第五章 习题解答
T?T873?3135-1 ⑴ ?t,c?12??64.14%
T1873⑵ W0??t,cQ1?0.6414?100?64.14 kW ⑶ Q2??1??t,c?Q1??1?0.6414??100?35.86 kW 5-2 ?t,c?T1?T21000?400??60% T11000W0??t,cQ1?0.6?1000?600 kJ < 700 kJ 该循环发动机不能实现
5-3 q1?cp?T2?T1??1.01??1000?300??707 kJ/kg
q2?RT3ln?T?p3p?RT3ln3?RT3ln?3?p1p2?T2?1.41.4?1???1
?300? ?0.287?300?ln???1000?w344.2??48.68% q1707??362.8 kJ/kgw?q1?q2?707?362.8?344.2 kJ/kg
??5-4 ?t,c?T1?T21000?300??70% T11000T2263Q1??100000?89765 kJ/h T1293T1293??9.77 T1?T2293?263w??t,cq1?0.7?707?495 kJ/kg 5-5 ⑴Q2?⑵?2,c?P?Q1?2,c?100000?2.84 kW
9.77?3600100000?27.78 kW 3600⑶P?100000 kJ/h?工程热力学 21
5-6 ⑴?2,c?T1293??14.65 T1?T2293?273P?由PQ1?2,c?20?1000?0.455 kW
9.77?3600?T?T??1200t?20℃ T2?122T1?T23600得T1?313 K?40℃
5-7 Q??t?2,cQ1?0.3?5?10000?15000 kJ/h 5-8 Q2?Q1?1??t??10000??1?0.3??7000 kJ/h
Q总?Q?Q2?15000?7000?22000 kJ/h 5-9 可逆绝热压缩终态温度T2
?p?T2?T1?2??p1???1??0.3??300????0.1?1.4?11.4?410.6K
可逆过程Q??U?W?0，不可逆过程Q??U??W??0 且W??1.1W，则?U??1.1?U
mcv?T2??T1??1.1mcv?T2?T1?
T2??T1?1.1?T2?T1??300?1.1??410.6?300??421.7K
?Tp?421.70.3???S?m?cpln2??Rln2??0.1??1.01ln?0.287ln?
Tp3000.1???11?=0.00286 kJ/kg.K 5-10 理论制冷系数：?1,c?制冷机理论功率：P?T2258??7.37 T1?T2293?258Q2?1,c?125700?4.74 kW
7.37?3600散热量：Q1?Q2?P?125700?4.74?3600?142756 kJ/h
??冷却水量：mQ1142756??4867.2 kg/h cH2O?t4.19?722
工程热力学
5-11 ⑴ W1?Q1??U1?100?30?70 kJ
热源在完成不可逆循环后熵增0.026kJ/kg.K 则第二个过程热源吸热：
?Q?Q2?T?1?0.026??100?600?0.026?115.6 kJ
?T?工质向热源放热：
W?Q2??U2??115.6???30???85.6 kJ 5-12 可逆定温压缩过程熵变：
?s??Rlnp21??0.287?ln??0.66 kJ/kg?K p10.1可逆过程耗功：
w?RT1lnp10.1?0.287?400?ln??264 kJ/kg p21实际耗功：w??1.25w?1.25???264???330 kJ/kg 因不可逆性引起的耗散损失：
q??w??w??330???264???66 kJ/kg 总熵变：?s???s?q?66??0.66???0.44 kJ/kg?K T03005-13 q1?cv?T2?T1?，q2?cp?T3?T1?
??cp?T3?T1?TT?1vv?1qw?1?2?1??1??31?1??31 q1q1cv?T2?T1?T2T1?1p2p1?15-14 q1?RT1lnp1p，q2?cv?T1?T2??RT2ln4 p2p3cv?T1?T2??RT2lnRT1lnp1p2p4p3T1?T2p?T2ln4??1p3?1?
p1T1lnp2??1?q2?1?q1工程热力学 23
5-15 ⑴T1??1940 K，T2??660 K
??1?T2?660?1??66% ?T11940⑵W0?Q1??1000?66%?660 kJ
?T?600??W0,max?Q1?1?2??1000??1???700 kJ
?2000??T1??W?W0,max?W0?700?660 kJ?40 kJ
5-16 m1?m2?p1V1400?0.1??0.445 kg RT10.287?313p2V2200?0.1??0.238 kg RT20.287?293?U?m1cv?T?T1??m2cv?T?T2??0
mT?m2T20.445?313?0.238?293T?11??306 K
m1?m20.445?0.238?m?m2?RT??0.445?0.238??0.287?306?0.3 MPa p?1V1?V20.1?0.1?S?m1?s1?m2?s2??Tp?Tp? ?m1?cpln?Rln??m2?cpln?Rln?T1p1?T2p2??? 3060.3?? ?0.445?1.01?ln?0.287?ln?3130.4??3060.3?? ?0.238?1.01ln?0.287?ln??0.0093 kJ/K2930.2??p5-17 ⑴T2?T12?400?2.5?1000 K
p1q1?cv?T2?T1??0.723??1000?400??433.8 kJ/kg
v1q2?RT3ln1?0.287?400ln??264.3 kJ/kg
v310⑵w?q1?q2?433.8?264.3?169.5 kJ/kg
q264.3??1?2?1??39.0%
q1433.8工程热力学
24
R?T1?T2???20 5-18 ⑴Ws?m?w?m???120???1?20?1.4?1?T2??T1??298??258.2 K
m?R0.5?1.4?0.2871.4?1?p2?⑵T2?T1???298?0.41.4?229.4 K
?p1?R?T1?T2?0.287??298?229.4?Ws?m?w?m??0.5?1.4? ??11.4?1 ?34.5 kW??1??p??1?5-19 T2?T1?2??303???515.5 K ??0.1??p1?n??1.3?1.40.287q?cv?T2?T1?????515.5?303? n?11.3?11.4?1 ??50.8 kJ/kgq50.8环境熵变：?s1???0.175 kJ/kg?K
T0290Tp空气熵变：?s2?cpln2?Rln2
T1p1515.51?1.005?ln?0.287ln??0.127 kJ/kg?K
3030.1孤立系统熵变：
?siso??s1??s2?0.175?0.127?0.048 kJ/kg?K ?p2??0.2?5-20 T2?T1???800???505.1 K ?p1???1?R?T1?T2?0.2968??800?505.1?w???218.8 kJ/kg
??11.4?1exu1?exu2?u1?u2?p0?v2?v1??T0?s2?s1??RTRT? ?cv?T1?T2??p0?2?1?
pp?21??505.1800? ?218.8?100?0.2968?????167.6 kJ/kg2001000??排开环境所作的功为作功能力损失（51.2kJ/kg）
工程热力学
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??1?1.4?11.4n?1n1.3?11.3