大学物理双语奥本汉姆ChapThermoGas

会计学1大学物理双语奥本汉姆ChapThermoGasQuasi-steadyprocess(准静态过程)andwork:Anequilibriumstateofasystemcanbedescribedbyseveralparameters,suchasthepressurep,thevolumeV,andthetemperatureT.Intheparameterspace(thatisp-V-Tphasediagram),itisexpressedbyapoint.p1,V1p2,V2Vp

1

2Nowthesystemexperiencesaserieschangesfromstate1tostate2.Eachstateisanewequilibriumstate.17-1TheFirstLawofThermodynamics(407)第1页/共45页F=pSdldW=Fdl=pAdl=pdVTheworkdonebythegasasthecaseinFig.17-7ofP410:wheredVisthedifferentialchangeinvolumeofthegasowingtothemovementofthepiston.WhenthepistonismovedslowlyandchangethevolumeofgasfromVitoVf,thetotalworkdonebythegasis:òò==.fiVVpdVdWW第2页/共45页(1)Itistheshadedareaunderthep-Vprocesscurvebetweeninitialtofinalstate功是过程曲线下的面积(P411).(2)Theworkdonebythegasdependsontheprocess功与过程有关,功是过程量.Descriptions:(3)Theworkdonebythegasispositivewhenitsvolumeexpands;otherwise,negative.pVO第3页/共45页Experimentally,itisfoundthatbothworkWandheatQ

aredependentonthenatureoftheprocess.However,asurprisingthingisthatthequantityQ-Wisthesameforallprocessesbetweentwostates

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

(内能是状态的单值函数(状态量).SoTheFirstLawofThermodynamics.Foradifferentialprocess,itcanbewrittenas:Itisholdforanysystemandanyprocess!第5页/共45页“系统从外界吸收的热量,一部分使系统的内能增加,另一部分用于对外做功”.AboutthesignofW,Q,andU:workdoneby

thesystem

W>0systemabsorbsheat

Q>0system’senergyincreasing

U>0包括热现象在内的能量守恒定律TheinternalenergyUofasystemtendstoincreaseifenergyisaddedasheatQandtendstodecreaseifenergyislostasworkdonebythesystem.(第一类永动机不需能量输入而能继续做功的机器不存在）第6页/共45页Twowaystochangesystem’sinternalenergy:“EnergymaybetransferredintooroutofasystemaseitherworkWorheatQ.”RelationshipbetweenWandQ:1cal=4.18JThetransformationbetweenworkandheatisnotdirect,butonthesystem.Thedirectresultsisthattheinternalenergyofthesystemchanges.第7页/共45页——Thechangeoftheinternalenergyisbytheamountofwork.DE<0,iftheworkisdonebythesystem.>0,iftheworkisdoneonthesystem.17-2SomeSpecialCasesoftheFirstLawofThermodynamics(P409)1.Adiabaticprocess(绝热过程)Itisonethatoccurssorapidlyoroccursinasystemwellisolatedthatnotransferofenergyasheatbetweenthesystemanditsenvironment.Q=0特征：Q=0第8页/共45页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页/共45页Theheatabsorbedbygasisusedforincreasingitsinternalenergyanddoingwork(气体吸收的热量一部分用于增加内能，另一部分用于对外作功).dW=pdV=p(Vf-Vi

)=nRT3.Isobaric(constant-pressure)

process(P410)Thepresureofthesystemisheldconstant.p

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

——Isotherm(等温线)

ishyperbolacurveonap-Vdiagram.恒温热源Stateequation:4.Isothermal(constant-temperature)process(P409)Gasexpands(orcompression

)

whilekeepthetemperatureconstant.第11页/共45页Degreeoffreedom

(自由度)—–

numbersofindependentlydescribingthemotionofamolecule

(确定物体的空间位置所需要的独立坐标数目).17-3DegreesofFreedom

andTheoremofEquipartitionofEnergy(P412)第12页/共45页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页/共45页JamesClerkMaxwellintroducedthetheoremofequipartitionofenergy(能量均分定理)

:Everykindofmoleculehasacertainnumberfofdegreesoffreedom,whichareindependentwaysinwhichthemoleculecanstoreenergy.Eachsuchdegreeoffreedomhasassociatedwithit(onaverage)anenergyof

kTpermolecule(orRTpermole).在温度为T的平衡态下,气体分子每个自由度的平均能量都相等T/K第14页/共45页(1)TheinternalenergyE17-4InternalEnergyandSpecificHeat(P406)Eint

ofmassMgas’smolecules：Forgas,E=K+U(分子内及分子之间的相互作用)Tosimplify,considerthemoleculesasonesofrigid

IGmodel

soBasedonthetheoremofequipartitionofenergy,averagetotalK

onemolecule:Eintof1molegas’smolecules:(f=3,5,6.)第15页/共45页Theinternalenergyofanidealgasisafunctionofthegastemperatureonly;itdoesnotdependonanyothervariables.(2)Molarspecificheatatconstantvolume(定容热容量)AccordingtoTher.-I–Law:Foraconstantvolumeprocess,V=const.,dV=0,soW=0OpVⅠⅡp2p1W=0VTV=C第16页/共45页BasedondefinitionofMolarspecificheatatconstantV,So,wemayexpressinternalenergyofIGas:orWecangeneralizetheaboverelationsfortheinternalenergyofanyidealgasandanyprocess.Wherefisthedegreeoffreedomofmolecules.LookatSections17-2,17-3and17-6第17页/共45页(3)Molarspecificheatatconstantpressure(摩尔定压热容)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页/共45页Adiabaticprocess:Q=0,dQ=017-5AdiabaticExpansion(绝热膨胀)

ofIG(P416)BasedonTher.-I-law,(foratinyprocess,letp=const.)IntermsoftheidealgaslawpV=nRT,wehave(2)(1)from(1)thensubstituteinto(2)可通过内能的变化计算功第19页/共45页Lookatexample17-7inP417.thenNoticingtheEq.:

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

准静态绝热过程的功.Solution:Example:第21页/共45页17-6CarnotEngineandCyclicEfficiencyAheatengine,orsimply,anengine,isadevicethatextractsenergyfromitsenvironmentintheformofheatanddoesusefulwork.Attheheartofeveryengineisaworkingsubstance,suchasgasoline-airmixtureinautomobileengines.(循环效率)(P430)第22页/共45页Schematicworkingprocessofsteamengine(P431).Theworkingsubstancesabsorbheatfromhightemperatureresource(i.e.theboiler);onepartofenergybecomeswork,andtheotherpartreleasetothelowtemperatureresource(i.e.condenser).Afteracycle,theworkingsubstancesresumetheiroriginalstate.第23页/共45页Ingeneral,ifasystemstartsfromacertaininitialstate,throughaclosedseriesofthermodynamicprocesses,thesystemreturnstoitsinitialstate,thentheseprocessesarecalledacycle.Theimportantfeatureofcyclicprocessis:ABCDpVOThecycleiscalledreversible

(可逆)

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

(>0)fromthehightemperature

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

Ineachcycle,substanceabsorbsheatQHfromTH,partlydoesworkoutside;partlytransfersQLtoTL

.第26页/共45页Foracyclicprocess,DE=0,Sotheefficiencyofanenginecanbewrittenas:Theefficiencyhofanyengineisdefinedby意义：在一次循环中工作物质对外所做的净功占它从高温热源吸收的热量的比例.Eq.(18-1)ofP432第27页/共45页(2)ACarnotengineanditsefficiency(P433)OneofimportantreversiblecyclesisCarnotcycle.Thisidealengineturnsouttobethebest(inprinciple)atusingenergyasheattodousefulwork.Inanidealengine,suchasCarnotengine,allprocessesarereversibleandnowastefulenergytransfersoccurduetofrictionandturbulence.第28页/共45页OpVV1ap1AdiabaticIsothermp2p3p4V2V3V4bcdQLQHCarnotcycleconsistsoftwoisothermalprocessesandtwoadiabaticprocessesastheFig.Stateparameters:(a)TH,p1,V1(b)TH,p2,V2(c)TL,p3,V3(d)TL,p4,V4ab,isothermalprocessTH

,featureis

DE=0.TL高温热源THQHQLWOperationofCarnotengine第29页/共45页cd,isothermalprocessTL,DE=0Fromtheadiabaticprocessequationsinbc&da:OpVV1ap1AdiabaticIsothermp2p3p4V2V3V4bcdQLQH第30页/共45页So,theefficiencyoftheCarnotengineisgivenby(1)TheefficiencyofthecycleofCarnotenginedependsonlyonTL,andTH

(高温、低温两热源的温度).Summary:(2)TheefficiencyofCarnotengineisalwayslessthan1(总是小于1).(3)Thedefinitionofthermodynamicsscaleoftemperature（热力学温标）.卡诺循环的效率:Eq.(18-3)第31页/共45页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页/共45页(3)Refrigerators(致冷机)

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

thebasicelementsofanidealrefrigeratorthatoperatesinthereverseoftheCarnotengine.AdiabaticIsothermOpVV1ap1p2p3p4V2V3V4bcdQLQHSinceCarnotrefrigeratorisaCarnotengineoperatinginreverse,so(卡诺致冷机致冷系数):or第34页/共45页Question:Canwemakeanengine,?SuitwiththefirstLaw!PrecisestatementsofsecondlawwereproposedbyLordKelvin,andbyRudolphClausiusintheearly1850s.Althoughwordeddifferently,theirstatementsareequivalent.17-7EngineEfficiencyand

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

(不可能从单一个热源吸取热量,使之全部变为功,而不产生其他影响)(P432).第二类永动机不可能制成，效率永远小于1Youshouldremember!II.Clausius(1822—1888)statement(P438):Nodeviceispossiblewhosesoleeffectsistotransferheatfromonesystematonetemperatureintoasecondsystematahighertemperature

(热量不可能自动地从低温物体传向高温物体).第36页/共45页(1)Irreversibleprocesses(不可逆)Allrealthermodynamicprocessinnaturalisinacertaindirection自然界一切实际热力学过程都是按一定方向进行的.Suchone-wayprocesseswhichcannotbereversedbymeansoffinitechangesintheirenvironmentarecalledirreversibleprocesses.So,innature,the2ndlawofthermodynamicsrevealsthatallspontaneouslythermodynamicprocessesinnaturalare

irreversibleprocessesalongasingledirection

自然界的一切自发过程都是单方向进行的不可逆过程.17-8Entropy&

TheSecondLawofThermody(P441)第37页/共45页(2)Entropy(熵)andchangeinentropy(P440)InthestudyoftheCarnotcycle,wefoundthatRecallingouroriginalconventionasusedbefore,Thesymbolmeanstaketheintegralaroundaclosedpath.系统经历任意可逆循环一周后，其热温比之和为零.pba第38页/共45页Let’sdividethecycleofFotwoparts,thenIfonepathistakeninreverse,dQateachpointbecoms–dQ,sincethepathisreversible,so(reversiblepaths)——theintegralofdQ/Tbetweenanytwoequilibriumstatesdoesnotdependonthepathoftheprocess.pab第39页/共45页Wedefineanewquantity——

entropySFromaboveEqu.,forreversiblecycle,wehave(reversiblecycle)ThechangeofentropyS

shouldbe(reversibleprocesses)Itisindependentofthepathbetweent