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1、第三章第三章热力学第一定律热力学第一定律Chapter3.Thefirstlawofthermodynamics系统的宏观和微观储存能系统的宏观和微观储存能Macroscopicandmicroscopicenergyofsystem热量、功量及质量引起的能量传递热量、功量及质量引起的能量传递-传递中的能量传递中的能量EnergytransferbyHeat,WorkandMass热力学第一定律与闭口系统的能量平衡方程热力学第一定律与闭口系统的能量平衡方程ThefirstlawofthermodynamicsandEnergybalanceequationofclosedsystem开口系统的
2、能量平衡方程开口系统的能量平衡方程Energybalanceequationofopensystem稳态稳定流动的能量平衡稳态稳定流动的能量平衡Energybalanceforsteady-flowsystems工程中的几种稳态稳定流动装置工程中的几种稳态稳定流动装置Somesteady-flowengineeringdevices热力学第一定律的本质热力学第一定律的本质EssenceoftheFirstLawofThermodynamics 1909年，年，C.Caratheodory最后完善热一律最后完善热一律本质：本质：能量能量转换转换及及守恒守恒定律定律在热过程中的应用在热过程中的应用
3、 18世纪初，工业革命，热效率只有世纪初，工业革命，热效率只有1%1842年，年，J.R.Mayer阐述热一律，但没有阐述热一律，但没有引起重视引起重视 1840-1849年，年，Joule用多种实验的一致性用多种实验的一致性证明热一律，于证明热一律，于1850年发表并得到公认年发表并得到公认能量守恒定律阐明能量既不能被创造，也不能消灭，能量守恒定律阐明能量既不能被创造，也不能消灭，它只能从一种形式转换成另一种形式，或从一个系统它只能从一种形式转换成另一种形式，或从一个系统转移到另一个系统，而其总量保持恒定。转移到另一个系统，而其总量保持恒定。Conservationofenergyprinc
4、iplestatesthatenergycanbeneithercreatednordestroyed;itcanonlychangefromoneformtoanotherbutthetotalamountofenergyremainsconstant.能量守恒定律能量守恒定律热力学第一定律主要说明热能与机械能在转换过热力学第一定律主要说明热能与机械能在转换过程中的能量守恒程中的能量守恒ThefirstlawofthermodynamicsisviewedastheConservationofenergyprinciplewhichgovernstheenergytransferproces
5、sfromthermalenergytomechanicalones.热力学第一定律热力学第一定律系统能量的变化量等于加给的热量与系统对外所系统能量的变化量等于加给的热量与系统对外所作功量之差。作功量之差。Thechangeinenergyofasystemisequaltothedifferencebetweentheheatadded tothesystemandtheworkdone bythesystem.l E=Q-W“第一类永动机是不可能制成的第一类永动机是不可能制成的”PerpetualmotionmachineofthefirstkindQPerpetualmotionmach
6、ineofthefirstkind锅锅炉炉汽轮机汽轮机发电机发电机给水泵给水泵凝凝汽汽器器WnetQout电电加加热热器器系统的宏观和微观储存能系统的宏观和微观储存能MacroscopicandmicroscopicenergyofsystemEnergyisaproperty ofevery system.It is denoted as E for a system,or e for a system with a unit mass.E=internalenergy+kineticenergy+potentialenergyMicroscopicenergy-Internalenergy
7、U热力学能指系统所有微观形式的能量之和热力学能指系统所有微观形式的能量之和.Internalenergyisdefinedasthesumofallthemicroscopicformsofenergyofasystem.热力学能的微观组成热力学能的微观组成分子动能分子动能分子位能分子位能bindingforces化学能化学能chemicalenergy核能核能nuclearenergy热力学能热力学能microscopicformsofinternalenergy 移动移动translation转动转动rotation振动振动vibration（1）分子的动能和势能）分子的动能和势能Kine
8、ticandpotentialenergiesofthemoleculesuisafunctionofthestateofthesystem.uisafunctionofthestateofthesystem.u=u(p,T),oru=u(p,v),oru=u(v,Tu=u(p,T),oru=u(p,v),oru=u(v,T).).热力学能热力学能内动能内动能内位能内位能T,vT(2)理想气体热力学能理想气体热力学能的物理解释的物理解释热力学能热力学能内动能内动能内位能内位能T,v理想气体无分子间作用力，理想气体无分子间作用力，热力学能热力学能只决定于只决定于内内动能动能?如何求理想气体的如何
9、求理想气体的热力学能热力学能uT理想气体理想气体u只与只与T有关有关 热力学能的说明热力学能的说明l热力学能热力学能是状态量是状态量statepropertyl U:广延参数广延参数 kJ l u :比参数比参数 kJ/kg l热力学能热力学能总以变化量出现，总以变化量出现，热力学能热力学能零点人为定义零点人为定义2.宏观储存能：动能和势能宏观储存能：动能和势能Macroscopicenergy-kineticenergyandpotentialenergy They are related to some outside reference frame。Kineticenergy is th
10、e energy a system possesses as a result of its motion relative to some reference frame.It is denoted as Eke.Potential energy is the energy a system possesses as a result of its elevation in a gravitational field.Onaunitmassbasis3.系统的总能量系统的总能量(Totalenergy）传热和热量（传热和热量（Heattransferandheat）热量是以温差为推动力时，系
11、统与外界之间传递的能量热量是以温差为推动力时，系统与外界之间传递的能量Heatisenergyinteractionbetweenasystemanditssurroundingsifitsdrivingforceistemperaturedifferenceonly.(1)热量是传递中的能量（热量是传递中的能量（Heatisenergyintransition.）Eg.Thebakedpotatocontainsenergy,thisenergyisheattransferonlyasitpassesthroughtheskinofpotatotoreachtheair.Onceinthes
12、urroundings,thetransferredheatbecomespartoftheinternalenergyofthesurroundings,orviseversa.3.2EnergytransferbyHeat,WorkandMass3.2EnergytransferbyHeat,WorkandMass(热量、功量及质量引起的能量传递热量、功量及质量引起的能量传递热量、功量及质量引起的能量传递热量、功量及质量引起的能量传递-传递中的能量）传递中的能量）传递中的能量）传递中的能量）(2)热量是有方向的量热量是有方向的量(Heatisdirectionalquantity.)Hea
13、taddition(加热）加热）isthetransferofheatintoasystem.Heatrejection（放热）（放热）isthetransferofheatoutofasystem.Formalsignconvention:heatadditionispositive,+.heatrejectionisnegative,-.(3)“Adiabatic”meansnoheatistransferred（“绝热绝热”意味着没有热量传递。）意味着没有热量传递。）.(4)Heattransfercanchangethestateofthesystem.（传热可以引起系统状态的变化。）
14、（传热可以引起系统状态的变化。）2.功功(EnergytransferbyWork）Work is the energy transfer associated with a force acting through a distance.(1)功量也是传递中的能量功量也是传递中的能量Workisalsoenergyintransition.Wecanhavepush-pullwork(.inapiston-cylinder,liftingaweight),electricandmagneticwork(.anelectricmotor),chemicalwork,surfacetension
15、work,elasticwork,arotatingshaft.(2)功量是有方向的量功量是有方向的量Workisalsodirectionalquantity.(Itisstipulated:Itisstipulated:workworkdonebydonebyasystemispositive,+.asystemispositive,+.Thatis,energyleavesthesystem.(Thatis,energyleavesthesystem.(系统作功，功为系统作功，功为系统作功，功为系统作功，功为正，也即能量离开系统。正，也即能量离开系统。正，也即能量离开系统。正，也即能量离
16、开系统。workworkdoneondoneonasystemisnegative,-.asystemisnegative,-.Thatis,energyaddedtothesystem,Thatis,energyaddedtothesystem,（外界对系统（外界对系统（外界对系统（外界对系统作功，功为负，即能量加入系统。）作功，功为负，即能量加入系统。）作功，功为负，即能量加入系统。）作功，功为负，即能量加入系统。）(Indefiningwork,wefocusontheeffectsthatthe(Indefiningwork,wefocusontheeffectsthatthesyst
17、em(.anengine)hasonitssurroundings.system(.anengine)hasonitssurroundings.适用条件：1）理想气体 2)准静态过程Air-conditioner稳态稳定流动过程的特点(2)The energy of a flowing fluidtechnically.therefore:=?如何求理想气体的热力学能 u功(Energy transfer by Work）节流前后h不变，不是等h过程。以房间为系统Energy Equation of closed system(闭口系统的能量方程)Equating the two first
18、law expressions given aboveq=du+w q=u+wA process during which a fluid flows through a control volumesteadily.4 on P166196.拉伸功 w拉伸=-dl(3)热热量和功量的相似之量和功量的相似之处处）Similaritiesbetweenheatandwork（l热热量和功量是系量和功量是系统统与外界能量交与外界能量交换换的机理。的机理。Heatandworkareenergytransfermechanismsbetweenasystemanditssurroundings.l功
19、量和功量和热热量都要穿越量都要穿越边边界。界。Bothheatandworkareboundaryphenomena.l系系统统具有能量，但不是功量或具有能量，但不是功量或热热量量Systempossessenergy,butnotheatorwork.Example.Workvs.heattransfer-whichiswhich?Canhaveone,theother,orboth?Itdependsonwhatcrossesthesystemboundary.Forexampleconsideraresistorthatisheatingavolumeofwater.两者都是过程量，而不
20、是状态量两者都是过程量，而不是状态量Bothareassociatedwithaprocess,notastate.Botharepathfunctions.（两者都是路径的函数）（两者都是路径的函数）If the change in a function is dependent on the route taken,then the function is known as a pathfunction.lIfthewateristhesystem,thenthestateofthesystemwillbechangedbyheattransferredfromtheresistor.lI
21、fthesystemisthewater+theresistor,thenthestateofthesystemwillbechangedby(electrical)work.(4)Movingboundarywork(移移动边动边界功，即膨界功，即膨胀胀功或功或压缩压缩功）功）A.Quasi-staticprocesses Use of pext instead of psys is often inconvenient because it is usually the state of the system that we are interested in.pext=psysB.Con
22、sideraquasi-staticprocessofacylinder-pistoninstallationwithasimplecompressiblesubstanceWork done on the systemtherefore:=or in terms of the specific volume,v:=u若系统克服一个力体积膨胀，则系统对外作功If system volume expands against a force,work is done by the system.u若系统受力而体积收缩，则外界对系统作功）If system volume contracts unde
23、r a force,work is done on the system.C.WorkisapathdependentprocessWorkdependsonpathMustspecifypathifweneedtodetermineworkAlong Path a:W=2p0(2V0-V0)=2p0V0Along Path b:W=p0(2V0-V0)=p0V0(5)轴功轴功(Shaftwork）Energytransmissionwitharotatingshaft.AforceFactingthroughamomentarmrgenerateatorqueTThisforceactsth
24、roughadistancesThentheshaftworkisdeterminedfrom(6)弹簧力功弹簧力功(SpringWork）Thelengthofaspringwillchangebyadifferentialamountdx,onwhichaforceFisapplied.Theworkdoneis Forlinearelasticsprings,thedisplacementxisproportionaltotheforceapplied.SubstituteFintothepreviousequationandintegratingyield3.质量守恒定律质量守恒定律(
25、ConservationofMassPrinciple）质量守恒定律可表述为：在一个过程中，传递给系统质量守恒定律可表述为：在一个过程中，传递给系统的净质量等于系统总质量的净变化量（增加或减小）。的净质量等于系统总质量的净变化量（增加或减小）。Netmasstransfertoorfromasystemduringaprocessisequaltothenetchange(increaseordecrease)inthetotalmassofthesystemduringtheprocess.（Totalmassenteringthesystem)-(Totalmassleavingthesy
26、stem)=(Netchangeinmasswiththesystem)质量守恒方程也被称作质量守恒方程也被称作质量守恒方程也被称作质量守恒方程也被称作连续性方程连续性方程连续性方程连续性方程TheconservationofmassequationisalsoTheconservationofmassequationisalsocalledascalledasContinuityEquationContinuityEquation 4.流动功与流动工质所携带的能量流动功与流动工质所携带的能量Flowworkandtheenergyofaflowingfluid.(1)FlowworkForo
27、pensystems,someworkisrequiredtopushthemassintooroutofthecontrolvolume,theworkisknownastheflowwork.(2)TheenergyofaflowingfluidWhenfluidentersorleavesacontrolvolume(massesflowacrosstheirboundaries),energiesarebroughtintothecontrolvolume.5.焓焓（A Useful New State Function Enthalpy）Enthalpy,a state functi
28、on,is defined as follows,h=u+pvThis energy is composed of two parts:the internal energy of the fluid(u)and the flow work(pv)associated with pushing the mass of fluid across the system boundary.开口系统中开口系统中,焓指流动工质所携带能量的一部分，焓指流动工质所携带能量的一部分，这部分能量取决于热力状态）这部分能量取决于热力状态）Inanopenflowsystem,enthalpyispartofene
29、rgythatistransferredacrossasystemboundarybyamovingflow,thispartdependsonthestate.热力学第一定律与闭口系统的热力学定律热力学第一定律与闭口系统的热力学定律The First Law of Thermodynamics and Energy Balance of closed system 1.TheStatementofthefirstLawofThermodynamicThechangeinenergyofasystemisequaltothedifferencebetweenthetotalenergyente
30、ringsystemandthatleavingthesystem.热一律的文字表达式热一律的文字表达式热一律热一律:能量守恒与转换定律能量守恒与转换定律=进入进入系统的系统的能量能量离开离开系统的系统的能量能量系统系统内部储存内部储存能量能量的的变化变化-TotalenergyenteringthesystemTotalenergyleavingthesystemChangeinthetotalenergyofthesystem=-2.2.闭口系能量方程闭口系能量方程Energybalanceforclosedsystem W QQ=U+Wq=u+w单位工质单位工质Thechangeinen
31、ergyofasystemisequalThechangeinenergyofasystemisequaltothedifferencebetweentheheattothedifferencebetweentheheatadded toadded to thesystemandtheworkthesystemandtheworkdone bydone bythethesystem.system.(1)Thesignsareimportant(正负号规定很重要正负号规定很重要)U is the internal energy of the system Q is positive(+),if
32、the heat transferred to the system Q is negative(-),if it is transferred from the system.W is positive(+),if the work is done by the system,W is negative(-),if work is done on the system.(2)QandWarepathdependent,Udependsonlyonthestateofthesystem.W Q一般式一般式 Q=dU+WQ=U+W q=du+wq=u+w单位工质单位工质适用条件：适用条件：1）任
33、何工质）任何工质2)任何过程任何过程Pointfunction-Exactdifferentials-dPathfunction-Inexactdifferentials-闭口系能量方程中的功闭口系能量方程中的功功功（w）是广义功是广义功GeneralizedWork闭口系与外界交换的功量闭口系与外界交换的功量 q=du+w准静态容积变化功准静态容积变化功pdv拉伸功拉伸功 w拉伸拉伸=-dl表面张力功表面张力功 w表面张力表面张力=-dA w=pdv-dl-dA+.在一个过程中，传递给系统的净质量等于系统总质量的净变化量（增加或减小)。Exercise(练习)控制体积的体积保持不变。迈耶公式
34、Mayers formulaThen the shaft work is determined fromcp 为真实比热(actual specific heat)Q is positive(+),if the heat is transferred to the system.the flow work pv associated with pushing the mass of fluid across the system boundary.Energy transmission with a rotating shaft.Perpetual motion machine of the
35、first kindConsider a system,consisting of both vessels which is perfectly thermally insulated.This energy is composed of two parts:the internal energy of the fluid(u)and the flow work(pv)associated with pushing the mass of fluid across the system boundary.or in terms of enthalpySome steady-flow engi
36、neering devices拉伸功 w拉伸=-dlUse of pext instead of psys is often inconvenient because it is usually the state of the system that we are interested in.q=du+w闭口系能量方程的通式闭口系能量方程的通式 q=du+w若在地球上研究飞行器若在地球上研究飞行器 q=de+w=du+dek+dep+w工程热力学用此式较少工程热力学用此式较少准静态和可逆闭口系能量方程准静态和可逆闭口系能量方程简单可压缩系简单可压缩系准静态过程准静态过程 w=pdv简单可压缩
37、系简单可压缩系可逆过程可逆过程(Forreversibleprocessinsimplecompressiblesystem)q=Tds q=du+pdv q=u+pdv热一律解析式之一热一律解析式之一Tds=du+pdv Tds=u+pdv热力学恒等式热力学恒等式理想气体内能的计算理想气体内能的计算理想气体，任何过程理想气体，任何过程理想气体理想气体 q=du+pdv 对理想气体的定容过程对理想气体的定容过程 q=du+pdv 又理想气体的焓理想气体的焓理想气体理想气体理想气体，任何过程理想气体，任何过程 q=du+pdv+vdp-vdp =dh-vdp 对理想气体的定压过程 q=dh-vd
38、p 定压比热容定压比热容c cp p任意准静态过程任意准静态过程h是状态量，设是状态量，设定压定压Specificheatatconstantpressure定容比热容定容比热容c cv v任意准静态过程任意准静态过程u是状态量，设是状态量，设定容定容Specificheatatconstantvolumec cv v和和c cp p的说明的说明(1)cv和和cp，过程已定，过程已定,可当作可当作状态量状态量。(2)前面的推导前面的推导没有没有用到用到理想气体理想气体性质性质(3)h、u、s的计算要用的计算要用cv和和cp。适用于适用于任何气体任何气体(fitforanykindofgas)c
39、v物理意义物理意义：v 时时1kg工质升高工质升高1K内能的增加量内能的增加量cp物理意义物理意义：p 时时1kg工质升高工质升高1K焓的增加量焓的增加量常见工质的常见工质的c cv v和和c cp p的数值的数值0时：时：cv,air=0.716cp,air=1.004cv,O2=cp,O2=0.9151000时：时：cv,air=0.804cp,air=1.091cv,O2=0.775cp,O2=1.03525时：时：cv,H2O=cp,H2O=一般工质一般工质:理想气体：理想气体：迈耶公式迈耶公式Mayersformula令令比热比比热比(4)(4)理想气体的定压和定容比热容的关系理想气
40、体的定压和定容比热容的关系 The relation between two kinds of specific heat of Ideal gases Inanopenflowsystem,enthalpyispartofenergythatistransferredacrossasystemboundarybyamovingflow,thispartdependsonthestate.（开口系统，焓指流动工质所携带能量的一部分，这部（开口系统，焓指流动工质所携带能量的一部分，这部分能量取决于热力状态）分能量取决于热力状态）对于闭口系统而言对于闭口系统而言,焓没有物理意义焓没有物理意义,但它
41、依旧是系统的但它依旧是系统的一个状态参数一个状态参数.熵熵的定义的定义:可逆过程可逆过程理想气体理想气体理想气体的熵理想气体的熵pv=RT仅可逆适用？仅可逆适用？T1 p1 v1 s1T2 p2 v2 s212理理想气体，任何过程想气体，任何过程1.2.cv为真实比热为真实比热3.cv为平均比热为平均比热理想气体理想气体 u u的计算的计算4.若为空气，直接查若为空气，直接查附表附表2理想气体，任何过程理想气体，任何过程T1 u1T2 u2121.2.cp为真实比热为真实比热(actualspecificheat)3.cp为平均比热为平均比热(meanspecificheat)理想气体理想气体
42、 h的计算的计算4.若为空气，直接查若为空气，直接查附表附表理想气体，任何过程理想气体，任何过程若定比热若定比热理想气体理想气体 s的计算的计算理想气体，任何过程理想气体，任何过程门窗紧闭房间用电冰箱降温门窗紧闭房间用电冰箱降温以房间为以房间为系统系统绝热闭口系绝热闭口系闭口系能量方程闭口系能量方程T电电冰冰箱箱RefrigeratorIcebox门窗紧闭房间用空调降温门窗紧闭房间用空调降温以房间为以房间为系统系统闭口系闭口系闭口系能量方程闭口系能量方程T空空调调 QAir-conditioner2.CorollariesoftheFirstLaw（热力学第一定律的推论）（热力学第一定律的推论
43、）(1)Workdoneinanyadiabatic(Q=0)processispathindependent.(2)Foracyclicprocessheatandworktransfersarenumericallyequalor3.Internal energy and enthalpy of idealgas（理想气体的内能与焓）（理想气体的内能与焓）(1).Theinternalenergyofidealgasisafunctionofonlytemperature(理理想想气气体体的的热力学能只是温度的单值函数热力学能只是温度的单值函数)。Consider a constant v
44、olume process for ideal gas,Or 内能是状态参数，因此内能的变化量与过程的路径无关。内能是状态参数，因此内能的变化量与过程的路径无关。Internalenergyisafunctionofstate,thereforethechangeininternalenergyisindependentofthepathofprocesses.理理想想气气体体在在任任意意过过程程中中热热力力学学能能的的改改变变量量都都等等于于相相同同温温度度范范围围内内定定容容过过程程中中吸吸收收的的热热量量。若若比比热热为为常常数数，则则u=cvt(2)Enthalpyofideagasi
45、salsoafunctionofonlytemperature.理理想想气气体体的的焓焓也也是是温温度度的单值函数的单值函数Consideraconstantpressureprocessforidealgas,Enthalpyisalsoastateproperty,itschangeisindependentofprocesspath.理理想想气气体体在在任任意意工工程程中中焓焓的的改改变变量量等等于于相相同同温温度度范范围围内内定定压压过过程程中中吸吸收收的的热热量量。若若比比热热为常数，则为常数，则h=cpt As shown in the figure,for ideal gas,i
46、f point 2、2、2”are on the same isothermal line（等温线）,1-2 is constant volume process,1-2 is constant pressure process and 1-2 is a random process.For reason that 2,2,2 is of the same temperature,u1-2=uu1-21-2=u=u1-2”1-2”hh1-21-2=h=h1-21-2=h=h1-21-2”如如图图所所示示，2、2、2”都都在在同同一一条条等等温温线线上上，1-2为为定定容容过过程程，1-2为为定
47、定压压过过程程，1-2”为为任任意意过过程程。因因为为2、2、2”各各点点温温度度相相同同，有：有：u1-2=uu1-21-2=u=u1-2”1-2”,hh1-21-2=h=h1-21-2=h=h1-2”1-2”=Example:4.理想气体热力学第一定律的表达式理想气体热力学第一定律的表达式FirstLawExpressionsforanIdealGas(1).Foranidealgasundergoingaquasi-staticprocess:dq=cvdT+pdv or in terms of enthalpy dq=cpdT-vdp适用条件：适用条件：1）理想气体）理想气体2)准静态
48、过程准静态过程(2).cv,与与cp,的关系的关系Relationshipsbetweenthermodynamicpropertiescv,cp,andRa.cp-cv=REquating the two first law expressions given above cpdT-vdp=cvdT+pdv (cp-cv)dT=d(pv)and pv=RT So cp-cv=Rb.Theratioofspecificheats,g g g=cp/cv Example:FreeorUnrestrainedExpansionConsider two vessels A and B which a
49、re connected to each other by a pipe and a valve.Vessel A is initially filled with a fluid at a certain pressure and B is completely evacuated.By opening the valve,the fluid in the vessel A will expand until it fills both vessels.Write out the energy balance equation for the process.Analysis:This pr
50、ocess is known as free or unrestrained expansion.It is an irreversible process because it needs external work to be done to restore the fluid to its initial condition.Consider a system,consisting of both vessels which is perfectly thermally insulated.(进行良好的隔热）进行良好的隔热）Apply the first law of thermodyn