華南理工大：物理化學(xué)(雙語(yǔ))03I

1、上一內(nèi)容下一內(nèi)容回主目錄O返回2021-10-17不可能把熱從低溫物體傳到高溫物體，而不引起其它變化 物理化學(xué)電子教案第三章（上）上一內(nèi)容下一內(nèi)容回主目錄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上一內(nèi)容下一內(nèi)容回主目錄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上一內(nèi)容下一內(nèi)容回主目錄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.上一內(nèi)容下一內(nèi)容回主目錄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.上一內(nèi)容下一內(nèi)容回主目錄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!上一內(nèi)容下一內(nèi)容回主目錄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. 上一內(nèi)容下一內(nèi)容回主目錄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.上一內(nèi)容下一內(nèi)容回主目錄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.上一內(nèi)容下一內(nèi)容回主目錄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上一內(nèi)容下一內(nèi)容回主目錄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上一內(nèi)容下一內(nèi)容回主目錄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.上一內(nèi)容下一內(nèi)容回主目錄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上一內(nèi)容下一內(nèi)容回主目錄O返回2021-10-17任意可逆循環(huán)的熱溫商 用相同的方法把任意可逆循環(huán)分成許多首尾連接的小卡諾循環(huán)，前一個(gè)循環(huán)的等溫可逆膨脹線就是下一個(gè)循環(huán)的絕熱可逆壓縮線，如圖所示的虛線部分，這樣兩個(gè)過(guò)程的功恰好抵消。 從而使眾多小卡諾循環(huán)的總效應(yīng)與任意可逆循環(huán)的封閉曲線相當(dāng)，所以任意可逆循環(huán)的熱溫商的加和等于零，或它的環(huán)程積分等于零。上一內(nèi)容下一內(nèi)容回主目錄O返回2021-10-17任意可逆循環(huán)的熱溫商上一內(nèi)容下一內(nèi)容回主目錄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.上一內(nèi)容下一內(nèi)容回主目錄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.上一內(nèi)容下一內(nèi)容回主目錄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.上一內(nèi)容下一內(nèi)容回主目錄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. 上一內(nèi)容下一內(nèi)容回主目錄O返回2021-10-17Deduce entropy用一閉合曲線代表任意可逆循環(huán)。R()0QT12BARRAB()()0QQTT可分成兩項(xiàng)的加和在曲線上任意取A，B兩點(diǎn)，把循環(huán)分成AB和

18、BA兩個(gè)可逆過(guò)程。根據(jù)任意可逆循環(huán)熱溫商的公式：上一內(nèi)容下一內(nèi)容回主目錄O返回2021-10-17熵的引出 說(shuō)明任意可逆過(guò)程的熱溫商的值決定于始終狀態(tài)，而與可逆途徑無(wú)關(guān)，這個(gè)熱溫商具有狀態(tài)函數(shù)的性質(zhì)。移項(xiàng)得： 12BBRRAA()()QQTT任意可逆過(guò)程上一內(nèi)容下一內(nèi)容回主目錄O返回2021-10-17Clausiuss inequality 設(shè)溫度相同的兩個(gè)高、低溫?zé)嵩撮g有一個(gè)可逆機(jī)和一個(gè)不可逆機(jī)。hchchR1TTTTTIRR根據(jù)卡諾定理：0hhccTQTQiIRii()0QT推廣為與多個(gè)熱源接觸的任意不可逆過(guò)程得：hchchIR1QQQQQ則：hlhlTTQQ11上一內(nèi)容下一內(nèi)容回主目錄

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=上一內(nèi)容下一內(nèi)容回主目錄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.上一內(nèi)容下一內(nèi)容回主目錄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上一內(nèi)容下一內(nèi)容回主目錄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上一內(nèi)容下一內(nèi)容回主目錄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 體系）環(huán)境）“” spontaneous “=” equilibrium上一內(nèi)容下

23、一內(nèi)容回主目錄O返回2021-10-17P1V1T1 P2V2T2P2V2 T1TQdSrevrevrevWQWQdUPdVdUQrevTPdVdUdS212121TPdVTdUTPdVdUS2212,12lnlnlnVVnRTTnCVVnRSmv上一內(nèi)容下一內(nèi)容回主目錄O返回2021-10-1712,12,1212,1212,lnlnlnlnlnlnVVnCPPnCSPPnRTTnCSVVnRTTnCSmPmVmPmV上一內(nèi)容下一內(nèi)容回主目錄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 相變）相變）相變）(THSdTTCTdHTQdSmprev,(For solid and liquid)上一內(nèi)容下一內(nèi)容回主目錄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.上一內(nèi)容下一內(nèi)容回主目錄O返回2021-10-17等溫過(guò)程的熵變例1：1mol理想氣體在等溫下：(1)可逆膨脹， (2)真空膨脹，體積增

26、加到10倍，分別求其熵變。解：（1）可逆膨脹maxR()WQSTT體系）12lnVVnR1ln1019.14 J KnR0（環(huán)境）（體系）（隔離）SSS（1）為可逆過(guò)程。上一內(nèi)容下一內(nèi)容回主目錄O返回2021-10-17熵是狀態(tài)函數(shù)，始終態(tài)相同，體系熵變也相同，所以：等溫過(guò)程的熵變（2）真空膨脹119.14 J KS（體系） 但環(huán)境沒(méi)有熵變，則：119.14 J K0SS （隔離）（體系）（2）為不可逆過(guò)程上一內(nèi)容下一內(nèi)容回主目錄O返回2021-10-17等溫過(guò)程的熵變例2：求下述過(guò)程熵變。已知H2O（l）的汽化熱為-140.620 kJ mol22H O(1 mol,l,373.15 K)H

27、 O(1 mol,g,373.15 K)pp$R）（體系）TQSbmvapTH140.620 kJ mol373.15 K11108.9 J Kmol解:如果是不可逆相變，可以設(shè)計(jì)可逆相變求 值。S上一內(nèi)容下一內(nèi)容回主目錄O返回2021-10-17等溫過(guò)程的熵變例3：在273 K時(shí)，將一個(gè) 的盒子用隔板一分為二， 一邊放 ，另一邊放 。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，兩種

28、氣體混合過(guò)程的熵變？上一內(nèi)容下一內(nèi)容回主目錄O返回2021-10-17等溫過(guò)程的熵變解法2：BBBmixlnxnRS2211(O )ln(N )ln22R nn 1ln2Rln2R上一內(nèi)容下一內(nèi)容回主目錄O返回2021-10-17The change of entropy when a system is heated (1)物質(zhì)的量一定的等容變溫過(guò)程21dm,TTVTTnCS21dm,TTpTTnCS(2)物質(zhì)的量一定的等壓變溫過(guò)程上一內(nèi)容下一內(nèi)容回主目錄O返回2021-10-17變溫過(guò)程的熵變(4)沒(méi)有相變的兩個(gè)恒溫?zé)嵩粗g的熱傳導(dǎo))()(21TSTSS)11(12TTQ*(5)沒(méi)有相變的兩個(gè)變溫物體之間的熱傳導(dǎo)，首先要求出終態(tài)溫度T212211)(CCTCTCT21SSS2211lnlnTTCTTC上一內(nèi)容下一內(nèi)容回主目錄O返回2021-10-17Entropy change in chemical reactions(1)在標(biāo)準(zhǔn)壓力下，298.1