和热力学第一定律28课件

18.Heat,Work,&FirstLawofThermodynamics

熱，功，和熱力學第一定律The1stLawofThermodynamics 熱力學第一定律ThermodynamicProcesses 熱力學程序SpecificHeatsofanIdealGas 理想氣體的比熱Ajetaircraftengineconvertstheenergyofburningfuelintomechanicalenergy.一具噴射機引擎把燃燒燃料所得的能量轉變成機械能。Howdoesenergyconservationapplyinthisprocess?如何把能量守恆用到這個程序？Ecombustion=Emech+QwasteE燃燒=E機械+Q廢棄18.1.The1stLawofThermodynamics

熱力學第一定律EitherheatingorstirringcanraiseTofthewater.加熱或攪拌都可以提升T。Joule’sapparatus焦耳的儀器1stLawofThermodynamics熱力學第一定律:Increaseininternalenergy=Heat

addedWorkdone 內能增幅=所加熱量所作功Thermodynamicstatevariable=variableindependentofhistory.熱力態變數=跟歷程無關的變數e.g.,U,T,P,V,…NotQ,W,…PEoffallingweight 下墜重物的位能KEofpaddle 旋槳的動能Heatinwater 水中熱能18.2.ThermodynamicProcesses熱力程序Quasi-staticprocess:Arbitrarilyslowprocesssuchthatsystemalwaysstaysarbitrarilyclosetothermodynamicequilibrium.准靜態程序:程序任意的慢，以使系統始終與熱力平衡隨意的近。Reversibleprocess:Anychangesinducedbytheprocessintheuniverse(system+environment)canberemovedbyretracingitspath.可逆程序:宇宙(系統+環境)因程序而引起的變化，都可由回溯其路徑而完全清除。Reversibleprocessesmustbequasi-static.可逆程序必為准靜態。Irreversibleprocess:systemisnotretraceable(outofequilibriumduringpart/alloftheprocess).不可逆程序:系統不可以回溯(在部份／整個程序裏，不在熱力平衡中)。e.g.,anyprocessesinvolvingfriction,freeexpansionofgas….例:任何涉及摩擦力的程序，氣體自由膨脹…。Twater=Tgas&risesslowlyT水=T氣&緩慢上升systemalwaysinthermodynamicequilibrium系統始終維持在熱力平衡中水氣體温度控制器可動活塞絕熱體傳熱體Work&VolumeChanges功&容積的變化面積Workdonebygasonpiston氣體對活塞所作功GOTIT懂嗎?18.1.Twoidenticalgas-cylindersystemsaretakenfromthesameinitialstatetothesamefinalstate,butbydifferentprocesses.兩個一樣的汽缸系統，從同一個初態，經由不同的程序，達到同一個終態。Whicharethesameinbothcases 下面那一項在兩者都一樣:theworkdoneonorbythegas, 氣體所作或被作的功，theheataddedorremoved,or 加入或移除的熱，或thechangeininternalenergy? 內能的變化？Example18.2.Bubbles氣泡!Ascubadiveris25mdown,wherethepressureis3.5atm(350kPa).一個潛水員在25m水深處，壓力為3.5atm(350kPa)。Theairsheexhalesformsbubbles8.0mminradius.她呼出的空氣形成半徑為8.0mm的氣泡。Howmuchworkdoeseachbubbledoasitarisestothesurface,assumingthebubblesremainat300K.每個氣泡升到水面時作功多少？假定氣泡保持在300K。T=constConstant-VolumeProcesses&SpecificHeat

定容程序&比熱Constant-volumeprocess(isometric,isochoric,isovolumic):V=constant 定容程序(等距，等積，等容):V=常數CV=molarspecificheatatconstantvolume=定(恆)容摩爾比熱Idealgas:U=U(T)理想氣體forallprocesses所有程序isometricprocesses等距(積)程序onlyforisometricprocesses祗有定容程序Non-idealgas:非理想氣體IsobaricProcesses&SpecificHeat等壓程序&比熱IsobaricProcess:constantP等壓程序:P固定isobaricprocesses等壓程序CP=molarspecificheatatconstantpressure=定(恆)壓摩爾比熱Idealgas,isobaric:理想氣體，等壓:Idealgas理想氣體Isotherms等温線TACTIC18.1.AdiabaticEquation絕熱方程Idealgas,anyprocess:理想氣體，任何程序：Adiabaticprocess:絕熱程序：ConceptualExample18.1.Ideal-GasLawvsAdiabaticEquation

理想氣體定律對絕熱方程TheidealgaslawsayspV=nRT, 理想氣體定律說pV=nRT

buttheadiabaticequationsayspV=const.絕熱方程卻說pV=const.Whichisright? 那一個對?Bothareright. 都對。TheadiabaticequationisaspecialcasewhereT

V+1

絕熱方程是個在T

V+1時的特例。MakingtheConnectionSupposeyouhalvethevolumeofanidealgaswith=1.4.Whathappenstothepressureiftheprocessisisothermalandadiabatic?

Ans:pV=constp

=2p0

(doubles)

pV

=constp=p0

2=2.64p0Application:SmogAlert!

應用:煙霧警報！Airispoorheatconductorconvectionisadiabatic. 空氣是不良熱導體對流是絕熱程序。Ifrisingaircoolsslowerthansurroundingair,如果上升空氣的冷卻比周邊的空氣慢，pollutionriseshigh&canbedispersed.汚染物就可以升很高而散掉。Otherwise,smog.反之，則成煙霧。GOTIT懂嗎?18.2.Namethebasicthermodynamicprocessinvolvedwheneachofthefollowingisdonetoapiston-cylindersystemcontainingidealgas,點出下列每項作用在一個理想氣體汽缸系統時，所牽涉的熱力程序，&tellalsowhetherT,p,V,&Uincreaseordecrease.也說出T,p,V,&U是增加還是減少。thepistonislockinplace&aflameisappliedtothebottomofthecylinder,活塞位置鎖定，汽缸底部以火燒之，thecylinderiscompletelyinsulated&thepistonispusheddownward,汽缸完全隔熱，活塞往下推，thepistonisexposedtoatmosphericpressure&isfreetomove,whilethecylinderiscooledbyplacingitonablockofice.活塞外通大氣壓且可以自由移動，汽缸則放在一塊冰上冷卻。isometric等容;T,

p

,V=const,U.adiabatic絕熱;T,

p

,V

,U.isobaric等壓;T,

p

=const,V

,U.IdealGasProcesses理想氣體程序等壓等温定容絕熱第一定律定義性特徵其他關係氣體所作功等温線等壓線絕熱線Example18.4.FindingtheWork找出所作之功Anidealgaswith=1.4occupies4.0Lat300K&100kPapressure.一個=1.4的理想氣體在300K和100kPa壓力下佔了4.0L。It’scompressedadiabaticallyto¼oforiginalvolume,它在絕熱下被壓到原來體積的¼，thencooledatconstantVbackto300K,然後在定V下冷回300K，&finallyallowedtoexpandisothermallytoitsoriginalV.最後則讓它以等温脹回原來的V。Howmuchworkisdoneonthegas? 有多少功作在氣體上？AB(adiabatic):絕熱BC(isometric):等容CA(isothermal):等温workdonebygas:氣體所作功18.3.SpecificHeatsofanIdealGas理想氣體的比熱

Idealgas:

理想氣體Experimentalvalues

(roomT): 實驗數據(室温)Formonatomicgases單原子氣體,5/3,e.g.,He,Ne,Ar,….Fordiatomicgases双原子氣體,7/5=1.4,CV=5R/2,e.g.,H2,O2,N2,….Fortri-atomicgases叁原子氣體,1.3,CV=3.4R,e.g.,SO2,NO2,….Degreesoffreedom(DoF)=numberofindependentcoordinatesrequiredtodescribethesystem自由度(DoF)=描述系統所需獨立變數的數目Singleatom單原子

:DoF=3(transl)ForlowT(vibmodesnotactive)低温(振動模式未啓動):Rigiddiatomicmolecule定形双原子分子:DoF=5(3transl+2rot)Rigidtriatomicmolecule定形叁原子分子:DoF=6(3transl+3rot)TheEquipartitionTheorem均隔定理Equipartitiontheorem

(kineticenergyversion):Forasysteminthermodynamicequilibrium,eachdegreeoffreedomofarigidmoleculecontributes½kTtoitsaverageenergy.均分定理(動能版)：在一個熱力平衡的系统中，一個定形分子的每一個自由度都對它的平均能量供獻½kT。Equipartitiontheorem

(generalversion):Forasysteminthermodynamicequilibrium,eachdegreeoffreedomdescribedbyaquadratictermintheenergycontributes½kTtoitsaverageenergy.均分定理(通用版)：在一個熱力平衡的系统中，每一個在能量中以二次項表達的自由度，都對它的平均能量供獻½kT。DoF(f)CVCPMonatomic33/25/25/3Diatomic55/27/27/5Triatomic6344/3QuantumEffects量子効應CVofH2gasasfunctionofT. H2氣體的CV隨T的變化。Below20Khydrogenisliquid, 20K以下氫是液體，above3200Kitdissociatesintoindividualatoms. 3200K以上它分解成個別原子。Quantumeffect: 量子効應:Eachmechanismhasathresholdenergy. 每個機制都有一個能量門檻。 Etransl<Erot<Evib E平移<E轉動<E振動TranslationTranslation+rotationTranslation+rotation+vibration定積比熱温度平移+轉動+振動平移+轉動平移Reprise 重奏Quasi-staticprocess:Arbitrarilyslowprocesssuchthat