复旦热力学与物理统计课件3均匀物质的热力学性质

第二章均匀物质的热力学性质1.基本热力学函数2.麦氏关系及应用3.气体节流和绝热膨胀§2.1基本热力学函数1.内能VpSTUdddVVUSSUUVSUUSVddd),,(),(),,(VSpVUpVSTSUTSVVSUSVU22VSSpVT2.焓pVSTHdddppHSSHHpSHHSpddd),,(),(),,(pSVpHVpSTSHTSppSHSpH22pVUHpSSVpT3.自由能VpTSFdddTVFTTFFVTFFTVddd),,((,),(,)VTFFSSTVppTVTVVTFTVF22TSUFVTFTFTSFUTVVFVTFTFpVUHVTTpVS4.吉布斯函数（自由焓）pVTSGdddppGTTGGpTGGTpddd),,(),(),,(pTVpGVpTSTGSTppTGTpG22pVFTSHGpTGTGTSGHTppGpTGTGpVHUpTTVpS§2.2麦氏关系及应用VSSpVTpSSVpTVTTpVSpTTVpSUHFGS)(p)(VT1.麦克斯韦关系2.基本热力学函数的确定内能VpSTUdddVVUTTUUVTUUTVddd),,(VVSTTSSVTSSTVddd),,(VpVSTTTSTUTVdddVTTpVSVVVTSTTUCpTpTVUVTVpTpTTCUVVdddVTpTTCSVVddd由实验测定，),(),,(00VTppVTCCVVVTVTpTVTSTTVSTVC2222VVVVVVTpTVTCVTC0d),(),(220),(),,(VTSSVTUU即可确定。VTTpVSTVC0VV焓pVSTHdddppHTTHHpTHHTpddd),,(ppSTTSSpTSSTpddd),,(pVpSTTTSTHTpdddpTTVpSpppTSTTHCpTTVTVpHpTVTVTCHppdddpTVTTCSppddd由实验测定，),(),,(00pTVVpTCCpppTpTVTpTSTTpSTpC2222ppppppTVTpTCpTC0d),(),(220),(),,(pTSSpTHH即可确定。pTTVpSTp0ppC定容和定压热容量VVVTSTTUCpppTSTTHCVVSTTSSVTSSTVddd),,(ppSTTSSpTSSTpddd),,(ppVTTVVpTVVTpddd),,(pTVpTVVSTSTSVTTpVSpVVpTVTpTCC由物态方程决定。等温和绝热压缩系数TTpVV1SSpVV1VVSppSSpVdddpVSpSSVSVpVpdd1dpVSVSpSpVpVTVTpTpVTSVVVpTTSpSVpSTCC平衡稳定性要求：以上四量皆为正。pppVTTSVSpVTVTpTpVTpVpVTVTp体胀系数pTVV1pVVpTVTpTCC02TVpVTCC1例范氏气体（计入分子体积和相互吸引修正后的气体模型）nRTnbVVanp22nbVnRTpV22VanpTpTV022VTVTpTVC)(TCCVVVVanTTCUVdd)(d2200220d)(UVanVanTTCUTTVVnbVnRTTTCSVdd)(d00lnd)(0SnbVnbVnRTTTCSTTV0,0ba极限为理想气体。§2.3气体节流和绝热膨胀1.节流1p2p焦－汤效应气体节流后温度改变。pTVTVTCHppddd221112VpVpUU12HH气体节流后焓不变。pVTVTCHCTpppd1d1d11TCVVTVTCpTpppH焦－汤系数1V2V1T2TTp实际气体的等焓线001T致冷1T致温001T温度不变0Tp0理想气体的等焓线反转曲线0温度愈低，制冷效果愈好，但气体必须预冷。2.绝热膨胀pTVTTCSppdddpTVCTSCTTpppdddpppSCVTTVCTpT气体0致冷致冷效果随温度降低而降低，但不需预冷。3.低温技术1934年卡皮查氦的液化1K以下绝热膨胀+节流液化+降低蒸气压例2气体自由膨胀后的温度变化nRTnbVVanp22VpTpTTCUVVddd0W0Q0ΔU气体自由膨胀后内能不变。11TCppTpTCVTVVVU理想气体0UVT自由膨胀后温度不变。范氏气体022VCanVTVU自由膨胀后温度降低。例3(1)某气体系统的内能VTuU)(，压强3)(Tup。确定其内能和熵的函数形式，并求该系统卡诺循环(2)现有两个体积相同并保持不变的上述系统，但温度不同，分别为1T和2T。以一热机工作于其间，使两者达到共同末温T。求末温的范围与热机最大功。的效率。VpTpTTCUVVddduVUT3dd3uTuTpTpTV3dd3uTuTu4aTuVaTU4VaTTUCVV34VTpTTCSVVdddVaTVaTTVaTS33234dd34d4dVaTS334OVP12341T2TW431aTp)(3443422VVaTQVaTpVUH434)(34d1241211VVaTHQ034dd3VaTS常量VT3432131VTVT332231VTVT121211TTQQ0)2()Δ(4424121TTTaVUUW4142412TTT0)2(34)Δ(Δ3231321TTTaVSSS3132312TTT)2(4min4241maxTTTaVW