).dW=pdV=p(Vf-Vi

)=nRT3.Isobaric(constant-pressure)

process(P410)Thepresureofthesystemisheldconstant.p

=Cdp=0特征：VpIIoIViVfStateEquation:第10頁/共45頁ViVfVpT=const.IIOIdT=0特征：pV=C

——Isotherm(等溫線)

ishyperbolacurveonap-Vdiagram.恒溫?zé)嵩碨tateequation:4.Isothermal(constant-temperature)process(P409)Gasexpands(orcompression

)

whilekeepthetemperatureconstant.第11頁/共45頁Degreeoffreedom

(自由度)—–

numbersofindependentlydescribingthemotionofamolecule

(確定物體的空間位置所需要的獨立坐標(biāo)數(shù)目).17-3DegreesofFreedom

andTheoremofEquipartitionofEnergy(P412)第12頁/共45頁Thekineticdegreeoffreedomis:Therearedifferentkindsofmolecules,monatomicmolecules(containonlyasingleatom,ashelium);diatomicmolecules(containtwoatoms,asoxygen);andpolyatomicmolecules(containmorethantwoatoms,asmethane甲烷).Besidestranslationalmotion(DF:t=3),moleculesmayhaverotationalmotion(DF:r)oroscillation(DF:s).第13頁/共45頁JamesClerkMaxwellintroducedthetheoremofequipartitionofenergy(能量均分定理)

:Everykindofmoleculehasacertainnumberfofdegreesoffreedom,whichareindependentwaysinwhichthemoleculecanstoreenergy.Eachsuchdegreeoffreedomhasassociatedwithit(onaverage)anenergyof

kTpermolecule(orRTpermole).在溫度為T的平衡態(tài)下,氣體分子每個自由度的平均能量都相等T/K第14頁/共45頁(1)TheinternalenergyE17-4InternalEnergyandSpecificHeat(P406)Eint

ofmassMgas’smolecules：Forgas,E=K+U(分子內(nèi)及分子之間的相互作用)Tosimplify,considerthemoleculesasonesofrigid

IGmodel

soBasedonthetheoremofequipartitionofenergy,averagetotalK

onemolecule:Eintof1molegas’smolecules:(f=3,5,6.)第15頁/共45頁Theinternalenergyofanidealgasisafunctionofthegastemperatureonly;itdoesnotdependonanyothervariables.(2)Molarspecificheatatconstantvolume(定容熱容量)AccordingtoTher.-I–Law:Foraconstantvolumeprocess,V=const.,dV=0,soW=0OpVⅠⅡp2p1W=0VTV=C第16頁/共45頁BasedondefinitionofMolarspecificheatatconstantV,So,wemayexpressinternalenergyofIGas:orWecangeneralizetheaboverelationsfortheinternalenergyofanyidealgasandanyprocess.Wherefisthedegreeoffreedomofmolecules.LookatSections17-2,17-3and17-6第17頁/共45頁(3)Molarspecificheatatconstantpressure(摩爾定壓熱容)Foraprocessof

p=const.,dp=0&V/T=const.OpVⅠⅡV2V1pTQisrelatedtoDTby,Cp

——

molarspecificheatatconstantpressure.W=pDV=nRDT

(pV=nRT)TorelatemolarspecificheatsCpandCV,westartwith

Ther.-I-law:(17-9)inP414(Mayerformula)第18頁/共45頁Adiabaticprocess:Q=0,dQ=017-5AdiabaticExpansion(絕熱膨脹)

ofIG(P416)BasedonTher.-I-law,(foratinyprocess,letp=const.)IntermsoftheidealgaslawpV=nRT,wehave(2)(1)from(1)thensubstituteinto(2)可通過內(nèi)能的變化計算功第19頁/共45頁Lookatexample17-7inP417.thenNoticingtheEq.:

pV=nRT(Poissionequation)第20頁/共45頁Findtherelationoftheworkdonebythegasesduringadiabaticprocess

準(zhǔn)靜態(tài)絕熱過程的功.Solution:Example:第21頁/共45頁17-6CarnotEngineandCyclicEfficiencyAheatengine,orsimply,anengine,isadevicethatextractsenergyfromitsenvironmentintheformofheatanddoesusefulwork.Attheheartofeveryengineisaworkingsubstance,suchasgasoline-airmixtureinautomobileengines.(循環(huán)效率)(P430)第22頁/共45頁Schematicworkingprocessofsteamengine(P431).Theworkingsubstancesabsorbheatfromhightemperatureresource(i.e.theboiler);onepartofenergybecomeswork,andtheotherpartreleasetothelowtemperatureresource(i.e.condenser).Afteracycle,theworkingsubstancesresumetheiroriginalstate.第23頁/共45頁Ingeneral,ifasystemstartsfromacertaininitialstate,throughaclosedseriesofthermodynamicprocesses,thesystemreturnstoitsinitialstate,thentheseprocessesarecalledacycle.Theimportantfeatureofcyclicprocessis:ABCDpVOThecycleiscalledreversible

(可逆)

ifthecyclecanbeconsideredasaseriesofequilibriumstates,andthewholeprocesscouldbedoneinreversewithnochangeintheworkdoneorheatexchanged,otherwise,irreversible(P433).DE=0第24頁/共45頁(1)EfficiencyofaengineAnEngineshouldoperateatleastbetweentwothermalsources,thehightemperaturereservoirTH,andthelowtemperaturereservoirTL.ThesystemabsorbsheatQH

(>0)fromthehightemperature

reservoir,andreleasesheatQL(<0)tothelowtemperaturereservoir,anddoesworkWtotheenvironmentatthesametime.第25頁/共45頁UsingTher.-I-lawtothewholecyclicprocess,——indicatestheprincipleofengine:

Ineachcycle,substanceabsorbsheatQHfromTH,partlydoesworkoutside;partlytransfersQLtoTL

.第26頁/共45頁Foracyclicprocess,DE=0,Sotheefficiencyofanenginecanbewrittenas:Theefficiencyhofanyengineisdefinedby意義：在一次循環(huán)中工作物質(zhì)對外所做的凈功占它從高溫?zé)嵩次盏臒崃康谋壤?Eq.(18-1)ofP432第27頁/共45頁(2)ACarnotengineanditsefficiency(P433)OneofimportantreversiblecyclesisCarnotcycle.Thisidealengineturnsouttobethebest(inprinciple)atusingenergyasheattodousefulwork.Inanidealengine,suchasCarnotengine,allprocessesarereversibleandnowastefulenergytransfersoccurduetofrictionandturbulence.第28頁/共45頁OpVV1ap1AdiabaticIsothermp2p3p4V2V3V4bcdQLQHCarnotcycleconsistsoftwoisothermalprocessesandtwoadiabaticprocessesastheFig.Stateparameters:(a)TH,p1,V1(b)TH,p2,V2(c)TL,p3,V3(d)TL,p4,V4ab,isothermalprocessTH

,featureis

DE=0.TL高溫?zé)嵩碩HQHQLWOperationofCarnotengine第29頁/共45頁cd,isothermalprocessTL,DE=0Fromtheadiabaticprocessequationsinbc&da:OpVV1ap1AdiabaticIsothermp2p3p4V2V3V4bcdQLQH第30頁/共45頁So,theefficiencyoftheCarnotengineisgivenby(1)TheefficiencyofthecycleofCarnotenginedependsonlyonTL,andTH

(高溫、低溫兩熱源的溫度).Summary:(2)TheefficiencyofCarnotengineisalwayslessthan1(總是小于1).(3)Thedefinitionofthermodynamicsscaleoftemperature（熱力學(xué)溫標(biāo)）.卡諾循環(huán)的效率:Eq.(18-3)第31頁/共45頁OnemoleofamonatomicidealgasistakenthroughthereversiblecycleshowninFig.Processbcisanadiabaticexpansion,withpb=10.0atmandVb=1.0010-3m3.Find(a)theenergyaddedtothegasasheat,(b)theenergyleavingthegasasheat,(c)networkdonebythegas,and(d)theefficiencyofthecycle.Solution:(a)

ab,V=const.,W=0Vb8VbVpidiabaticocbaExample:第32頁/共45頁(3)Refrigerators(致冷機)

anditsefficiency(P438)Arefrigeratorisadevicethatusesworktotransferenergyfromalowtemperaturereservoirtoahightemperaturereservoirasitcontinuouslyrepeatedasetofseriesofthermodynamicprocesses.Theefficiencyofanyrefrigerator(致冷系數(shù)coefficientofperformance)canbedefinedasTheTher-I-lawinrefrigerator:|W|=|QH|-|QL|第33頁/共45頁CarnotRefrigerator

thebasicelementsofanidealrefrigeratorthatoperatesinthereverseoftheCarnotengine.AdiabaticIsothermOpVV1ap1p2p3p4V2V3V4bcdQLQHSinceCarnotrefrigeratorisaCarnotengineoperatinginreverse,so(卡諾致冷機致冷系數(shù)):or第34頁/共45頁Question:Canwemakeanengine,?SuitwiththefirstLaw!PrecisestatementsofsecondlawwereproposedbyLordKelvin,andbyRudolphClausiusintheearly1850s.Althoughwordeddifferently,theirstatementsareequivalent.17-7EngineEfficiencyand

TheSecondLaw第35頁/共45頁I.Kelvin-Planck(1824—1907)statement):Nodeviceispossiblewhosesoleeffectsistotransformagivenamountofheatcompletelyintowork

(不可能從單一個熱源吸取熱量,使之全部變?yōu)楣?而不產(chǎn)生其他影響)(P432).第二類永動機不可能制成，效率永遠小于1Youshouldremember!II.Clausius(1822—1888)statement(P438):Nodeviceispossiblewhosesoleeffectsistotransferheatfromonesystematonetemperatureintoasecondsystematahighertemperature

(熱量不可能自動地從低溫物體傳向高溫物體).第36頁/共45頁(1)Irreversibleprocesses(不可逆)Allrealthermodynamicprocessinnaturalisinacertaindirection自然界一切實際熱力學(xué)過程都是按一定方向進行的.Suchone-wayprocesseswhichcannotbereversedbymeansoffinitechangesintheirenvironmentarecalledirreversibleprocesses.So,innature,the2ndlawofthermodynamicsrevealsthatallspontaneouslythermodynamicprocessesinnaturalare

irreversibleprocessesalongasingledirection

自然界的一切自發(fā)過程都是單方向進行的不可逆過程.17-8Entropy&

TheSecondLawofThermody(P441)第37頁/共45頁(2)Entropy(熵)andchangeinentropy(P440)InthestudyoftheCarnotcycle,wefoundthatRecallingouroriginalconventionasusedbefore,Thesymbolmeanstaketheintegralaroundaclosedpath.系統(tǒng)經(jīng)歷任意可逆循環(huán)一周后，其熱溫比之和為零.pba第38頁/共45頁Let’sdividethecycleofFotwoparts,thenIfonepathistakeninreverse,dQateachpointbecoms–dQ,sincethepathisreversible,so(reversiblepaths)——theintegralofdQ/Tbetweenanytwoequilibriumstatesdoesnotdependonthepathoftheprocess.pab第39頁/共45頁Wedefineanewquantity——

entropySFromaboveEqu.,forreversiblecycle,wehave(reversiblecycle)ThechangeofentropyS

shouldbe(reversibleprocesses)Itisindependentofthepathbetweent