第三章 热力学第一定律 Chapter 3. The first law of thermodynamics

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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 balance 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

2 热力学第一定律的本质 Essence of the First Law of Thermodynamics
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  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  年，C. Caratheodory最后完善热一律

3 能量守恒定律 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.

4 热力学第一定律 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
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.

5 Perpetual –motion machine of the first kind
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 added to the system and the work done by the system. ΔE = Q - W “第一类永动机是不可能制成的” Perpetual –motion machine of the first kind

6 Perpetual –motion machine of the first kind
Q 汽轮机 电加热器 锅 炉 Wnet 发电机 凝汽器 Qout 给水泵

7 §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 is 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U Microscopic 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.

8   移动 translation 分子动能 转动 rotation 分子位能 binding forces 振动 vibration
热力学能的微观组成 microscopic forms of internal energy 移动 translation 分子动能 分子位能 binding forces 化学能 chemical energy 核能 nuclear energy  转动 rotation 振动 vibration  热力学能

9 热力学能＝内动能＋内位能 T, v T （1）分子的动能和势能
Kinetic and potential energies of the molecules 热力学能＝内动能＋内位能 T, v T u is a function of the state of the system. u = u (p, T), or u = u (p, v), or u = u(v,T).

10 理想气体无分子间作用力，热力学能只决定于内动能
(2)理想气体热力学能的物理解释 理想气体u只与T有关 热力学能＝内动能＋内位能 T 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

11

12 热力学能是状态量 state property
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

13 Macroscopic energy---kinetic energy and potential energy
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 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.

14 3.系统的总能量 (Total energy） On a unit mass basis

15 §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） ⒈传热和热量（Heat transfer and heat） 热量是以温差为推动力时，系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 air. Once in the surroundings, the transferred heat becomes part of the internal energy of the surroundings, or vise versa.

16 (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 rejection（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。）

17 2.功 ( Energy transfer by Work ）
Work 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, a rotating shaft. (2)功量是有方向的量 Work is also directional quantity. (

18 work done by a system is positive, ‘+’.
　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 focus on the effects that the system (e.g. an engine) has on its surroundings.   

19 (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 System possess energy, but not heat or work.

20 Both are associated with a process, not a state.
两者都是过程量，而不是状态量 Both are associated with a process, not a 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.  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.

21 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 resistor, 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 process of a cylinder-piston installation with a simple compressible substance       

22 Work done on the system

23 = 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 a force, work is done on the system.

24 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

25 (5)轴功 ( Shaft work ） Energy transmission with a rotating shaft.
A force F acting through a moment arm r generate a torque T This force acts through a distance s Then 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

26 Substitute F into the previous equation and integrating yield
For linear elastic springs, the displacement x is 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 total mass of the system during the process.

27 （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

28 Flow work and the energy of a flowing fluid. (1) Flow work
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) Flow work For 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.

29 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.

30 开口系统中,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）
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.

31 1. The Statement of the first Law of Thermodynamic
§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 Thermodynamic The change in energy of a system is equal to the difference between the　total energy entering system and that leaving the system.

32 = - = - 热一律: 能量守恒与转换定律 进入系统的 能量 离开系统的能量 系统内部储存 能量的变化
热一律的文字表达式 热一律: 能量守恒与转换定律 = 进入系统的 能量 离开系统的能量 系统内部储存 能量的变化 - Total energy entering the system Total energy leaving the system Change in the total energy of the system = -

33 闭口系能量方程 Energy balance for closed system
 Q  W The change in energy of a system is equal to the difference between the heat added to the system and the work done by the system. Q = U + W q = u + w 单位工质

34 Q is positive (+), if the heat transferred to the system
(1) The signs are important (正负号规定很重要) U is the internal energy of the system Q is positive (+), if 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) Q and W are path dependent, U depends only on the state of the system.    

35 Point function---Exact differentials--- d
Path function---Inexact differentials---  一般式  Q  W Q = dU + W Q = 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

36 w = pdv - dl -  dA +…... q = du + w 准静态容积变化功 pdv 拉伸功 w拉伸= - dl
闭口系能量方程中的功 q = du + w 功 （ w） 是广义功Generalized Work  闭口系与外界交换的功量 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 +…...

37 q = du + w 工程热力学用此式较少 若在地球上研究飞行器 q = de + w = du + dek + dep + w
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

38 w = pdv q = du + pdv q =  u +  pdv  q = Tds Tds = du + pdv
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 q = du + pdv 热一律解析式之一 q =  u +  pdv 简单可压缩系可逆过程 (For reversible process in simple compressible system)  q = Tds Tds = du + pdv 热力学恒等式  Tds =  u +  pdv

39 理想气体内能的计算 q = du + pdv 对理想气体的定容过程 q = du + pdv 又 理想气体 理想气体，任何过程

40 q = du + pdv +vdp-vdp =dh-vdp q =dh-vdp 对理想气体的定压过程 理想气体 理想气体，任何过程
理想气体的焓 q = du + pdv +vdp-vdp =dh-vdp 对理想气体的定压过程 q =dh-vdp 理想气体 理想气体，任何过程

41 Specific heat at constant pressure
定压比热容cp Specific heat at constant pressure 任意准静态过程 h是状态量，设 定压

42 Specific heat at constant volume
定容比热容cv Specific heat at constant volume 任意准静态过程 u是状态量，设 定容

43 适用于任何气体(fit for any kind of gas)
cv和cp的说明 (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 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 (3) h、u 、s的计算要用cv 和 cp 。

44 cv,air= 0.716 kJ/kg.K cp,air= 1.004 kJ/kg.K
常见工质的cv和cp的数值 0 ℃ 时： cv,air= kJ/kg.K cp,air= kJ/kg.K cv,O2= kJ/kg.K cp,O2= kJ/kg.K 1000℃时： cv,air= kJ/kg.K cp,air= kJ/kg.K cv,O2= kJ/kg.K cp,O2= kJ/kg.K 25 ℃ 时： cv,H2O= cp,H2O= kJ/kg.K

45 一般工质: 理想气体： 迈耶公式Mayer’s 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 一般工质: 理想气体： 迈耶公式Mayer’s formula 令 比热比

46 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. （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.

47 T2 p2 v2 s2 2 1 理想气体，任何过程 T1 p1 v1 s1 pv = RT 熵的定义: 可逆过程 理想气体 仅可逆适用？
理想气体的熵 T1 p1 v1 s1 T2 p2 v2 s2 熵的定义: 1 2 可逆过程 理想气体，任何过程 理想气体 pv = RT 仅可逆适用？

48 T2 u2 2 1 T1 u1 1. 理想气体u的计算 理想气体，任何过程 2. cv 为真实比热 3. cv 为平均比热
4. 若为空气，直接查 附表2

49 理想气体 h的计算 理想气体，任何过程 1. 2. cp 为真实比热(actual specific heat)
3. cp 为平均比热 (mean specific heat) 4. 若为空气，直接查 附表

50 理想气体s的计算 理想气体，任何过程 若定比热

51 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 Refrigerator Icebox 电冰箱 T

52 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 Air-conditioner 空调 Q T

53 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 transfers are numerically equal or

54 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

55 Internal energy is a function of state,
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, therefore 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Δu=cvΔt

56 (2) Enthalpy of idea gas is also a function of only temperature
Consider a constant pressure process for ideal gas,

57 Enthalpy is also a state property, its change 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Δh=cpΔt

58 Example: Δu1-2=Δu1-2’=Δu1-2” Δh1-2=Δh1-2’=Δh1-2”
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 the same temperature, Δu1-2=Δu1-2’=Δu1-2” Δh1-2=Δh1-2’=Δh1-2” 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： Δu1-2=Δu1-2’=Δu1-2”, Δh1-2=Δh1-2’=Δh1-2”=

59 适用条件： 1）理想气体 2) 准静态过程 or in terms of enthalpy dq = cpdT - vdp
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 + pdv or in terms of enthalpy dq = cpdT - vdp 适用条件： 1）理想气体 2) 准静态过程

60 (2).   cv,与cp, 的关系 Relationships between thermodynamic properties cv, cp, and R a. cp - cv = R  Equating the two first law expressions given above cpdT - vdp = cvdT + pdv (cp - cv)dT = d(pv) and pv = RT So cp - cv = R b.   The ratio of specific heats, g g = cp/cv

61 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 both 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 which 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 because 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.

62 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 reversible process w = pdv q = du + pdv q =  u +  pdv

63 理想气体，任何过程 q = cv dT+ w 理想气体，可逆过程 q = cv dT+ pdv
理想气体为工质时 For Ideal Gas 理想气体，任何过程 q = cv dT+ w 理想气体，可逆过程 q = cv dT+ pdv

64 焓 (Enthalpy) h = u + pv 理想气体的焓 For Ideal Gas 理想气体，任何过程

65 §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)

66 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 total mass of the system during the process. 2.开口系统的能量方程 Energy Balance for an Open System

67 Q is called moving boundary work. Ws Ｗcv,ex
Let’s define the inlet state as “1”, and the outlet state as 2. is called moving boundary work.

68

69 §3.5稳定流动的能量方程 Energy Equation For Steady Flow
１．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.

70 2.稳态稳定流动过程的特点 Characteristics of steady-flow process 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 process A 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.

71 状态参数可沿流动空间中的各点而变化,但对于其中任意一点,状态参数在整个过程中保持不变.)
In the control volume, the properties can only change from point to point, but at any point they remain constant during the entire process. 流入控制体积的总质量和能量一定等于流出系统的总质量和能量. The total mass or energy entering the control volume must be equal to the total mass or energy leaving it.

72 稳态稳定流动系统与外界的热量及功量交换不随时间而变化。
The heat and work interactions between a steady-flow system and its surroundings do not change with time. 控制体积的体积保持不变。 The volume of the control volume remains constant. 稳态稳定流动系统中不涉及移动边界功。 No moving boundary work is involved in steady flow. 2．Energy Balance for Steady Flow (稳定流动的能量守恒方程)  

73 No moving boundary work is involved.
(１)方程的推导 Derivation of the Energy Balance Equation 稳态稳定流动系统中不涉及移动边界功。 No moving boundary work is involved.

74 （２）每一项的物理意义 The physical meaning of each item Q and W means the heat added to the system and work done by the system respectively. No moving boundary work is involved. (稳态稳定流动系统中不涉及移动边界功。） Q is positive (+), if the heat is 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 the work is done on the system.

75 方程直观地显示出焓的物理意义 Physical interpretation for enthalpy. In an open flow system, enthalpy is the amount of energy that is transferred across a system boundary by a moving flow which depends on the system states. This energy is composed of two parts: the internal energy of the fluid u the flow work pv associated with pushing the mass of fluid across the system boundary.

76 (3) 技术功 Technical work The kinetic energy, potential energy and shaft work can be used easily. we define 如果动能和势能可以忽略不计，那么技术功就等于轴功Technical work is equal to shaft work if kinetic and potential energy is negligible. Then, the energy balance equation can be rewritten as

77 We know, for the flow fluid,
Then This equation indicates the relationship between flow work, moving boundary work and technical work

78 Not all moving boundary work can be used technically.
并非所有的膨胀功在技术上都是可用的 Not all moving boundary work can be used technically. For example.

79 For reversible process
1 Substitute it into wt 2 v We get

80 §3.5 工程中的几种稳态稳定流动装置 Some steady-flow engineering devices
1.气轮机与压缩机 Turbines and Compressors The kinetic and potential energy difference between the inlet and outlet can be neglected as well as the heat rejection.

81 汽轮机中所做的功为正,且等于流动工质的焓降
The work done in a turbine is positive and that equals to the enthalpy decrease of the flowing fluid. 类似地,压缩机所消耗的功量等于流动工质的焓增 Similarly, the work consumed in a compressor is equal to the enthalpy increase of the flowing fluid.

82 2.喷管和扩压管 Nozzles and Diffusers ()
通过变截面短管的流动,可视为绝热流动,且无输入、输出功的装置 Flow through very short tubes with variable cross sectional area, the flow is adiabatic. No work input and output installation. The change in potential energy is also negligible.

83 ws = 0  c2 = 0  z = 0 q = 0  h = 0 h1=h2 绝热节流 Adiabatic Throttling

84 4 换热设备 Heat Exchanger 没有作功部件: ws = 0 加热量 = 焓升

85 Internal Energy u (系统的内能) Total energy of a system (系统的总能量)
Summary (小结) Internal Energy u (系统的内能) Total energy of a system (系统的总能量) Q and W (热量和功量) Enthalpy (焓) Energy Equation of closed system (闭口系统的能量方程) Energy Equation of open system (开口系统的能量方程)

86 The increase in kinetic energy comes from the decrease in enthalpy of flowing fluid.（流动工质的动能增加来自于其焓值的降低）

87 Exercise (练习) 纠正下列各式中的错误 Correct the error in the following equations.
(1) (2) (3) (4) (5)

88 2.叙述下列各公式的适用条件 Make a statement of suitable conditions under which the following equations can be adopted. (1) (2) (3) (4)

89 3. The inlet properties of a turbine are:
The outlet properties of the turbine are: Calculate the amount of work we can get when working fluid flow through the turbine. 4. Initially, there is m working fluid in an adiabatic and rigid container, its state is denoted as ‘1’.Then m working fluid of state ‘2’ is charged into the container. The process finished until the state of the working fluid reaches ‘3’ . Write out the energy equation for the process.

90 Reading and Review Book in English version (英文版教材) Section 4. 1~4
Reading and Review Book in English version (英文版教材) Section 4.1~4.4 on P166~196. (第166~196页第4.1~4.4节) Book of Chinese version (中文版教材) 第3章