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?Ssys??nRln(p2/p1)
= {- 1¡Á8.314¡Áln£¨50/100£©} J¡¤K = 5.764 J¡¤K
-1
-1
?Samb??Qsys/Tamb= £¨-1247¡Â300£©J¡¤K-1= - 4.157 J¡¤K-1
¡÷S iso= ¡÷Ssys + ¡÷Samb = {5.764 +£¨- 4.157£©} J¡¤K = 1.607 J¡¤K £¨3£©¡÷U = 0£¬W = 0£¬Q=0
-1
-1
?Samb??Qsys/Tamb= 0
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?Ssys?nRln(V2/V1)?nRln(2V1/V1)
= {1¡Á8.314¡Áln2 } J¡¤K = 5.764 J¡¤K
-1
¡÷S iso= ¡÷Ssys + ¡÷Samb = 5.764 J¡¤K
3
3-11 ij˫Ô×ÓÀíÏëÆøÌå´ÓT1=300K£¬p1= 100 kPa£¬V1= 100 dmµÄʼ̬£¬¾²»Í¬¹ý³Ì±ä»¯µ½ÏÂÊö״̬£¬Çó¸÷¹ý³ÌµÄ¡÷S¡£
3
£¨1£©T2 = 600K£¬V2= 50 dm£»£¨2£©T2 = 600K£¬p2= 50 kPa£»
3
£¨3£©p2= 150 kPa£¬V2= 200 dm£» ½â£ºÏÈÇó¸ÃË«Ô×ÓÆøÌåµÄÎïÖʵÄÁ¿n£º
-1
-1
pV?100?103?100?10?3??n???mol?4.01mol ??RT?8.314?300?£¨1£©?S?nCV,mln(T2/T1)?nRln(V2/V1) ??4.01???5R60050?-1?1ln?4.01?Rln?J?K= 34.66 J¡¤K 2300100?£¨2£©?S?nCp,mln(T2/T1)?nRln(p2/p1) ??4.01???7R60050?-1?1ln?4.01?Rln?J?K= 103.99 J¡¤K 2300100?£¨3£©?S?nCV,mln(p2/p1)?nCp,mln(V2/V1) ??4.01???5R1507R100?-1?1ln?4.01?ln?J?K= 114.65 J¡¤K 21002200?3
3-12 2 molË«Ô×ÓÀíÏëÆøÌå´Óʼ̬300K£¬50 dm£¬ÏȺãÈݼÓÈÈÖÁ 400 K£¬ÔÙºãѹ¼ÓÈÈÖÁÌå»ý
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Ôö´óÖÁ 100m£¬ÇóÕû¸ö¹ý³ÌµÄQ£¬W£¬¡÷U£¬¡÷H¼°¡÷S¡£
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2mol Ë«Ô×ÓÆøÌå2mol Ë«Ô×ÓÆøÌå2mol Ë«Ô×ÓÆøÌåºãÈݼÓÈȺãѹ¼ÓÈÈ T1?300K?????T0?400K?????T2?£¿50dm3,p150dm3,p0100dm3,p0p1?2RT/V1?{2?8.3145?300/(50?10?3)}Pa?99774Pa
p0?p1T0/T1?{99774?400/300}Pa?133032Pa
33
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T2?p0V2/(nR)1?{133032?100?10?3/(2?8.3145)}K?800.05K
W1=0£» W2= -pamb£¨V2-V0£©= {-133032¡Á£¨100-50£©¡Á10} J= - 6651.6 J ËùÒÔ£¬W = W2 = - 6.652 kJ
7?H?nCp,m(T2?T1)?{2?R?(800.05?300)}J?29104J?29.10kJ
25?U?nCV,m(T2?T1)?{2?R?(800.05?300)}J?20788J?20.79kJ
2-3
Q = ¡÷U ¨C W = £¨27.79 + 6.65£©kJ¡Ö 27.44 kJ
?S??SV??Sp?nCV,mlnT0T?nCp,mln2 T1T0-1 -1
= {2?5Rln400?2?7Rln800.05} J¡¤K= 52.30 J¡¤K
230024003-13 4 mol µ¥Ô×ÓÀíÏëÆøÌå´Óʼ̬750 K£¬150 kPa£¬ÏȺãÈÝÀäȴʹѹÁ¦½µÖÁ 50 kPa£¬ÔÙºãοÉ
ÄæÑ¹ËõÖÁ 100 kPa¡£ÇóÕû¸ö¹ý³ÌµÄQ£¬W£¬¡÷U£¬¡÷H£¬¡÷S¡£
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4mol µ¥Ô×ÓÆøÌå4mol µ¥Ô×ÓÆøÌå4mol µ¥Ô×ÓÆøÌåºãÈÝÀäÈ´ T1?750K?????T0?£¿?¿ÉÄæÑ¹Ëõ????T2?T0V1,p1?150kPaV1,p0?50kPaV2,100kPaT0?T1p0/p1?{50?750/150}K?250K W1?0£¬
W?W2?nRT0ln(p2/p0)?{4?8.3145?250ln(100/50)}J?5763J?5.763kJ
3?U2?0£¬?U??U1?{4?R?(250?750)}J??24944J??24.944kJ
2 ?H2?0£¬?H??H1?{4?5R?(250?750)}J??41570J??41.57kJ
2Q = ¡÷U ¨C W = £¨-24.944 ¨C 5.763£©kJ = - 30.707 kJ ¡Ö 30.71 kJ
?S??SV??ST?nCV,mlnT0p?nRln2 T1p0-1
-1
= {4?3Rln250?4?Rln100} J¡¤K= - 77.86 J¡¤K
2750503-14 3 mol Ë«Ô×ÓÀíÏëÆøÌå´Óʼ̬100 kPa £¬75 dm£¬ÏȺãοÉÄæÑ¹ËõʹÌå»ýËõСÖÁ 50 dm£¬ÔÙ
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ºãѹ¼ÓÈÈÖÁ100 dm¡£ÇóÕû¸ö¹ý³ÌµÄQ£¬W£¬¡÷U£¬¡÷H£¬¡÷S¡£
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3mol Ë«Ô×ÓÆøÌå3mol Ë«Ô×ÓÆøÌå3mol Ë«Ô×ÓÆøÌåºãοÉÄæÑ¹Ëõºãѹ¼ÓÈÈ V1?75dm3??????V0?50dm3?????V2?100dm3T1,p1?100kPaT1,p0?£¿T2,p0?p2T1?p1V1/(nR)?{100?103?75?10?3/(3?8.3145)}K?300.68K
p0?nRT1/V0?{3?8.3145?300.68/(50?10?3)}K?150000Pa?150kPa
3
3
T2?p2V2/(nR)?{150?103?100?10?3/(3?8.3145)}K?601.36K W?W1?W2??nRT1ln(V0/V1)?p0(V2?V0)
?{?3?8.3145?300.68ln(50/75)?150?103?(100?50)?10?3}J
= - 4459 J = - 4.46 kJ
34
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5?U1?0£¬?U??U2?{3?R?(601.36?300.68)}J?18750J?18.75kJ
2 ?H1?0£¬?H??H2?{3?7R?(601.36?300.68)}J?26250J?26.25kJ
2Q = ¡÷U ¨C W = £¨18.75 + 4.46 £©kJ = 23.21 kJ
?S??ST,r??Sp??nRlnp0T?nCp,mln2 p1T0-1 -1
= {?3?R?ln150?3?7Rln601.36} J¡¤K= 50.40 J¡¤K
1002300.683-15 5 mol µ¥Ô×ÓÀíÏëÆøÌå´Óʼ̬ 300 K£¬50kPa£¬ÏȾøÈÈ¿ÉÄæÑ¹ËõÖÁ 100 kPa£¬ÔÙºãѹÀäȴʹ3
Ìå»ýËõСÖÁ 85 dm£¬ÇóÕû¸ö¹ý³ÌµÄQ£¬W£¬¡÷U£¬¡÷H£¬¡÷S¡£
½â£º¹ý³ÌʾÒâÈçÏ£º 5mol µ¥Ô×ÓÆøÌå5mol µ¥Ô×ÓÆøÌå5mol µ¥Ô×ÓÆøÌå¾øÈÈ¿ÉÄæÑ¹ËõºãѹÀäÈ´ÈÈ , T0,V1?£¿,T1?300K,??????V0?£¿?????V2?85dm3,T2,p2p1?50kPa p0?100kPa
T0?(p0/p1)R/Cp,mT1?{(100/50)2/5?300}K?395.85K
V0?nRT0/p0?{5?8.3145?395.85/(100?103)}m3?0.16456m3
3Q1?0£¬W1??U1?{5?R?(395.85?300)}J?5977J?5.977kJ
2T2?p2V2100000?0.085?{}K?204.47K nR5?8.3143
-3
W2 = - pamb ( V2 ¨C V1 ) = {- 100¡Á10¡Á£¨85 ¨C 164.56£©¡Á10} J = 7956 J W = W1 + W2 = 13933 J = 13.933 kJ 3?U2?{5?R?(204.47?395.85)}J??11934J
2¡÷U = ¡÷U1 + ¡÷U2 = -5957 J = - 5.957 kJ 5?H?{5?R?(204.47?300)}J??9929J??9.930kJ
2Q?Q2??U?W2?(?11.934?7.956)kJ??19.89kJ
5204.47?S??S¾øÈÈ£¬r??SP?0?nCp,mln(T2/T0) ?{5?R?ln}J?K?1??68.66J?K?1
2395.85 3-16 ʼ̬ 300 K£¬1Mpa µÄµ¥Ô×ÓÀíÏëÆøÌå 2 mol£¬·´¿¹ 0.2 MpaµÄºã¶¨Íâѹ¾øÈȲ»¿ÉÄæÅò
ÕÍÆ½ºâ̬¡£ÇóÕû¸ö¹ý³ÌµÄW£¬¡÷U£¬¡÷H£¬¡÷S¡£
½â£ºQ = 0£¬W = ¡÷U
3?pamb(V2?V1)?n?R(T2?T1)2
?nET2nRT1?3??pamb???n?R(T2?T1)?p?p21??amb´úÈëÊý¾ÝÕûÀíµÃ 5T2 = 3.4 T1 = 3.4¡Á300K£»¹Ê T2 = 204 K 3W??U2?{2?R?(204?300)}J??2395J??2.395kJ25?H?{2?R?(204?300)}J??3991J??3.991kJ
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?S?nCp,mlnT2p?nRln2T1p152040.2 ?{2?R?ln?2?Rln}J?K?123001 ?{?16.033?26.762}J?K?1?10.729J?K?1?10.73J?K?1 3-17 ×é³ÉΪy£¨B£©= 0.6µÄµ¥Ô×ÓÆøÌåAÓëË«Ô×ÓÆøÌåBµÄÀíÏ뻯ºÏÎï¹² 10 mol£¬´Óʼ̬T1 =300K£¬p1 = 50kPa£¬¾øÈÈ¿ÉÄæÑ¹ËõÖÁp2= 200 kPaµÄƽºâ̬¡£Çó¹ý³ÌµÄW£¬¡÷U£¬¡÷H£¬¡÷S£¨A£©£¬¡÷S£¨B£©¡£
½â£ºÏÈÇó»ìºÏÎïµÄĦ¶û¶¨Ñ¹ÈÈÈÝ
75Cp,m,mix??yBCp,m(B)?0.6?R?0.4?R?3.1R
22BT2?(p2/p1)R/Cp,mT1?{(200/50)1/3.1?300}K?469.17K
?H?{10?3.1R?(469.17?300)}J?43603J?43.60kJ
CV,m,mix?Cp,m,mix?R?2.1R nA?yAn?0.4?10mol?4mol nB?6mol
?U?{10?2.1R?(469.17?300)}J?29538J?29.54kJ pB,1?ybp1?0.6?50kPa?30kPa, pA,1?20kPa pB,2?ybp2?0.6?200kPa?120kPa, pA,2?80kPa
?S(A)?nACp,m(A)lnpA,2T25483.8780?nARln?{4?R?ln?4?Rln}J?K?1 T1pA,1230020 ?{37.18?46.105}J?K?1??8.924J?K?1
ÒòÊǾøÈÈ¿ÉÄæ¹ý³Ì£¬¡÷S=¡÷SA+¡÷SB=0£¬¹ÊÓС÷SB = - ¡÷SA = 8.924J¡¤K-1 »ò
?S(B)?nBCp,m(B)lnpB,2T27483.87120?nBRln ?{6?R?ln?6?Rln}J?K?1 T1pB,1230030 ?8.924J?K?13-18 µ¥Ô×ÓÆøÌåAÓëË«Ô×ÓÆøÌåBµÄÀíÏëÆøÌ廯ºÏÎï¹²8 mol£¬×é³ÉΪ y£¨B£©= 0.25£¬Ê¼Ì¬ T1 =
400 K£¬V1 = 50 dm¡£½ñ¾øÈÈ·´¿¹Ä³ºã¶¨Íâѹ²»¿ÉÄæÅòÕÍÖÁĩ̬Ìå»ýV2 = 250 dm3µÄƽºâ̬¡£¡£Çó¹ý³ÌµÄW£¬¡÷U£¬¡÷H£¬¡÷S¡£
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53CV,m,mix??yBCp,m(B)?0.25?R?0.75?R?1.75R
22BQ = 0£¬W = ¡÷U
?pamb(V2?V1)?nCV,m,mix(T2?T1)3
nET2?V2?V1??n?1.75R(T2?T1)?V2½«Êý¾Ý´úÈ룬µÃ 2.55 T2 = 1.75 T1= 1.75¡Á400K£¬¹Ê T2 = 274.51 K W??U?{8?1.75R?(274.51?400)}J??14610J??14.61kJ Cp,m,mix?CV,m,mix?R?1.75R?R?2.75R
?H?{8?2.75R?(274.51?400)}J??22954J??22.95kJ
36