1、第三章 热力学第一定律 Chapter 3. The first law of thermodynamics,3.1系统的宏观和微观储存能Macroscopic and microscopic energy of system 3.2热量、功量及质量引起的能量传递-传递中的能量Energy transfer by Heat, Work and Mass 3.3热力学第一定律与闭口系统的能量平衡方程The first law of thermodynamics and Energy balance equation of closed system 3.4开口系统的能量平衡方程Energy ba
2、lance equation of open system 3.5稳态稳定流动的能量平衡Energy balance for steady-flow systems 3.6工程中的几种稳态稳定流动装置Some steady-flow engineering devices,热力学第一定律的本质 Essence of the First Law of Thermodynamics, 1909年，C. Caratheodory最后完善热一律,本质：能量转换及守恒定律在热过程中的应用, 18世纪初，工业革命，热效率只有1%, 1842年，J.R. Mayer阐述热一律，但没有引起重视, 1840-1
3、849年，Joule用多种实验的一致性证明热一律，于1850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，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。Conservation of energy principle states that energy can be neither created nor destroyed; it can only change from one form to another but the total amount of energy remains constant.,能量守恒定律,热力学第一定律
4、主要说明热能与机械能在转换过程中的能量守恒The first law of thermodynamics is viewed as the Conservation of energy principle which governs the energy transfer process from thermal energy to mechanical ones.,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作功量之差。The change in energy of a system is equal to the difference between the heat add
5、ed to the system and the work done by the system.E = Q - W,“第一类永动机是不可能制成的”,Perpetual motion machine of the first kind,Q,Perpetual motion machine of the first kind,锅 炉,汽轮机,发电机,给水泵,凝汽器,Wnet,Qout,电加热器,3.1系统的宏观和微观储存能 Macroscopic and microscopic energy of system,Energy is a property of every system. It i
6、s denoted as E for a system, or e for a system with a unit mass. E = internal energy + kinetic energy + potential energy 1.热力学能UMicroscopic energy-Internal energy U 热力学能指系统所有微观形式的能量之和.Internal energy is defined as the sum of all the microscopic forms of energy of a system.,热力学能的微观组成,分子动能分子位能 binding
7、 forces化学能 chemical energy核能 nuclear energy,热力学能,microscopic forms of internal energy,移动 translation,转动 rotation,振动 vibration,（1）分子的动能和势能Kinetic and potential energies of the molecules,u is a function of the state of the system.u = u (p, T), or u = u (p, v), or u = u(v,T).,热力学能内动能内位能,T, v,T,(2)理想气体热
8、力学能的物理解释,热力学能内动能内位能,T, v,理想气体无分子间作用力，热力学能只决定于内动能,? 如何求理想气体的热力学能 u,T,理想气体u只与T有关,热力学能的说明,热力学能是状态量 state property,U : 广延参数 kJ u : 比参数 kJ/kg,热力学能总以变化量出现，热力学能零点人为定义,2.宏观储存能：动能和势能 Macroscopic energy-kinetic energy and potential energy They are related to some outside reference frame。 Kinetic energy is the
9、 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.,On a unit mass basis,3.系统的总能量 (Total energy）,传热和热量（Heat transfer and heat）热量是以温差为推动力时，系
10、统与外界之间传递的能量Heat is energy interaction between a system and its surroundings if its driving force is temperature difference only.(1) 热量是传递中的能量（Heat is energy in transition. ） Eg. The baked potato contains energy, this energy is heat transfer only as it passes through the skin of potato to reach the a
11、ir. Once in the surroundings, the transferred heat becomes part of the internal energy of the surroundings, or vise versa.,3.2 Energy transfer by Heat, Work and Mass(热量、功量及质量引起的能量传递-传递中的能量）,(2)热量是有方向的量(Heat is directional quantity. )Heat addition (加热） is the transfer of heat into a system.Heat rejec
12、tion（放热） is the transfer of heat out of a system.Formal sign convention:heat addition is positive, +.heat rejection is negative, -. (3) “Adiabatic ” means no heat is transferred （“绝热”意味着没有热量传递。）. (4) Heat transfer can change the state of the system.（传热可以引起系统状态的变化。）,2.功 ( Energy transfer by Work ）Wor
13、k is the energy transfer associated with a force acting through a distance. (1)功量也是传递中的能量Work is also energy in transition. We can have push-pull work (e.g. in a piston-cylinder, lifting a weight), electric and magnetic work (e.g. an electric motor), chemical work, surface tension work, elastic work
14、, a rotating shaft. (2)功量是有方向的量 Work is also directional quantity. (,It is stipulated: work done by a system is positive, +. That is, energy leaves the system. ( 系统作功，功为正，也即能量离开系统。work done on a system is negative, -. That is, energy added to the system, （外界对系统作功，功为负，即能量加入系统。）(In defining work, we f
15、ocus on the effects that the system (e.g. an engine) has on its surroundings.,(3)热量和功量的相似之处）Similarities between heat and work （热量和功量是系统与外界能量交换的机理。Heat and work are energy transfer mechanisms between a system and its surroundings. 功量和热量都要穿越边界。Both heat and work are boundary phenomena.系统具有能量，但不是功量或热量
16、System possess energy, but not heat or work.,Example. Work vs. heat transfer - which is which? Can have one, the other, or both? It depends on what crosses the system boundary. For example consider a resistor that is heating a volume of water.,两者都是过程量，而不是状态量 Both are associated with a process, not a
17、 state. Both are path functions.（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 path function.,If the water is the system, then the state of the system will be changed by heat transferred from the resistor.If the system is the water + the resi
18、stor, then the state of the system will be changed by (electrical) work.(4) Moving boundary work (移动边界功，即膨胀功或压缩功） A. Quasi-static processes Use of pext instead of psys is often inconvenient because it is usually the state of the system that we are interested in. pext =psys B. Consider a quasi-static
19、 process of a cylinder-piston installation with a simple compressible substance,Work done on the system,therefore: =or in terms of the specific volume, v:=,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. 若系统受力而体积收缩，则外界对系统作功）If system volume contracts under
20、a force, work is done on the system.,C. Work is a path dependent process Work depends on path Must specify path if we need to determine work Along Path a: W = 2p0(2V0 - V0) = 2p0V0 Along Path b: W = p0(2V0 - V0) = p0V0,(5)轴功 ( Shaft work ）Energy transmission with a rotating shaft. A force F acting t
21、hrough a moment arm r generate a torque TThis force acts through a distance sThen the shaft work is determined from(6)弹簧力功 (Spring Work ） The length of a spring will change by a differential amount dx , on which a force F is applied. The work done is,For linear elastic springs, the displacement x is
22、 proportional to the force applied. Substitute F into the previous equation and integrating yield 3.质量守恒定律( Conservation of Mass Principle ） 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）。Net mass transfer to or from a system during a process is equal to the net change (increase or decrease) in the
23、total mass of the system during the process.,（Total mass entering the system)-(Total mass leaving the system)=(Net change in mass with the system),质量守恒方程也被称作连续性方程 The conservation of mass equation is also called as Continuity Equation,4 .流动功与流动工质所携带的能量 Flow work and the energy of a flowing fluid. (1
24、) Flow workFor open systems, some work is required to push the mass into or out of the control volume, the work is known as the flow work.(2) The energy of a flowing fluid When fluid enters or leaves a control volume (masses flow across their boundaries), energies are brought into the control volume
25、.,5.焓 （ A Useful New State Function Enthalpy） Enthalpy, a state function, is defined as follows,h= u + pv 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.,开口系统中,焓指流动工质所携带能量的一部分，这部分能
26、量取决于热力状态）In an open flow system, enthalpy is part of energy that is transferred across a system boundary by a moving flow, this part depends on the state.,3.3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. The Statement of the first Law of ThermodynamicThe c
27、hange in energy of a system is equal to the difference between the total energy entering system and that leaving the system.,热一律的文字表达式,热一律: 能量守恒与转换定律,闭口系能量方程 Energy balance for closed system, W, Q,Q = U + W q = u + w,单位工质,The change in energy of a system is equal to the difference between the heat a
28、dded to the system and the work done by the system.,(1) The signs are important (正负号规定很重要)U is the internal energy of the systemQ is positive (+), if the heat transferred to the systemQ is negative (-), if it is transferred from the system. W is positive (+), if the work is done by the system, W is
29、negative (-), if work is done on the system. (2) Q and W are path dependent, U depends only on the state of the system., W, Q,一般式,Q = dU + WQ = U + W,q = du + w q = u + w,单位工质,适用条件： 1）任何工质 2) 任何过程,Point function-Exact differentials- d Path function-Inexact differentials- ,闭口系能量方程中的功,功 （ w） 是广义功Gener
30、alized Work 闭口系与外界交换的功量,q = du + w,准静态容积变化功 pdv 拉伸功 w拉伸= - dl 表面张力功 w表面张力= - dA,w = pdv - dl - dA +.,闭口系能量方程的通式,q = du + w,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,准静态和可逆闭口系能量方程,简单可压缩系准静态过程,w = pdv,简单可压缩系可逆过程 (For reversible process in simple compressible system), q = Tds,q = du + pdv,q
31、= u + pdv,热一律解析式之一,Tds = du + pdv, Tds = u + pdv,热力学恒等式,理想气体内能的计算,理想气体,q = du + pdv,对理想气体的定容过程,q = du + pdv,又,理想气体的焓,理想气体,q = du + pdv +vdp-vdp=dh-vdp,对理想气体的定压过程,q =dh-vdp,定压比热容cp,任意准静态过程,h是状态量，设,定压,Specific heat at constant pressure,定容比热容cv,任意准静态过程,u是状态量，设,定容,Specific heat at constant volume,cv和cp的
32、说明,(1) cv 和 cp ，过程已定, 可当作状态量 。,(2) 前面的推导没有用到理想气体性质,(3) h、u 、s的计算要用cv 和 cp 。,适用于任何气体(fit for any kind of gas),cv物理意义： v 时1kg工质升高1K内能的增加量,cp物理意义： p 时1kg工质升高1K焓的增加量,常见工质的cv和cp的数值,0 时：,cv,air= 0.716 kJ/kg.K cp,air= 1.004 kJ/kg.K,cv,O2= 0.655 kJ/kg.K cp,O2= 0.915 kJ/kg.K,1000时：,cv,air= 0.804 kJ/kg.K cp,a
33、ir= 1.091 kJ/kg.K,cv,O2= 0.775 kJ/kg.K cp,O2= 1.035 kJ/kg.K,25 时：,cv,H2O= cp,H2O= 4.1868 kJ/kg.K,一般工质:,理想气体：,迈耶公式Mayers formula,令,比热比,(4)理想气体的定压和定容比热容的关系 The relation between two kinds of specific heat of Ideal gases,In an open flow system, enthalpy is part of energy that is transferred across a sys
34、tem boundary by a moving flow, this part depends on the state. （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）对于闭口系统而言,焓没有物理意义,但它依旧是系统的一个状态参数.,熵的定义:,可逆过程,理想气体,理想气体的熵,pv = RT,仅可逆适用？,1.,2. cv 为真实比热,3. cv 为平均比热,理想气体u的计算,4. 若为空气，直接查 附表2,1.,2. cp 为真实比热(actual specific heat),3. cp 为平均比热 (mean specific heat),理想气体 h的计算
35、,4. 若为空气，直接查 附表,若定比热,理想气体s的计算,门窗紧闭房间用电冰箱降温,以房间为系统,绝热闭口系,闭口系能量方程,T,电冰箱,Refrigerator Icebox,门窗紧闭房间用空调降温,以房间为系统,闭口系,闭口系能量方程,T,空调,Q,Air-conditioner,2. Corollaries of the First Law （热力学第一定律的推论） (1) Work done in any adiabatic (Q=0) process is path independent. (2) For a cyclic process heat and work transf
36、ers are numerically equal,or,3. Internal energy and enthalpy of ideal gas （理想气体的内能与焓）(1) The internal energy of ideal gas is a function of only temperature (理想气体的热力学能只是温度的单值函数)。Consider a constant volume 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。Internal energy is a function of state, theref
37、ore the change in internal energy is independent of the path of processes.理想气体在任意过程中热力学能的改变量都等于相同温度范围内定容过程中吸收的热量。若比热为常数，则u=cvt,(2) Enthalpy of idea gas is also a function of only temperature. 理想气体的焓也是温度的单值函数Consider a constant pressure process for ideal gas,Enthalpy is also a state property, its cha
38、nge is independent of process path.理想气体在任意工程中焓的改变量等于相同温度范围内定压过程中吸收的热量。若比热为常数，则h=cpt,As shown in the figure, for ideal gas, if 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 th
39、e same temperature, u1-2=u1-2=u1-2” h1-2=h1-2=h1-2”如图所示， 2、2、2”都在同一条等温线上，1-2为定容过程，1-2为定压过程，1-2”为任意过程。因为2、2、2”各点温度相同，有： u1-2=u1-2=u1-2”, h1-2=h1-2=h1-2”=,Example:,4. 理想气体热力学第一定律的表达式 First Law Expressions for an Ideal Gas(1). For an ideal gas undergoing a quasi-static process: dq = cvdT + pdvor in ter
40、ms of enthalpydq = cpdT - vdp,适用条件： 1）理想气体 2) 准静态过程,(2) cv,与cp, 的关系 Relationships between thermodynamic properties cv, cp, and R a. cp - cv = REquating the two first law expressions given abovecpdT - vdp = cvdT + pdv(cp - cv)dT = d(pv)and pv = RTSo cp - cv = Rb. The ratio of specific heats, gg = cp/
41、cv,Example: Free or Unrestrained Expansion,Consider two vessels A and B which are 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 b
42、oth vessels. Write out the energy balance equation for the process. Analysis: This process 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 w
43、hich is perfectly thermally insulated. (进行良好的隔热）Apply the first law of thermodynamics to the system, i.e. Q + W = U2 - U1 where indices 1 and 2 represent initial and final states. Q = 0, because the thermal insulation will not allow any heat transfer between the system and the surroundings. W=0 beca
44、use the boundaries of the system are not moved. The result will then be: U2=U1 The free expansion process is adiabatic but irreversible. If the working fluid is an ideal gas, then U2=U1 is equivalent to T2=T1.,闭口系能量方程的通式 (Energy Balance Equation for Closed System),q = du + w,闭口系可逆过程能量方程 For reversib
45、le process,w = pdv,q = du + pdv,q = u + pdv,理想气体为工质时 For Ideal Gas,q = cv dT+ w,q = cv dT+ pdv,焓 (Enthalpy),h = u + pv,理想气体的焓 For Ideal Gas,3.4 开口系统的能量方程 Energy Balance For Open System,1.开口系统的质量守恒方程Mass Balance for an Open System (Control Volume),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)。 Net mass transfe
46、r to or from a system during a process is equal to the net change (increase or decrease) in the total mass of the system during the process.2.开口系统的能量方程 Energy Balance for an Open System,Q,Ws cv,ex,Lets define the inlet state as “1”, and the outlet state as 2.,is called moving boundary work.,3.5稳定流动的
47、能量方程 Energy Equation For Steady Flow,稳态稳定流动的定义 Definition of Steady-flow 稳定就指流动空间中各点的状态不随时间而变化.) Steady-flow is a process during which a fluid flows through a control volume steadily.Steady means no change with time.,(1) 稳定和均匀 Steady and uniform Steady implies no change with time.Uniform implies no change with location over specific region. (2) Steady-flow processA process during which a fluid flows through a control volumesteadily. That is, the properties remain the same at a fixed point during the entire process.,2.稳态稳定流动过程的特点 Characteristics of steady-flow process,
