华南理工大：物理化学(双语)03I

1、上一内容下一内容回主目录O返回2021-10-17不可能把热从低温物体传到高温物体，而不引起其它变化 物理化学电子教案第三章（上）上一内容下一内容回主目录O返回2021-10-17Chapter 3 The second law of thermodynamics3.1 Common feature of spontaneous change3.2 The second law of thermodynamics3.3 Carnot cycle and Carnot principle3.4 Definition of entropy3.5 Clausius inequality ; prin

2、ciple of increase of entropy 3.6 Calculate the change of entropy3.7 Statistical view of entropy上一内容下一内容回主目录O返回2021-10-17The second law of thermodynamics3.9 Direction of change and conditions in equilibrium3.10 Calculate of G3.11 Relations of thermodynamic functions3.12 Clapeyron equation 3.13 The th

3、ird law and conventional entropy3.8 Helmholtz function and Gibbs function上一内容下一内容回主目录O返回2021-10-173.1 Common featureSpontaneous change :Some things happen spontaneously, some things dont.Common feature irreversible A gas expands to fill the available volume; it does not spontaneously contract into s

4、omething smaller.A hot body cools to the temperature of its surroundings;it does not spontaneously get hotter at their expense.上一内容下一内容回主目录O返回2021-10-17Can the direction of the spontaneous change be related to some aspect of the distribution of energy?We shall see that this is so. Spontaneous change

5、s are always accompanied by a reduction in the quality of energy,in the sense that it is degraded into a more dispersed, chaotic form.Spontaneous, natural changes are simply manifestation of the natural tendency of the universe towards greater chaos.上一内容下一内容回主目录O返回2021-10-173.2 The Second Law of The

6、rmodynamicsClausius statement：“it is impossible for any device to operate in a cycle in such a manner that the sole effect is the transfer of heat from one body to another body at a higher temperature.”Kelvin-Planck statement：“no process is possible whose sole result is the absorption of heat from a

7、 reservoir and the conversion of this heat into work.” The second perpetual motion machine is no way!上一内容下一内容回主目录O返回2021-10-17The First Law led to the introduction of the internal energy, a property of state. The Second Law also leads to a property, the entropy. The First Law uses the internal energ

8、y to identify the permissible changes; the Second Law uses the entropy to identify the natural changes among these permissible changes. 上一内容下一内容回主目录O返回2021-10-17One way of introducing the entropy develops the view that the extent of the dispersal of energy can be calculated: this leads to the statis

9、tical definition of entropy.Another develops the view that the dispersal can be related to the amount of heat involved in a process: this leads to the thermodynamic definition.上一内容下一内容回主目录O返回2021-10-17 Carnot CycleOf particular interest is an idealized engine, known as the Carnot engine, which emplo

10、ys two heat reservoirs at different temperatures and operates on the following cycle.上一内容下一内容回主目录O返回2021-10-17Carnot cycleProcess 4: A reversible adiabatic compressionProcess 3: A reversible isothermal compression at T2Process 2: A reversible adiabatic expansion.Process 1: A reversible isothermal ex

11、pansion at Th上一内容下一内容回主目录O返回2021-10-17The efficiency of engine hchhQQWQQ) 0(cQ1hchch1TTTTTThe thermal efficiency of the cycle, defined as the ratio of the net work output to the heat input,is given by上一内容下一内容回主目录O返回2021-10-17No engine can be more efficient than a reversible engine operating between

12、the same temperature limits, and all reversible engines operating between the same temperature limits have the same efficiency.上一内容下一内容回主目录O返回2021-10-17Arrive at a conclusion from Carnot ChchchhhQQTTWQQThchc11TTQQhhccTQTQchch0QQTT or：For a reversible engine: the sum of the ratio of the heat to the t

13、emperature is equal to zero.Irrev.less than上一内容下一内容回主目录O返回2021-10-17任意可逆循环的热温商 用相同的方法把任意可逆循环分成许多首尾连接的小卡诺循环，前一个循环的等温可逆膨胀线就是下一个循环的绝热可逆压缩线，如图所示的虚线部分，这样两个过程的功恰好抵消。 从而使众多小卡诺循环的总效应与任意可逆循环的封闭曲线相当，所以任意可逆循环的热温商的加和等于零，或它的环程积分等于零。上一内容下一内容回主目录O返回2021-10-17任意可逆循环的热温商上一内容下一内容回主目录O返回2021-10-17A reversible cycle as

14、 represented by the continuous curve of Fig. It is possible to subdivide this cycle into a number of small Carnot cycles as indicated.As the number of Carnot cycles is increased, the zigzag curve can be made to approach the original cycle to any desired degree.02211TQTQ02211TQTQetc.上一内容下一内容回主目录O返回20

15、21-10-17.22112211TQTQTQTQ0TQIn the limit, upon replacement of the summation of finite terms by a cyclic integral, we obtain0TQrevwhere the subscript “rev” has been used to recall that the original cycle as well as the small Carnot cycles must all be reversible.上一内容下一内容回主目录O返回2021-10-17the integral o

16、f dQ/T when carried out over a reversible cycle is equal to zero.It follows that the differential dQrev/T is a perfect differential of a state function.This property, called entropy, is denoted by the symbol S.上一内容下一内容回主目录O返回2021-10-17the entropy.TQdSrevIntegrating along a reversible path between tw

17、o equlibrium states 1 and 2 gives 211212TQSSSrevSince entropy is a point function, it does not matter what particular reversible path is followed in the integration as long as it is reversible. 上一内容下一内容回主目录O返回2021-10-17Deduce entropy用一闭合曲线代表任意可逆循环。R()0QT12BARRAB()()0QQTT可分成两项的加和在曲线上任意取A，B两点，把循环分成AB和

18、BA两个可逆过程。根据任意可逆循环热温商的公式：上一内容下一内容回主目录O返回2021-10-17熵的引出 说明任意可逆过程的热温商的值决定于始终状态，而与可逆途径无关，这个热温商具有状态函数的性质。移项得： 12BBRRAA()()QQTT任意可逆过程上一内容下一内容回主目录O返回2021-10-17Clausiuss inequality 设温度相同的两个高、低温热源间有一个可逆机和一个不可逆机。hchchR1TTTTTIRR根据卡诺定理：0hhccTQTQiIRii()0QT推广为与多个热源接触的任意不可逆过程得：hchchIR1QQQQQ则：hlhlTTQQ11上一内容下一内容回主目录

19、O返回2021-10-17Clausius inequalityAIR,ABRBi()()0QQTTthenFor a cycle, if A B is a irreversible, B A is a rev.0revABirBATQTQ0revBAirBATQTQirBArevBATQTQ S = SB SA=上一内容下一内容回主目录O返回2021-10-17Clausius inequalityThese are Clausius inequality ，mathematic expression of thermodynamic second law.ABABi()0QSTdQSTd0

20、QSTWhere the sign of equality applies to a reversible process, and the sign of inequality applies to an irreversible process.上一内容下一内容回主目录O返回2021-10-17The principle of increase of entropy0Q d0S The entropy of an isolated system increases for irreversible processes and remains constant in the course o

21、f reversible processes. The entropy of an isolated system never decreases.For an isolated system上一内容下一内容回主目录O返回2021-10-17The implication of Clausius inequality using Clsusius inequality to determine the direction of spontaneous change .dQST“” applies to irreversible processes“=” applies to reversibl

22、e processes0disoS“” a spontaneous change takes place “=” is in an equilibrium state上一内容下一内容回主目录O返回2021-10-17For a big isolated system Sometimes take into account the system and surroundings which has relation with the system as a big isolated system.iso(0SSS 体系）环境）“” spontaneous “=” equilibrium上一内容下

23、一内容回主目录O返回2021-10-17P1V1T1 P2V2T2P2V2 T1TQdSrevrevrevWQWQdUPdVdUQrevTPdVdUdS212121TPdVTdUTPdVdUS2212,12lnlnlnVVnRTTnCVVnRSmv上一内容下一内容回主目录O返回2021-10-1712,12,1212,1212,lnlnlnlnlnlnVVnCPPnCSPPnRTTnCSVVnRTTnCSmPmVmPmV上一内容下一内容回主目录O返回2021-10-17Entropy change in isothermal processes(1) Isothermal change of

24、perfect gases)ln(12VVnRS )ln(21ppnR(2) Reversible phase transition 相变）相变）相变）(THSdTTCTdHTQdSmprev,(For solid and liquid)上一内容下一内容回主目录O返回2021-10-17a phase transition.Under the conditions of constant pressure the heat of a phase transition is its enthalpy of transition, H t.At the temperature of the tra

25、nsition,Tt the system is in equilibrium (for instance, at the boiling point liquid and vapour are in equibrium and the systems temperature is the same as its surroundings),and so heat is transferred reversibly from the surroundings.上一内容下一内容回主目录O返回2021-10-17等温过程的熵变例1：1mol理想气体在等温下：(1)可逆膨胀， (2)真空膨胀，体积增

26、加到10倍，分别求其熵变。解：（1）可逆膨胀maxR()WQSTT体系）12lnVVnR1ln1019.14 J KnR0（环境）（体系）（隔离）SSS（1）为可逆过程。上一内容下一内容回主目录O返回2021-10-17熵是状态函数，始终态相同，体系熵变也相同，所以：等温过程的熵变（2）真空膨胀119.14 J KS（体系） 但环境没有熵变，则：119.14 J K0SS （隔离）（体系）（2）为不可逆过程上一内容下一内容回主目录O返回2021-10-17等温过程的熵变例2：求下述过程熵变。已知H2O（l）的汽化热为-140.620 kJ mol22H O(1 mol,l,373.15 K)H

27、 O(1 mol,g,373.15 K)pp$R）（体系）TQSbmvapTH140.620 kJ mol373.15 K11108.9 J Kmol解:如果是不可逆相变，可以设计可逆相变求 值。S上一内容下一内容回主目录O返回2021-10-17等温过程的熵变例3：在273 K时，将一个 的盒子用隔板一分为二， 一边放 ，另一边放 。322.4 dm20.5 mol O (g)20.5 mol N (g)解法1：122ln)O(VVnRS2 .124 .22ln5 . 0 R222.4(N0.5 ln12.2SR)N()O(22mixSSS2ln2 .124 .22lnRR求抽去隔板后，两种

28、气体混合过程的熵变？上一内容下一内容回主目录O返回2021-10-17等温过程的熵变解法2：BBBmixlnxnRS2211(O )ln(N )ln22R nn 1ln2Rln2R上一内容下一内容回主目录O返回2021-10-17The change of entropy when a system is heated (1)物质的量一定的等容变温过程21dm,TTVTTnCS21dm,TTpTTnCS(2)物质的量一定的等压变温过程上一内容下一内容回主目录O返回2021-10-17变温过程的熵变(4)没有相变的两个恒温热源之间的热传导)()(21TSTSS)11(12TTQ*(5)没有相变的两个变温物体之间的热传导，首先要求出终态温度T212211)(CCTCTCT21SSS2211lnlnTTCTTC上一内容下一内容回主目录O返回2021-10-17Entropy change in chemical reactions(1)在标准压力下，298.1