第六章水和水蒸氣的性質(zhì)

1、 Chapter 6. The property of Water and Vapor (第第6章章. 水和水蒸氣的性質(zhì)水和水蒸氣的性質(zhì))6.1 Basic conceptions (基本概念基本概念)6.2 Phase change Process of Pure Substance (純質(zhì)的純質(zhì)的相變過(guò)程相變過(guò)程)6.3 Property Tables (水蒸氣性質(zhì)表水蒸氣性質(zhì)表) 6.4 h-s diagrams for Water Vapor (水蒸氣的水蒸氣的h-s圖圖)6.5 Thermodynamic Processes of Water Vapor (水蒸氣的熱力過(guò)程水蒸氣的熱

2、力過(guò)程)水和水蒸氣是實(shí)際氣體的代表水和水蒸氣是實(shí)際氣體的代表水蒸氣水蒸氣在空氣中含量極小，當(dāng)作在空氣中含量極小，當(dāng)作理想氣體理想氣體一般情況下，為一般情況下，為實(shí)際氣體實(shí)際氣體，使用圖表，使用圖表18世紀(jì)，蒸氣機(jī)的發(fā)明，是唯一工質(zhì)世紀(jì)，蒸氣機(jī)的發(fā)明，是唯一工質(zhì)直到內(nèi)燃機(jī)發(fā)明，才有燃?xì)夤べ|(zhì)直到內(nèi)燃機(jī)發(fā)明，才有燃?xì)夤べ|(zhì)目前仍是火力發(fā)電、核電、供暖、化工的工質(zhì)目前仍是火力發(fā)電、核電、供暖、化工的工質(zhì) 優(yōu)點(diǎn)優(yōu)點(diǎn): 便宜，易得，無(wú)毒，便宜，易得，無(wú)毒， 膨脹性能好，傳熱性能好膨脹性能好，傳熱性能好是其它實(shí)際氣體的代表是其它實(shí)際氣體的代表 6-1 純物質(zhì)的熱力學(xué)面及相圖純物質(zhì)的熱力學(xué)面及相圖物質(zhì)三種聚集狀

3、態(tài)：物質(zhì)三種聚集狀態(tài)： 固態(tài)、固態(tài)、 液態(tài)、液態(tài)、 氣態(tài)氣態(tài)水的三態(tài)：水的三態(tài)：冰、冰、 水、水、 蒸汽蒸汽Pure substance Solid Liquid Gas Ice Water Steam 任何一種物質(zhì)都可以經(jīng)歷下列所述的相變?nèi)魏我环N物質(zhì)都可以經(jīng)歷下列所述的相變. Any kind of substance may undergo various types of phase changes as following : 溶解溶解(Fusion/melting) = solid to liquid 凝固凝固(Freezing) = liquid to solid 氣化氣化(Vap

4、orization)= liquid to gas 凝結(jié)凝結(jié)(Condensation)= gas to liquid 升華升華(Sublimation) = solid to gas Phase changes (相變相變):純物質(zhì)的純物質(zhì)的p-T相圖相圖ppTT液液液液氣氣氣氣固固固固水水一般物質(zhì)一般物質(zhì)三相點(diǎn)三相點(diǎn)三相點(diǎn)三相點(diǎn)臨界點(diǎn)臨界點(diǎn)臨界點(diǎn)臨界點(diǎn)流體流體流體流體升華線升華線升華線升華線融解線融解線融解線融解線汽化線汽化線汽化線汽化線p-T diagram of pure substancespTLiquidVaporSolidTriple pointCritical pointFlu

5、idSublimationMeltingVaporizationThe sublimation line separates the solid and vapor regions;The vaporization line separates the liquid and vapor regions; it ends at the critical point.The melting line separates the solid and liquid regions;The three lines meet at the triple point.Triple point(三相點(diǎn)）：三相

6、點(diǎn)）：all three phases coexist in equilibrium. (三種相態(tài)以平衡共存三種相態(tài)以平衡共存)Critical point (臨界點(diǎn)臨界點(diǎn)): The point at which the saturated liquid and saturated vapor states are identical. No distinction can be made between liquid and vapor phases above the critical point. (臨界點(diǎn)就是氣相與液相一致的狀態(tài)點(diǎn)臨界點(diǎn)就是氣相與液相一致的狀態(tài)點(diǎn),溫度高于臨界溫度高于

7、臨界點(diǎn)之上點(diǎn)之上,氣相與液相沒有明顯的區(qū)別氣相與液相沒有明顯的區(qū)別) 臨界點(diǎn)臨界點(diǎn) Critical pointcoc3c22.129MPa647.30K (374.15 C)m0.00326kgpTv水的臨界點(diǎn)水的臨界點(diǎn)狀態(tài)狀態(tài)飽和液線與飽和氣線的交點(diǎn)飽和液線與飽和氣線的交點(diǎn)氣液兩相共存的氣液兩相共存的pmax,Tmax等溫線是鞍點(diǎn)等溫線是鞍點(diǎn)臨臨界界點(diǎn)點(diǎn) 思考題思考題3. 有沒有有沒有500C的水的水？1. 溜冰冰刀溜冰冰刀2. 北方冬天晾在外邊的衣服，北方冬天晾在外邊的衣服，是否經(jīng)過(guò)液相是否經(jīng)過(guò)液相4. 有沒有有沒有-3 的蒸汽的蒸汽？5. 一密閉容器內(nèi)有水的汽液混合物，對(duì)其一密閉容器內(nèi)

8、有水的汽液混合物，對(duì)其 加熱，是否一定能變成蒸汽？加熱，是否一定能變成蒸汽？復(fù)習(xí)：純物質(zhì)的復(fù)習(xí)：純物質(zhì)的p-T相圖相圖ppTT液液液液氣氣氣氣固固固固水水一般物質(zhì)一般物質(zhì)三相點(diǎn)三相點(diǎn)三相點(diǎn)三相點(diǎn)臨界點(diǎn)臨界點(diǎn)臨界點(diǎn)臨界點(diǎn)流體流體流體流體coc3c22.129MPa647.30K (374.15 C)m0.00326kgpTv飽和線、三相線和臨界點(diǎn)飽和線、三相線和臨界點(diǎn)pv飽和氣線三相線飽和液線飽和固線T臨界點(diǎn)Vapor and Liquid (汽相和液相汽相和液相)鍋鍋爐爐汽輪機(jī)汽輪機(jī)發(fā)電機(jī)發(fā)電機(jī)給水泵給水泵凝凝汽汽器器過(guò)熱器過(guò)熱器因固相不流動(dòng)，因固相不流動(dòng)，更關(guān)心汽液兩相更關(guān)心汽液兩相冰蓄冷冰

9、蓄冷6-2 汽化與飽和汽化與飽和氣化氣化(Vaporization): 由液態(tài)變成氣態(tài)的物理過(guò)程由液態(tài)變成氣態(tài)的物理過(guò)程 (不涉及化學(xué)變化不涉及化學(xué)變化)凝結(jié)凝結(jié)(Condensation)： 由氣態(tài)變成液態(tài)的物理過(guò)程由氣態(tài)變成液態(tài)的物理過(guò)程 6.2.1 6.2.1 汽化與凝結(jié)汽化與凝結(jié) The rate of condensation depends upon the density of vapor in the space above the liquid.(凝結(jié)的速率取決于液面上方氣相空間氣體分子的密度凝結(jié)的速率取決于液面上方氣相空間氣體分子的密度,即蒸氣壓力即蒸氣壓力)Liquid

10、molecule has to overcome the surface tension to become vapor, therefore vaporization consumes energy. ( 液相分子必須克服表面張力才能進(jìn)入氣相空間而氣化液相分子必須克服表面張力才能進(jìn)入氣相空間而氣化,因此氣化是要耗因此氣化是要耗能的能的)The rate of Vaporization depends on the liquid temperature.(氣化的速率取決于液相的溫度氣化的速率取決于液相的溫度)()(vcpfgw)(1Tgwv凝結(jié)）(on condensati cvww 氣化）(

11、zation vaporicvww 平衡狀態(tài)）( mequilibriu cvww The equilibrium is called Saturation State.(飽和狀態(tài)）飽和狀態(tài)） The properties at this state is called Saturation Properties. (飽和飽和參數(shù)）參數(shù)）sTsp6.2.2 飽和狀態(tài)飽和狀態(tài)Saturation state飽和狀態(tài)：汽化與凝結(jié)的動(dòng)態(tài)平衡飽和狀態(tài)：汽化與凝結(jié)的動(dòng)態(tài)平衡At the equilibrium state, the pressure corresponding to only one t

12、emperature. That is, .飽和溫度飽和溫度Ts飽和壓力飽和壓力ps一一對(duì)應(yīng)一一對(duì)應(yīng)放掉一些水，放掉一些水，Ts不變，不變， ps？TspsSaturation temperatureSaturation pressure)(Tfp ps=1.01325barTs=100 青藏青藏ps=0.6barTs=85.95 高壓鍋高壓鍋ps=1.6barTs=113.32 )(ssTfp 6.2.3 汽化汽化 Vaporization沸騰：沸騰：表面和液體內(nèi)部同時(shí)發(fā)生的汽化表面和液體內(nèi)部同時(shí)發(fā)生的汽化 It is an intensive vaporization phenomenon

13、 occurs in the liquid.( (氣體和液體均處在飽和狀態(tài)下氣體和液體均處在飽和狀態(tài)下) )汽化汽化: 由液態(tài)變成氣態(tài)的物理過(guò)程由液態(tài)變成氣態(tài)的物理過(guò)程 (不涉及化學(xué)變化不涉及化學(xué)變化) 蒸發(fā)：蒸發(fā)：汽液表面上的汽化汽液表面上的汽化 BoilEvaporationEvaporation occurs at any temperature and pressure.（蒸發(fā)可在任何溫度和壓力下發(fā)生）（蒸發(fā)可在任何溫度和壓力下發(fā)生） Evaporation rate depends on the free surface area, the temperature, the flow

14、 rate above,etc.（蒸發(fā)的速度與自由液面表面積，液體溫度，液面風(fēng)速等有關(guān)（蒸發(fā)的速度與自由液面表面積，液體溫度，液面風(fēng)速等有關(guān)Boiling can only occur as temperature reaches the saturation temperature corresponding to the specified pressure or the pressure drops below the saturation pressure corresponding to the specified temperature. （沸騰只能當(dāng)溫度達(dá)到給定壓力所對(duì)應(yīng)的飽和溫

15、度或壓力降到給定（沸騰只能當(dāng)溫度達(dá)到給定壓力所對(duì)應(yīng)的飽和溫度或壓力降到給定溫度所對(duì)應(yīng)的飽和壓力時(shí)溫度所對(duì)應(yīng)的飽和壓力時(shí),才能發(fā)生才能發(fā)生)6-3 水蒸氣的定壓發(fā)生過(guò)程水蒸氣的定壓發(fā)生過(guò)程t tsv vv = vv = vv v v未飽和水未飽和水飽和水飽和水 飽和濕蒸汽飽和濕蒸汽 飽和干蒸汽飽和干蒸汽 過(guò)熱蒸汽過(guò)熱蒸汽h hh = hh = hh h hs ss = ss = ss s s水預(yù)熱水預(yù)熱汽化汽化過(guò)熱過(guò)熱6.3.1 P=constant (壓力壓力 p 是定值是定值) Preheat Stage (預(yù)熱階段預(yù)熱階段)Compressed liquid to Saturated li

16、quid.(未飽和液體未飽和液體 飽和液體飽和液體)Compressed liquid/subcooled liquid is not about to vaporization.As heat added, t slightly . When It becomes Saturated liquid. The liquid is about to vaporize. It is the state at which it is still a liquid, but any heat addition will cause some of the liquid to vaporize.)(pf

17、ttsvvstt sttt過(guò)冷Vaporization Stage (氣化階段氣化階段)Saturated liquid to Saturated vapor (飽和液體飽和液體 飽和蒸氣飽和蒸氣)Saturated vapor is a vapor about to condense.A substance at state between Saturatedliquid and Saturated Vapor is calledSaturated liquid-vapor mixture/wetvapor. Latent heat of Vaporization (氣化潛熱氣化潛熱):Th

18、e amount of energy absorbed during vaporizationvvstt Superheat Stage (過(guò)熱階段過(guò)熱階段)Superheated vapor is the vapor that is not about to condense. stt vtsttt 過(guò)熱注意：水蒸氣定壓發(fā)生過(guò)程說(shuō)明注意：水蒸氣定壓發(fā)生過(guò)程說(shuō)明(1)()QUWUpdVUp VUpVH (2)fg0SSS (3) 理想氣體理想氣體( )hf T實(shí)際氣體汽化時(shí)，實(shí)際氣體汽化時(shí)，TTs不變，但不變，但h增加增加hh汽化潛熱汽化潛熱(4) 未飽和水未飽和水過(guò)冷度過(guò)冷度sttt過(guò)冷過(guò)冷

19、水過(guò)冷水過(guò)熱蒸汽過(guò)熱蒸汽過(guò)熱度過(guò)熱度sttt過(guò)熱只有熵加熱時(shí)永遠(yuǎn)增加只有熵加熱時(shí)永遠(yuǎn)增加State of Liquid and vapor未飽和液，過(guò)冷液未飽和液，過(guò)冷液飽和液飽和液飽和濕蒸氣飽和濕蒸氣飽和蒸氣飽和蒸氣過(guò)熱蒸氣過(guò)熱蒸氣Saturated liquidSaturated vaporSaturated liquid-vapor mixtureSuperheated vaporCompressed liquidSubcooled liquid汽化潛熱汽化潛熱Latent heat of Vaporization壓縮液壓縮液 6.3.2 定壓氣化過(guò)程的定壓氣化過(guò)程的P-v P-v 圖和

20、圖和T-s T-s 圖圖 P-v and T-s diagramscpcTcTABCACBcTTcTT cppcpp3a3b3d3e3c3a3b3d3e3c2c2a2b2d2e2c2a2b2d2e1c1a1b1d1e1c1a1b1d1eTsp-v圖，圖，T-s圖上的水蒸氣定壓加熱過(guò)程圖上的水蒸氣定壓加熱過(guò)程pvcp一點(diǎn)，二線，三區(qū)，五態(tài)一點(diǎn)，二線，三區(qū)，五態(tài)Saturated liquid line, SLL is formed by connecting a series of boiling points. saturated vapor line, SVL：Connecting a se

21、ries of points at dry saturated vapor builds a line, known as saturated vapor line, SVL. Vaporization continues by further heat supply to the system until no liquid is left. This state is known as dry saturated vapor, e.g. point d. If the system is slightly cooled at this state, then droplets of liq

22、uid will begin to form. The state of substance between saturated liquid and dry vapor is called wet vapor. Further heating of a dry saturated vapor at constant pressure causes a rise of vapor temperature and it becomes superheated vapor. The state of substance is completely defined by its pressure a

23、nd temperature if it is in liquid or superheated vapor phase.vOne point (一點(diǎn)一點(diǎn)):critical point (臨界點(diǎn)臨界點(diǎn))Two lines (兩線兩線):SLL and SVL (飽和液體線和飽和蒸氣線飽和液體線和飽和蒸氣線)Three regions(三區(qū)三區(qū)): Subcooled liquid region (未飽和液體區(qū)未飽和液體區(qū)) Saturated liquid-vapor mixture region(濕蒸氣區(qū)濕蒸氣區(qū)) Superheated vapor region (過(guò)熱蒸氣區(qū)過(guò)熱蒸氣區(qū))

24、Five states(五態(tài)五態(tài)): Subcooled liquid(未飽和液體未飽和液體) Saturated liquid (飽和液體飽和液體) Saturated liquid-vapor mixture (濕蒸氣濕蒸氣) Saturated vapor (干飽和蒸氣干飽和蒸氣) Superheated vapor (過(guò)熱蒸氣過(guò)熱蒸氣) 6.4.1 Types of Property Tables (水蒸汽表的分類水蒸汽表的分類) 1. Saturated water Tables (飽和水和飽和蒸汽表飽和水和飽和蒸汽表) Saturated water-T Tables(以溫度以溫度

25、t為獨(dú)立變量排列為獨(dú)立變量排列) Saturated water-p Tables(以壓力以壓力p為獨(dú)立變量排列為獨(dú)立變量排列) 2. Subcooled water and Superheated vapor Table (未飽未飽和水和過(guò)熱水蒸汽表和水和過(guò)熱水蒸汽表) P and t are dependent variables (以以p和和t為自變量為自變量) 2、Reference State and Reference Values (基準(zhǔn)點(diǎn)的規(guī)定基準(zhǔn)點(diǎn)的規(guī)定) For water, the saturated liquid at 0.01 is taken as referenc

26、e state. (取水的三相點(diǎn)，即取水的三相點(diǎn)，即0.01 oC為基準(zhǔn)點(diǎn)，規(guī)定在為基準(zhǔn)點(diǎn)，規(guī)定在此溫度下液態(tài)水的熱力學(xué)能和熵為零。此溫度下液態(tài)水的熱力學(xué)能和熵為零。) The internal energy and entropy are assigned zero at this state.kgkJu/ 00)/( 00KkgkJs3. Properties of Saturated liquid-vapor mixture at Pressure p (壓力為壓力為p的濕飽和蒸汽的濕飽和蒸汽) The state of wet vapor can not be defined by j

27、ust pressure and temperature until one other property is given. The condition or quality of wet vapor is often defined by its dryness or wetness fraction. 定義干度定義干度x才可以確定濕蒸汽的狀態(tài)。才可以確定濕蒸汽的狀態(tài)。 We define dryness as dryness fractiondryness fraction, x = the mass of dry vapor in 1 kg of the mixture, , x =

28、the mass of dry vapor in 1 kg of the mixture, wetness fractionwetness fraction, 1 - x = the mass of liquid in 1 kg of the mixture. , 1 - x = the mass of liquid in 1 kg of the mixture. mmxvvxvxvx )1 (hxhxhx )1 (sxsxsx )1 ( vxvxvx )1 (hxhxhx )1 (sxsxsx )1 (注意注意:飽和表的起始點(diǎn)飽和表的起始點(diǎn)ptsv(m3/kg)vsskJ/(kg.K)0.0

29、061120.01 0.00100022 206.1750.09.15621.099.63 0.00104341.6946 1.3027 7.36085.0151.85 0.00109280.374811.8604 6.821550.0263.92 0.00128580.03941 2.9209 5.9712221.29374.15 0.003260.00326 4.4294.429(bar)()bdbd4. Exercise. Consulting property tables of water vapor to determine the state of each point and

30、their h，s，x.(利用水蒸氣表判斷下列各點(diǎn)的狀態(tài)，并確利用水蒸氣表判斷下列各點(diǎn)的狀態(tài)，并確定其定其h，s，x的值。的值。) o （1）由飽和水和飽和蒸汽表查得p=2MPa時(shí)， 顯然 ，可知該狀態(tài)為過(guò)熱蒸汽過(guò)熱蒸汽。 查未飽和水過(guò)熱蒸汽表，得p=2MPa，t=300 時(shí) o （2） 查飽和表得查飽和表得p=9MPa時(shí)時(shí) 可見可見 ， 該狀態(tài)為該狀態(tài)為濕蒸汽濕蒸汽，其干度為，其干度為 又查飽和表得又查飽和表得=2489.0kJ/kg按濕蒸汽的參數(shù)計(jì)算式得按濕蒸汽的參數(shù)計(jì)算式得 ( 3 ) 顯然，該狀態(tài)為濕蒸汽狀態(tài)。由已知參數(shù)查飽和水和飽和顯然，該狀態(tài)為濕蒸汽狀態(tài)。由已知參數(shù)查飽和水和飽和蒸

31、汽表得蒸汽表得 按濕蒸汽的參數(shù)計(jì)算公式得按濕蒸汽的參數(shù)計(jì)算公式得 （4）由飽和水和飽和蒸汽表查得）由飽和水和飽和蒸汽表查得:當(dāng)當(dāng)p=1.0MPa時(shí)，時(shí)，ts=179.9，顯然顯然tts，所以該狀態(tài)為，所以該狀態(tài)為未飽和水未飽和水。通常通常t=175的狀態(tài)參數(shù)可利用的狀態(tài)參數(shù)可利用t=170與與t=180的對(duì)應(yīng)狀態(tài)的對(duì)應(yīng)狀態(tài)參數(shù)內(nèi)插得到，參數(shù)內(nèi)插得到，但此處但此處t=170與與t=180跨越了未飽和表中的黑粗線，跨越了未飽和表中的黑粗線，說(shuō)明它們分別處于不同相區(qū)。說(shuō)明它們分別處于不同相區(qū)。應(yīng)使內(nèi)插在未飽和水區(qū)內(nèi)進(jìn)行，選取離最接近的應(yīng)使內(nèi)插在未飽和水區(qū)內(nèi)進(jìn)行，選取離最接近的t=170與與ts=17

32、9.9的未飽和水參數(shù)內(nèi)插。的未飽和水參數(shù)內(nèi)插。查未飽和水和過(guò)熱蒸汽表得查未飽和水和過(guò)熱蒸汽表得p=1.0MPa，t=170時(shí) p=1.0MPa，t=179.9時(shí) 于是t=175時(shí) 對(duì)于未飽和水干度對(duì)于未飽和水干度x無(wú)意義。無(wú)意義。 （5） 時(shí)，飽和蒸汽比體積時(shí)，飽和蒸汽比體積 ， 該狀態(tài)該狀態(tài)為為過(guò)熱蒸汽過(guò)熱蒸汽。查過(guò)熱蒸汽表得。查過(guò)熱蒸汽表得 t=260時(shí)，時(shí)， , t=270時(shí)，時(shí)， 該狀態(tài)的溫度可由比體積值求得該狀態(tài)的溫度可由比體積值求得 o 討論討論應(yīng)該注意，在利用未飽和水與過(guò)熱蒸汽作應(yīng)該注意，在利用未飽和水與過(guò)熱蒸汽作內(nèi)插時(shí)，不允許跨越表中的粗折線，如遇內(nèi)插時(shí)，不允許跨越表中的粗折線

33、，如遇這種情況，應(yīng)選用更詳細(xì)的表，或使內(nèi)插這種情況，應(yīng)選用更詳細(xì)的表，或使內(nèi)插計(jì)算在未飽和水（或過(guò)熱蒸汽）區(qū)內(nèi)進(jìn)行。計(jì)算在未飽和水（或過(guò)熱蒸汽）區(qū)內(nèi)進(jìn)行。 6.5 h-s diagram of water vapor (水蒸汽的水蒸汽的h-s圖圖)1.SLL and SVL (界限曲線，界限曲線，x=0、x=1兩條曲線兩條曲線)2. Constant Pressure Line and Constant Temperature Line (定壓線和定溫線定壓線和定溫線)In Saturated liquid-vapor region, constant pressure line and co

34、nstant temperature line are identical. ( 在濕蒸汽區(qū)定壓線與定溫線重合。在濕蒸汽區(qū)定壓線與定溫線重合。)3. Constant Volume Line（定容線。（定容線。)4. Constant Dryness Line (定干度線。定干度線。) Given Two Properties, all the other state properties can be determined from the Diagram.(給定兩個(gè)參數(shù)，即可查出其余全部參數(shù))。 Priorities (優(yōu)點(diǎn)優(yōu)點(diǎn))：Fast and convenient. 方便、快速。方便

35、、快速。Drawbacks (缺點(diǎn)缺點(diǎn))：Not so accurate as Property tables 精確性稍差精確性稍差。 s (kJ/kg*K)h (kJ/kg)6.6.1 Characteristics of water vapor (水蒸汽的特點(diǎn)水蒸汽的特點(diǎn))1. Water vapor can not be treated as ideal gas (水蒸汽不水蒸汽不是理想氣體是理想氣體) pv=RT is not suitable. （理想氣體狀態(tài)方程不適用。）（理想氣體狀態(tài)方程不適用。）2. Analysis and Calculation on Water vapor

36、 can be solved by using Tables and Diagrams ( 水蒸汽的分析和水蒸汽的分析和計(jì)算采用水蒸汽圖和表。計(jì)算采用水蒸汽圖和表。)3. The First and the Second Laws must be obeyed during processes of water vapor (熱力學(xué)第一定律和第二熱力學(xué)第一定律和第二定律成立定律成立)6.6 Thermodynamic Processes of Water Vapor (水蒸氣的熱力過(guò)程水蒸氣的熱力過(guò)程)wuqpvuh For reversible processes, (對(duì)于可逆過(guò)程：對(duì)于可逆

37、過(guò)程：)21pdvw21Tdsqwzgchq2216.6.2 Procedures (步驟步驟)(1) Based on the given conditions, determine the initial state and its properties .(根據(jù)已知條件，確定初始狀態(tài)，查出其余參數(shù)。根據(jù)已知條件，確定初始狀態(tài)，查出其余參數(shù)。)(2) Based on the characteristics of the process and one of the properties of the final state, determine the final state and its properties. ( 根據(jù)過(guò)程特點(diǎn)和一個(gè)終態(tài)參數(shù)，確定終態(tài)，再查出其余終態(tài)參數(shù)。根據(jù)過(guò)程特點(diǎn)和一個(gè)終態(tài)參數(shù)，確定終態(tài)，再查出其余終態(tài)參數(shù)。)(3) Based on the initial and final state, ca