第三章習(xí)題解答

1、1第三章純流體的熱力學(xué)性質(zhì)計算思考題3-1氣體熱容，熱力學(xué)能和粉與哪些因素有關(guān)？由熱力學(xué)能和溫度兩個狀態(tài)參數(shù)能否確定氣體的狀態(tài)？答：氣體熱容，熱力學(xué)能和粉與溫度壓力有關(guān)，由熱力學(xué)能和溫度兩個狀態(tài)參數(shù)能夠確定氣體的狀態(tài)。3-2理想氣體的內(nèi)能的基準點是以壓力還是溫度或是兩者同時為基準規(guī)定的?答：理想氣體的內(nèi)能的基準點是以溫度為基準規(guī)定的。3-3理想氣體熱容差cvR是否也適用于理想氣體混合物?pv答：理想氣體熱容差CpcR不適用于理想氣體混合物，因為混合物的組成對此有關(guān)。3-4熱力學(xué)基本關(guān)系式dHTdSVdp是否只適用于可逆過程？答：否。熱力學(xué)基本關(guān)系式dHTdSVdp不受過程是否可逆的限制3-5有

2、人說：曲于剩余函數(shù)是兩個等溫狀態(tài)的性質(zhì)之差，故不能用剩余函數(shù)來計算性質(zhì)隨著溫度的變化”，這種說法是否正確？答：不正確。剩余函數(shù)是針對于狀態(tài)點而言的；性質(zhì)變化是指一個過程的變化，對應(yīng)有兩個狀態(tài)。3-6水蒸氣定溫過程中，熱力學(xué)內(nèi)能和粉的變化是否為零？答：不是。只有理想氣體在定溫過程中的熱力學(xué)內(nèi)能和粉的變化為零。3-7用不同來源的某純物質(zhì)的蒸氣表或圖查得的粉值或痼值有時相差很多， 為什么？能否交叉使用這些圖表求解蒸氣的熱力過程？答：因為做表或圖時選擇的基準可能不一樣，所以用不同來源的某純物質(zhì)的蒸氣表或圖查得的粉值或痼值有時相差很多。不能夠交叉使用這些圖表求解蒸氣的熱力過程。3-8氨蒸氣在進入絕熱透平

3、機前，壓力為2.0MPa,溫度為150C,今要求絕熱透平膨脹機出口液氨不得大于5%,某人提出只要控制出口壓力就可以了。你認為這意見對嗎？為什么？請畫出T-S圖示意說明。答：可以。因為出口狀態(tài)是濕蒸汽，確定了出口的壓力或溫度，其狀態(tài)點也就確定了。3-9很純的液態(tài)水，在大氣壓力下，可以過冷到比0C低得多的溫度。假設(shè)1kg已被冷至-5C的液體。現(xiàn)在，把一很小的冰晶（質(zhì)量可以忽略）投入此過冷液體內(nèi)作為晶種。如果其后2答：壓力增高，又是絕熱過程，所以是一個壓縮過程（痼增加，若為可逆過程則是等痼過程），故系統(tǒng)的終態(tài)仍是過冷液體。此過程不可逆。3-10A和B兩個容器，A容器充滿飽和液態(tài)水，B容器充滿飽和蒸氣

4、。二個容器的容積均為1000cm3,壓力都為1MPa。如果這兩個容器爆炸，試問哪一個容器被破壞得更嚴重？答：A容器被破壞得更嚴重。因為在壓力、體積相同的情況下，飽和液態(tài)水的總熱力學(xué)能遠遠大于飽和蒸氣。二、計算題：5在1.013105Pa下絕熱地發(fā)生變化，試問:（1）系統(tǒng)的終態(tài)怎樣？（2）過程是否可逆?3-1試推導(dǎo)方程VP式中T,V為獨立變量。3證明：dUTdSpdV由maxwell關(guān)系知:3-2證明狀態(tài)方程P(Vb)RT表達的流體:(1)（2）證明：（1）Cp與壓力無關(guān)；在等粉變化過程中，溫度是隨壓力的下降而上升。P(Vb)RTVbPRT又dHCpdTVT-pdP=RTPTRPCPPTCP與壓

5、力無關(guān)(2)dH04_-1-1Cp1.18890.00381TJgKp/0.1013,MPa104060100140160180200V/cm3mol7388.0279.2245.2219.2198.61VVTp1.0161.0161.0881.1351.1711.1821.1911.176解：設(shè)計過程如下:3-3解:3-4dHCdTVpCpdT亦即故：_TpRT某類氣體的狀態(tài)方程式為RT可得:RTHRRT同理SRT4dppTRpdp0QCp0在等粉變化過程中，溫度是隨壓力的下降而上升。P（Vb）dpTRdpdppRdp0p應(yīng)用圖解微分積分法計算由SRT2=473.2

6、K時31mol甲烷的粉變。試推導(dǎo)這類氣體計算的HR和V的表達式。P0bdpbpp1=0.1013已知甲烷的MPa,Ti=273.2K壓縮到p2=20.265MPa,p-V-T數(shù)據(jù)及低壓下熱容與溫度關(guān)聯(lián)式為51理想氣體的粉變T2ididdHCdTpT1473.15473.15HidC；ddTp273.15273.151.1889473.15237.78284.342473.15K,20.265MPa下.Rp_V._1.HVTdp10398Jmol325Jg0TpHHidHR522.12325197.12Jg13-5使用合適的普遍化關(guān)聯(lián)式計算1kmol的丁二烯-1,3從127C,2.53MPa壓縮

7、至277C,12.67MPa時的AH,S,2V,赤。已知丁二烯-1,3在理想狀態(tài)時的恒壓摩爾熱容為：一3_6_2一一一一-1一一-1Cp22.738222.79810T73.87910TkJkmolK理想氣體273.15K真實氣體473.15K0.1013MPaH20.265MPa理想氣體473.15K20.265MPa1.18890.00381TdT122273.150.00381473.152273.1522522.12Jg-16解：設(shè)計過程如下：HT07查表知，Tc=425K,Pc=4.327MPa,co=0.195Tr竺史0.94p箜425r4.327查圖2-14知用普遍化維利系數(shù)法計

8、算。業(yè)B0B10.3830.1950.08403994RTC乙取1四1衛(wèi)B0B1RTRTTr0.58510.3830.1950.0840.75140.94-4.8013H,AS,H,AS,U,AVU,AV真實氣體277C(1)127C,2.53MPa下真實氣體轉(zhuǎn)變成理想氣體B=0.0830422詈=0.383B1=0.1390.1720.084ZRT0.75148.314400.152.53106_一43.-19.881310mmoldB00.675dTr0.793dB10.772dTr0.996HIRRTdBB0dB1B1dTrTrdTrTr0.826HR0.826RT0.8268.314_

9、-1400.152748.22kJkmoldBPdTdB1dTr1.0414-0.57755R1.04148.3148.658kJkmol-1k-1Pr0.585HT08(2)理想氣體恒溫加壓9(3)10618.3STRln12.6713.39kJkmol-1K-12.53理想氣體恒溫升溫HPT2CpdTT122.738550.15400.15222.796103550.152400.1521-73.879316788kJ106kmol-1300Sp273.15T73.879106550.153400.15322.738_2550.15理想氣體轉(zhuǎn)變?yōu)檎媸菤怏w550.15/仁1.3425用普遍化

10、壓縮因子法計算,查圖可知Z0ZRT(H2R)RTcH；550.15ln400.15222.7963-10550.15400.15一_2400.1535.3929.4778kJ-1-1kmolKPr12.674.3272.912Z00.64R0(H)RT；R0(SR)_1_Z0.640.1952.11.21.421.428.314550.1512.671065.126Z10.2R0(HR)(HR)RTcRTc2.1981.20.195(0.45)1.2882.1988.314425(HR)RTc(SR)0.6721040.50.45mol-12.8827766.5kJkmol-1SR1.2888

11、.31410.708kJkmol-1K-1VV2Vf15.1299.88131044.7553nfmol1-6.999H=HRH；dH：(H；)11769.7kJkmol-1S=SRididSTSp(SR)-1-114.0378kJkmolKUH(pV)11769.7_6_一_4一一(12.67105.126102.531069.881310_.-17775.03kJkmol4)103-6計算氨的熱力學(xué)性質(zhì)時，通常把0C飽和液氨的粉規(guī)定為418.6kJkg-1,此時的飽和蒸氣壓為0.43MPa,汽化熱為21432kJkmol-1，飽和液氨的痼為4.186kJkg-1K-1,試由此基準態(tài)數(shù)據(jù)求：

12、(1) 1.013MPa,300K氣氨的粉和痼；(2) 30.4MPa,500K氣氨的粉和痼。解：(1)設(shè)計過程如下：273K,0.43MPa下液氨汽化2273K,0.43MPa下真實氣體轉(zhuǎn)變成理想氣體查表知，Tc=405.6K,Pc=11.28MPa,co=0.250查圖知用普遍化維利系數(shù)法計算。0.675T-2.6TrB=0.0830.422L.712B1=0.1390.172T421r0.769dB1RH1PTr0dBdTr0B_Tr1dBdTr1旦TrS1RdB0dB1Pr0.126RdTrdTr故H1R0.119RTC0.1198.314405.6sR0.126R0.1268.314

13、1.048273K,0.43MPa下理想氣體變化為300K查表已知CidCP27.31 0.02383T1.707105T5.66dTr0.119401.287-1kJkmol21.185108T30.772T-5.2Tr-1kJkmol-1k,1.013MPa的理想氣體1273.15K0.43MPa飽和液氨9P-273.15K0.43MPa氣氨r273.15K0.43MPa理想氣氨一HV21432kJkmolSV78.462kJkmol-1K-1亍273.15-Tr0.6730.43Pr11.280.0381dBdTr1.89300K1.013MPa理想氣氨300K1.013MPa11412

14、idHPT2一idT1CPdT27.31300273.151.7071053003273.153122-0.023833002273.15221-1.1854_84_410300273.15kJSPd961.585id300CpdT273.15Tkmol-1Rln101327.310.43.300ln273.150.02383300273.151.7071058.31421.013ln0.432_2300273.151.185108-3003273.1533300K,Tr.-13.766kJkmolK-11.013MPa的理想氣體變化為300K,1.013MPa的真實氣體3000.740405

15、.6Pr1.01311.280.0898查圖知用普遍化維利系數(shù)法計算。B00.0830.422-r1.6Tr0.60.1390.172T4.2Tr0.47dB0dTr0.6751r0.6750.742.61.477dB0.722dTr0.7220.745.23.456H2RRTCPrL0.898B、/dB1B1、)()TrdTrTr1.4770.60.2513.4560.470.740.74dB0(dL0.740.219SRPrdB0dB1dTrdTr0.898(1.4770.253.456)0.210HRS2R0.2190.210又因HO8.3148.314418.6S0=4.186H=HO

16、(405.61.746738.5kJkmol-1-1-1kJkmolK177116.2kJkmol-117=71.162H）時S=S)(SR)(M)kJSVkmol-1K-1HVidSHid28370kJkmol-1143.1kJkmol-1K-1同理可求出30.4MPa,500K氣氨的粉和痼。過程和的結(jié)果與上述相同過程的粉變和痼變?yōu)?500HP273./127.31500273.150.02383-250022731531.1851083-13080.56kJkmol11.7071051445004273.15441314spdid500CdT273.15Tr,P2

17、,500Rln227.31ln0.02383300273.15pi273.151.7078.314105230.4ln0.432_2500273.151.18511.578 kJkmol-1-1K過程的粉變和痼變計算如下為:500Tr1.23405.6Pr30.411.28查圖用普遍化壓縮因子法。查圖可知R0(HR)RTc2.9(HR)RTc1.1H；SR故H=HO(1082.7_R0(SR)R(H2R)RTcS2R節(jié)1.7(SR)R1.213_3500273.153R0(H)RTT(HR)RTc3.1751.70.253.7158.31428.314RRHI)(H2)S=SO(SIR)(SR

18、)405.616.628HVSVSid(1.2)110706.6kJkmol11kJkmol1K1Hid21323122.466kJ3-7求丁烯-1在477.4K和6.89MPa的條件下的V,U,273K時的H,S為零。已知：TC420Kpc4.02MPa理想氣體狀態(tài)時解:kJkmol-1kmol-1K-1H,S。設(shè)飽和液態(tài)的丁烯-1在=0.187Tb=267K-362-1-1Cp16.363263.08210T82.11710TkJkmolKTr1四1.14420用普遍化壓縮因子法查圖得:0zzV竺pp16.891.714.021,z0.4770.1870.5028.314477.40.13

19、60.502289cm3mol-16.89查得T=273.15K時，ps1.27105pa273.15K0.127MPa飽和液一273.15K0.127MPa飽和氣273.15K0.127MPa理想氣477.4K6.89MPa理想氣體-477.4K6.89MPa真實氣體273.15K飽和液體丁烯-1的汽化1516查得HV21754kJkmol-1&衛(wèi)21735479.68kJkmol1K1T273273.15K,0.127MPa的真實氣體轉(zhuǎn)變?yōu)?73.15K,0.127MPa的理想氣體用普遍化壓縮因子法:HRRL0.03160.65(0.060.756)0.187(16.730.904

20、)0.0872R01色R(也咀)RrdTrdTr0.0316(2.060.1876.73)0.1049H1R0.0872RTc0.08728.314420305.5kJkmol1R一_一一1一一1S11.0498.3148.721kJkmolK273.15K,0.127MPa的理想氣體轉(zhuǎn)變?yōu)?77.4K,6.89MPa的理想氣體477.4HidC：ddT273322612216.363(477.4273)263.0821030.5(477.422732)82.117106-(477.422732)323.418kJkmol1K1c,6.89Rln0.127263.082103(477.4273

21、)82.117106(477.422732)477.4K,6.89MPa的理想氣體轉(zhuǎn)變?yōu)?77.4K,6.89MPa的真實氣體171用普遍化壓縮因子法,pr2.1查得(H2R)0(H2.351.87(0.68)2.48RTcRTcRTcHR2.488.3144208659.9kJkmol-1S2(ST)0(S2R)1.640.187(0.56)1RRRSR1.74_.-1_-18.31414.47kJkmolKH=(R一H-1HI)(H2)HV24499kJkmolS=(SIR)(SR)SV一-1-1S89.5kJkmolK1.14.74Tr2uHpV344996.89106289106325

22、08kJkmol-13-8某CO2壓縮機四段入口溫度為42C，壓力為8.053MPa，出口溫度為124C,壓力為15.792MPa，求此壓縮過程的AH,AS,AV,AUo解：設(shè)計過程2730.65420Pr20.1274.020.0316id477.4CpdSdT273T16.363ln坐90.1278.314ln-690.127dTrdB0PrTr(告打dTrTr1718315K8.053MPa實際氣體315K8.053MPa理想氣體415K15.792MPa理想氣體415K15.792MPa實際氣體查表T304.2Kcpc7.376MPa=0.225315.15Tr1304.2用普遍化壓縮

23、因子法1.048.0537.3761.09查圖0Z10.505Z10.04Zi0.5125V1ZiRT166.743cmmolP1又QT2397.151.31304.2Pr2性2.147.376用普遍化壓縮因子法得0Z20.675Z20.200過程0Z2Z2V2笠P2Z20.6750.2250.2149.9cm3mol1V=V2V1=149.9166.74=16.84用普遍化壓縮因子法查圖得(H1R)RTc過程0.7203cm2.34mol-1也0.89RTcHl=)0RTcRTcH=2.54查圖得： 也RSR(SR)0RRsR1.588.314304.2=64248.314+重RTc2.54

24、-1kJkmol1.40(SR)R0.82(SR)R1.58-1-113.14kJkmol1K1cidCp26.7542.258103T(14.2510idHP397.15dCddT3279.6kJ315.15pkmol-16_2)T1920過程用普壓法:H2=(H2)+(Hk!1.720.2250.201.78RTcRTcRTcSR(S2R)0(SR)0.95 0.2250.201.02RRRR21.788.314304.24501.8-1kJkmol發(fā)熱；并與用下面的實驗數(shù)據(jù)計算出在411K時的蒸發(fā)熱進行比較。t,P,MPaVsl,cm23kg-1Vsv,cm3kg-1126.672.49

25、22.45313.859132.222.7412.54711.986137.783.0092.76410.301143.333.2962.8598.615151.98()3.7864.4454.445解：(1)常壓沸點時的蒸發(fā)熱可用下式計算Hnvap2.17(lnpc1)4.184Tn(0.930QTn273.15(0.5)由表中數(shù)據(jù)知，正丁烷的臨界壓力，Pc3.786MPa38atmoidSP397.15CddTRln315.15T15.7928.053113.635kJkmol1K1SR1.028.314_-1-18.48kJkmolKR)(HRHid64243279.64501.8520

26、2kJkmol-1RS=(SI)VSpid(SR)-1-113.143.6358.488.3kJkmolKpV5202_-1115.792149.98.053219.34601kJkmol13-9估算正丁烷在其正常沸點(-0.5C)時的蒸發(fā)熱。用所得結(jié)果，估計在137.78C時的蒸Tm)272.65K臨界溫度，如下:Tc425.13K2.17(ln37.861)八E272.650.93425.13-1vapVHn4.1845.7236-1Jmol0.2888VHn213-10查水蒸氣表回答下列問題:(1)70C，干度為95%的濕蒸氣的H,S值;(2)4.0MPa,s=6.4kJkg-1K-1的

27、水蒸氣是什么狀態(tài)？溫度和粉各是多少？(3)4.0MPa,s=5.8kJkg-1K-1的水蒸氣是什么狀態(tài)？溫度和粉各是多少？解：1)查飽和蒸氣表得：70C時一.-1Hl292.98kJkg_.-1Hg2626.8kJkg一_一_一-1-1S0.9549kJkgK1._1Sg7.7553kJkgKH0.95Hg10.95Hl0.952626.8(10.95)292.682510.1kJkg-1_._._一_.-1一1S0.95Sgl10.95S0.957.7553(10.95)0.95497.4153kJkgK故水蒸氣處于過熱狀態(tài)。由表可知4.0MPa,280C時，H=2901.8kJkg-1,S

28、=6.2568kJkg-1K-1320C時，H=30154.4kJkg-1,S=6.4553kJkg-1K-1由內(nèi)插法求得，S=6.4kJkg-1K-1時，對應(yīng)的溫度T=308.9C,H=2983.75kJkg-13)查飽和蒸氣表得，4.0MPa時，Hl1087.3kJkgVHirVapVH2rVaP1T1r0.38T2r272.65T2r425.13410.93T T1r0.64130.9666VHvap19.8205(10.9666)8.0415kJkmol-1410.或10.6413(3)由Clapeyron方程知,vapdpdTHvapHvapTvvapdpTVv-dT由數(shù)據(jù)擬合lnp

29、河:J得到lnpvap21.7522808.4/T1dpvap兩dT2808.4dPvap2808.4PvapdTHvap411(10.30162808.46-12.764)1062-3.0091068.988kJmol1411相對誤差:8.9888.04158.988100%10.53%2)由表可知4.0MPa時，Sg.-1._-16.0701kJkgK_-1._-1S6.4kJkg1K122Hg2801.4kJkg-1S2.7964kJkg-1K-111Sg6.070kJkgK由于S Sl處于Sg之間，故水蒸氣為濕蒸氣，且滿足SxSg1xS即5.86.0701x1x2.7964，得x0.9

30、175故HxHg1xHl0.91752801.410.91751087.32660kJkg對應(yīng)的溫度為T=250.4C3-110.304MPa時飽和氨氣經(jīng)絕熱可逆膨脹到0.1013MPa時的干度是多少解：查氨的飽和蒸氣表，通過內(nèi)插法得，0.304MPa時，SI=8.8932kJkg-1K-1絕熱可逆膨脹到0.1013MPa后，S不變，通過內(nèi)插得s3.5855kJkg-1K-1Sg9.2751kJkg-1K-1而S位于S與Sg之間，設(shè)干度為x,則SxS1xSg18.89329.2751x1x3.5855解得：x0.93293-12壓力為1.906MPa（絕）的濕蒸氣經(jīng)節(jié)流閥膨脹到壓力為0.098

31、5MPa（表）的飽和蒸氣。假設(shè)環(huán)境壓力為0.1MPa,試求原始蒸氣的干度是多少？-1解：查表知0.1985MPa（飽和）的飽和蒸汽壓H=2706.3kJkg因為節(jié)流膨脹是等粉過程，過1.906MPa時濕蒸氣的H=2706.3kJ,kg-1查表知，L L906MPa906MPa時，電2798.1kJkg-1，Hl896.8kJkg-1干度為 x,x,則HxHg1xHlg1即2706.32798.1x1x896.8解得x0.95173-13溫度為230C的飽和蒸氣和水的混合物處于平衡， 如果混合相的比容是0.04166m3kg-1,試用蒸氣表中的數(shù)據(jù)計算：（1）混合相中蒸氣的含量；（2）混合相的粉

32、；（3）混合相的痼。23vf(1x)vgXHHf(1x)Hgx990.12(10.5748)2804.00.57482032.7kJkgSSf(1x)Sgx2.6099(10.5748)6.21460.57484.682kJkg-1k-13-14A和B兩股水蒸氣，A股是壓力為0.5MPa， 流量為1kgs-1,干度為0.98的濕蒸氣,B股是壓力為0.5MPa,溫度是473.15K的過熱蒸氣，試求B股過熱蒸氣的流量該為多少？解：A、B兩物流進行絕熱換熱，終態(tài)為c狀態(tài)1A股濕烝汽pA0.5MPaXA0.98GA1kgsB股過熱蒸汽p.0.5MPaTB473.15K1查飽和水蒸氣表知：p0.5MPa

33、時，A?解：1)v0.041663|1mkgvf1.2088103m3kg1331vg71.58103m3kg1vvvgvf0.041661.2088100.5748171.581.2088102)2)Hf990.12kJkg1，Hg2804.0kJkg3)Sf2.6099kJkg-1K-1Sg6.2146kJkg-1k-1243-15有溫度為423.15K,壓力為0.14MPa的蒸氣8kg， 經(jīng)過活塞-氣缸設(shè)備等溫可逆壓縮到正好處于飽和氣體狀態(tài)的終態(tài)，試求過程的熱效應(yīng)Q和功W。解：（1）查423.15K,飽和水蒸汽查423.15K,0.1MPa,過熱蒸汽，h2776.3kJkg-1S7.61

34、37kJkg-1K-13一-1v1.936mkg423.15K,0.15MPa,過熱蒸汽h2760.75kJkg-1S7.4164kJkg-1K-1v1.221m3kg-1(2)423.15K,0.14MPa,過熱蒸汽粉痼由線性內(nèi)插求出：hhhh0.140.10.150.1,hh,、h(0.140.1)2776.30.150.12763.86kJkg-1cSS,、7.41647.6137,、S(0.140.1)7.6137(0.140.1)7.61370.150.10.150.17.4559kJkg-1K-1(3)Q等T可逆過程，s1QRmTdSmT$S2S28423.15(SgS)8423.15(6.83587.4559)2099.03kJ體系放出熱量為2099.03Kj由熱力學(xué)第一定理知，uqwQuhPvU1hPVI2763.860.141061.2211032592.92kJkg-1U2hbv22745.40.4761060.39241032558.62kJkg-11uU2U134.3024kJkgw2099.038(34.3024)1824.61kJ體系獲得功量為1824.061kJ3-16將4MPa,過熱度150C的蒸氣，經(jīng)絕熱可逆膨脹降壓到50kPa。將過程定性地表示h,632.15kJ1.8416kJ2745.4kJkg-1kg-1kg-1K-16.8358kJkg