（The First Law of Thermodynamics) 回顾(Review) 热力学第一定律 （The First Law of Thermodynamics) 能量守恒与转换定律 能量之间数量的关系

A process must satisfy the first law of Thermodynamics to occur. (一个过程必须满足热力学第一定律才能发生) 是否满足能量守恒与转换定律的过程一定都能自动发生? Satisfying the first law alone does not ensure that the process will actually take place. (但是，满足热力学第一定律的过程未必都能发生）

（第五章 热力学第二定律） Chapter 5.The Second Law of Thermodynamics 5.1自发过程的方向性） The Direction of Spontaneous Process 5.2热力学第二定律的表述 Statement of the Second Law of Thermodynamics 5.3卡诺循环与卡诺定律 Carnot cycle and Carnot Theorem 5.4熵、熵增原理及熵方程 Entropy, The increase principle of Entropy and Entropy Equation 5.5熵的意义及应用 Significance of Entropy and its application

§5.1 Spontaneous Process （自发过程） 过程的方向性 §5.1 Spontaneous Process （自发过程） 温差传热 (Heat Transfer under temperature difference) 自由膨胀 (Free Expansion) √ QA= QB QA A TA> TB, QA= QB × B QB U1=U2 √ A B U1=U2 × 温差传热和自由膨胀均为不平衡势差推动下的非准静态过程,也即不可逆过程

摩擦生热 电容－电阻电路 U2=U1+mc2/2 U1=U2+mc2/2

(Direction of Spontaneous Process) 自发过程的方向性 (Direction of Spontaneous Process) 自发过程：不需要任何外界作用而自动进行的过程。 Such as (例如：) a. heat transfer driven by finite temperature difference (有限温差传热) b. work is converted into heat by friction (通过摩擦功转变为热) c. Free or unrestrained expansion (空气向真空自由膨胀)。 d. Mixing process of different substances (不同的流体混合)

自发过程的方向性 (Direction of Spontaneous Process) 自发过程只能沿某一方向进行，而不能反向自动发生 自然界自发过程都具有方向性 摩擦生热 功量 热量 100% 发电厂 热量 功量 放热 40% 自发过程具有方向性、条件、限度

3.热力学第二定律的任务 Essence of the Second Law of Thermodynamics 自然界过程的方向性表现在不同的方面 能不能找出共同的规律性? 能不能找到一个判据? 热力学第二定律 研究过程的方向性和补偿限

热二律的表述有 60-70 种 传 热 热功转换 1850年 克劳修斯表述 热量传递的角度 1851年 开尔文－普朗克表述 热功转换的角度 §5.2 Statement and Essence of the Second Law of Thermodynamics （热力学第二定律的表述和实质） 热二律的表述有 60-70 种 传 热 热功转换 1850年 克劳修斯表述 热量传递的角度 1851年 开尔文－普朗克表述 热功转换的角度

不可能将热从低温物体传至高温物体而不引起其它变化。 1. 克劳修斯表述 Clausius statement 不可能将热从低温物体传至高温物体而不引起其它变化。 It is impossible to construct a device that operates in a cycle and produces no effect other than the transfer of heat from a lower-temperature body to a higher-temperature body.

克劳修斯表述 Clausius statement Transfer heat from high temperature reservoir to low temperature ones is a spontaneous process. However it is irreversible. (从高温物体向低温物体的传热是一个自发过程,但是不可逆) Transfer heat from low temperature reservoir to high temperature ones is possible. However it will leave influence on environment. (从低温物体向高温物体的传热过程是可以实现的,但会给环境造成一定影响)

热量不可能自发地、不付代价地从低温物体传至高温物体。 空调,制冷 (Air-Conditioning, Refrigerating) 代价：耗功 (Cost: Energy Consumption) 热量不可能自发地、不付代价地从低温物体传至高温物体。

不可能从单一热源取热，并使之完全转变为有用功而不产生其它变化。 2. 开尔文－普朗克表述 Kelvin－Planck Statement 不可能从单一热源取热，并使之完全转变为有用功而不产生其它变化。 It is impossible for any device that operates on a cycle to receive heat from a single reservoir and produce a net amount of work.

热机不可能将从热源吸收的热量全部转变为有用功，而必须将某一部分传给冷源。 开尔文－普朗克表述 Kelvin－Planck Statement No heat engine can achieve a 100 percent thermal efficiency. (热机的效率不可能达到100%) For a heat engine, the working fluid must exchange heat with the environment. (对于热机来说,工质必然和环境交换热量) 热机不可能将从热源吸收的热量全部转变为有用功，而必须将某一部分传给冷源。

Thermal Energy Heat reservoirs Source Sink 冷热源:容量无限大，取、放热其温度不变 Heat

第二类永动机 perpetual-motion machine of the second kind 第二类永动机：设想的从单一热源取热并 使之完全变为功的热机。 但违反了热 力学第二定律 这类永动机 并不违反热力 学第一定律 第二类永动机是不可能制造成功的 环境是个大热源

Perpetual –motion machine of the second kind 汽轮机 Q 锅 炉 Wnet 发电机 凝汽器 Qout 给水泵

3.克劳修斯说法与开尔文-普朗克说法等价 Equivalence of Clausius and Kelvin-Planck Statements Suppose we can construct a heat pump which transfers heat from a low temperature reservoir to a high temperature one without using external work. Then, we can couple it with a heat engine in such a way that the heat removed by the heat pump from the low temperature reservoir is the same as the heat rejected by the heat engine, so that the combined system is now a heat engine which converts heat to work without any external effect. This is thus in violation of the Kelvin-Planck statement of the second law.

Now suppose we have a heat engine which can convert heat into work without rejecting heat anywhere else. We can combine it with a heat pump so that the work produced by the engine is used by the pump. Now the combined system is a heat pump which uses no external work, violating the Clausius statement of the second law. Thus, we see that the Clausius and Kelvin-Planck statements are equivalent, and one necessarily implies the other.

两种表述的关系 开尔文－普朗克 表述 克劳修斯表述： 完全等效!!! 违反一种表述,必违反另一种表述!!!

??? t >100％不可能 t =100％不可能 热机的热效率最大能达到多少？ 又与哪些因素有关？ 热一律否定第一类永动机 热一律与热二律 热一律否定第一类永动机 t >100％不可能 热二律否定第二类永动机 t =100％不可能 ??? 热机的热效率最大能达到多少？ 又与哪些因素有关？

热二律的实质 • 自发过程都是具有方向性的 • 表述之间等价不是偶然，说明共同本质 • 若想逆向进行，必付出代价,代价为多少方可进行?

§5.3 Carnot Cycle and Carnot Theorem 　　 　(卡诺循环及卡诺定理) 法国工程师卡诺 (S. Carnot)， 1824年提出 卡诺循环 热二律奠基人 效率最高 Carnot Cycle is a a particular cycle that has the best possible efficiency, which is important in practice. It sets an upper limit on what is possible for real engines.

Heat is transferred to the working fluid during p V Heat is transferred to the working fluid during 1-2 (Qh) and heat is rejected during 3-4 (Ql).

卡诺循环 Carnot Cycle an isothermal expansion at high temperature Th (2) an adiabatic expansion （可逆绝热膨胀过程） (3) an isothermal compression at low temperature Tl 　 （在低温Ｔl下的等温放热过程） (4) an adiabatic compression （可逆绝热压缩过程）

Thermal efficiency of Carnot Cycle 卡诺循环热机效率 Thermal efficiency of Carnot Cycle T1 Applying first law, q1 Rc w q2 卡诺循环热机效率 T2

Thermal efficiency of Carnot Cycle (卡诺循环的热效率) For Isothermal Process of Ideal gas: (对理想气体的等温过程) For ideal gas

2.Carnot‘s Theorems (卡诺定理) 在相同的高温热源和相同的低温热源间工作的可逆热机的热效率恒高于不可逆热机的热效率； The efficiency of an irreversible heat engine is always less than that of a reversible one operating between the same two thermal reservoirs.

2.Carnot‘s Theorems (卡诺定理) 在相同的高温热源和相同的低温热源间工作的一切可逆热机有相同的热效率，而与工质无关。 The efficiencies of all reversible heat engines operating between the same two thermal reservoirs are the same.

(Investigation on the Carnot Theorem) 卡诺定理的证明 (Investigation on the Carnot Theorem) W irreversible reversible W Assumed that the work done by these two heat engines is the same. (假定两个热机所做的功相等)

For a Carnot engine, the efficiency simplifies to This is the highest efficiency a heat engine operation between the two thermal energy reservoirs at temperatures and can have. The thermal efficiencies of actual and reversible heat engines operating between the same temperature limits compares as follows

3. The significance of the Carnot Theorems (卡诺定理的意义) (1)卡诺定理指明了热变功的最高效率 The Carnot Theorem indicates the maximum thermal efficiency of heat engine, which converts heat into work.

(2)卡诺定理指明可以通过提高高温热源的温度,降低低温冷源的温度或减少过程的不可逆因素等方式来提高热效率 The Carnot Theorem point out thermal efficiency can be improved by means of raising the temperature of high temperature thermal reservoir, lowering the temperature of lower temperature reservoir, or reducing irreversibilities.

(3) 卡诺热效率表明了热量的最大可用能 The Carnot thermal efficiency value reveals the maximum amount of high temperature thermal energy which can be converted to work. (4)卡诺定理表明能量不仅有数量的差别，还有品质的高低 The Carnot Theorem indicates that energy has quality as well as quantity.

功量比热量更可贵，因为它可以100%地转化为热量，而热量只能部分转化为功 Work is a more valuable form of energy than heat since 100 % of work can be converted to heat, but only a fraction of heat can be converted to work.

热源温度越高，热量的品质就越高,其可转化为的可用能就越大。 The higher the temperature, the higher the quality of thermal energy. (5) 基于卡诺定理,才证明熵是一个状态参数 It is based on Carnot theorem that entropy is investigated to be a property.()

A 热机是否能实现 1000 K 2000 kJ 1200 kJ A 可能 1500 kJ 800 kJ 500 kJ 300 K 不可能 卡诺定理举例 例题: A 热机是否能实现 1000 K 2000 kJ 1200 kJ A 可能 1500 kJ 800 kJ 如果：W=1500 kJ 500 kJ 300 K 不可能

4.工作在相同温限范围内的任意可逆循环与卡诺循环 For any reversible cycle and Carnot cycle working between the same temperature difference T T1 TM1 TM2 T2 s s1 s2

For every small Carnot cycle 5. Entropy (熵) For every small Carnot cycle p a 1 2 b v Then, Entropy is defined as

６. Clausius Inequality (克劳修斯不等式) For every small irreversible cycle p a 1 2 b v

克劳修斯不等式 克劳修斯不等式的研究对象是循环方向性的判据 正循环 逆循环 可逆循环 不可逆循环 克劳修斯不等式的推导

克劳修斯不等式的推导 1、正循环（卡诺循环） ∵可逆时 （2）不可逆循环 T1 吸热 Q1’ Q1 假定 Q1=Q1’ ，tIR < tR，W’<W W’ W IR R Q2 Q2’ T2 ∴

克劳修斯不等式的推导 2、反循环（卡诺循环） （1）可逆循环 T1 放热 Q1 W R Q2 ∴ T2

克劳修斯不等式的推导 2、反循环（卡诺循环） 可逆时 （2）不可逆循环 T1 放热 Q1’ Q1 假定 Q2 = Q2’ W’>W IR R Q2 Q2’ ∴ T2

克劳修斯不等式推导总结 正循环（可逆、不可逆） 吸热 反循环（可逆、不可逆） ??? 放热 可逆 = 不可逆 < 仅卡诺循环

克劳修斯不等式 将循环用无数组 s 线细分，abfga近似可看成卡诺循环 ∴ 对任意循环 克劳修斯 不等式 热源温度 热二律表达式之一 = 可逆循环 < 不可逆循环 > 不可能 热二律表达式之一

克劳修斯不等式例题 A 热机是否能实现 1000 K 可能 2000 kJ A 1200 kJ 1500 kJ 800 kJ 500 kJ 如果：W=1500 kJ A 1200 kJ 1500 kJ 800 kJ 500 kJ 不可能 300 K 注意： 热量的正和负是站在循环的立场上

5.3 The increase principle of Entropy and Entropy Equation （熵增原理与熵方程） Performance of Entropy (熵的性质) (1) we define 　　Entropy is a state property. Any substance possesses this property . ( 熵是一个状态参数，任何物质都具有熵这个参数） It depends only on state. (它仅取决于状态） (2) Entropy is an extensive property. It possess addition 　　(熵是一个广延参数，具有可加性） (3) Heat absorption during reversible process can be calculated by the following equation. ( 可逆过程的吸热量可用下列公式计算）

Entropy decreases as it rejects heat.（可逆过程放热，则导致熵减小） Entropy of a substance increases as it absorbs heat.(可逆过程吸热，则导致熵增大） Entropy decreases as it rejects heat.（可逆过程放热，则导致熵减小） (4) > , for irreversible process (不可逆过程)。 =, for reversible process (可逆过程)

For Example. Initially, a system with air , undertakes an isothermal expansion process and reaches . undertake a adiabatic process and reaches . Calculate the change in entropy.

2.孤立系统的熵增原理 The increase principle of Entropy we know For isolated system The entropy of an isolated system during a process always increases or, in the limiting case of a reversible process remains constant. In other word, it never decreases. (孤立系统中的过程总是向着熵增大的过程进行,若为可逆过程,则熵不变。换句话说，即孤立系统的熵不会减小）

heat transfer across a finite temperature difference（温差传热） Why does not entropy of isolated system decrease? (为什么孤立系统的熵不会减少？） Only irreversibilities can lead to the increase in entropy of an isolated system.（不可逆性是导致孤立系统熵增大的唯一原因） Such as heat transfer across a finite temperature difference（温差传热） friction（摩擦） Free or unrestrained expansion（自由膨胀） mixing of two fluids（液体的混合） electric resistance（电阻） inelastic deformation of solid（固体的塑性变形） chemical reactions（化学反应） 3.Entropy generation and Entropy flow (熵产与熵流) Entropy generation is caused by any irreversibility. ( 熵产是由不可逆因素引起的熵变)

> , for irreversible process (不可逆过程)。 =, for reversible process (可逆过程) (2) Entropy Flow/Transfer (熵流) Entropy can be transferred to or from a system by two mechanisms: heat transfer and mass flow. Entropy transfer by heat transfer (热量熵流) The direction of entropy transfer is the same as that of heat transfer. (热量熵流的方向与热流的方向相同) Energy is transferred by both heat and work,whereas, entropy is only transferred by heat. No entropy is transferred by work. (能量可以由热量和功量的交换实现传递,但是, 熵流却只能有热量传递引起,做功不引起熵的流动)

Entropy transfer by mass flow (质量熵流) Mass contains energy as well as entropy. Both entropy and energy are carried into or out of system by streams of matter.(物质具有能量和熵的属性,随着物流的迁移,能量和熵都会被带进或带出系统) The rates of energy and entropy transport into or out of a system is proportional to the mass flow rate. (能量及熵流率与质量流率成正比.) The entropy of a system increases by when mass in the amount of enters and decreases by the same amount when the same amount of mass at the same amount leaves the system. (当质量为 的物质进入系统时,系统的熵将增大 ; 当当质量为 的物质离开系统时,系统的熵将减少 )

4. Entropy Equation (熵方程) (1) Entropy balance of any system undergoing any process can be expressed as (任何系统经过任何过程的熵平衡可表达为) (2) For closed system (对于闭口系统) The entropy change of a closed system during a process is equal to the sum of the net entropy transferred through the system boundary by heat transfer and the entropy generation within the system boundaries. (经过一个过程,闭口系统的熵变等于通过边界的热量熵流与系统内部的熵产之和)

For adiabatic closed system For any closed system and its surroundings

(2) For Open System (对于开口系统) The entropy change of a Open system during a process consists of （经过一个过程,开口系统的熵变由下列部分组成） the net entropy transferred through the system boundary by heat transfer (通过边界的热量熵流) B. the net entropy transfer into the system by mass flow (进入系统的净质量熵流) C. the entropy generation within the system boundaries as the result of irreversibility. (系统内部不可逆所导致的熵产)

For steady-flow system (对于稳态稳定流动系统） For single stream, adiabatic, steady flow （对于单股绝热的稳态稳定流动系统）

5.5 Significance of Entropy and its application (熵的意义及应用) 1. Heat absorption and heat rejection during a reversible process can be calculated by resorting to Entropy. (可逆过程中的吸热或放热量可借助熵来计算）

2. Entropy generation indicates the direction of process in isolated system. (熵产是孤立系统中过程进行方向的标志）

heat transfer across a finite temperature difference（温差传热） Free or unrestrained expansion（自由膨胀）

3. Entropy is a measurement of the amount of thermal energy which can not be converted to work. (熵是热量不可用能大小的量度） 4.Entropy Generation indicates the amount of loss in energy which can be converted to work. (熵产是做功能力损失的量度） T TH T0 s s1 s2

heat transfer across a finite temperature difference（温差传热） Friction Loss (摩擦损失） TH TH Q1 Q1 Wmax TL Q2 Q1 T0 W T Q2 TH TL T0 T0 s s1 s2 s3

Reading and Review (阅读和复习） 5.1 Introduction （简介）p.246~p.252 5.2 Statement of the Second Law of Thermodynamics （热力学第二定律的表述）P.253~P.265 5.3 Carnot cycle and Carnot Theorem （卡诺循环与卡诺定律）P.269~P281 5.4 Entropy, The increase principle of Entropy and Entropy Equation （熵、熵增原理及熵方程） 5.5 Significance of Entropy and its application (熵的意义及应用) p.302~359