第五章 习题解答5-1 ⑴ 12,187331364.14%873t c T T T η--===⑵ 0,10.641410064.14 kW t c W Q η==⨯= ⑶ ()()2,1110.641410035.86 kW t c Q Q η=-=-⨯= 5-2 12,1100040060%1000t c T T T η--=== 0,10.61000600 kJ < 700 kJ t c W Q η==⨯= 该循环发动机不能实现5-3 ()()121 1.011000300707 kJ/kg p q c T T =-=⨯-=133323331221.41.41lnln ln 300 0.287300ln 362.8 kJ/kg1000p pT q RT RT RT p p T κκ--⎛⎫=== ⎪⎝⎭⎛⎫=⨯⨯=- ⎪⎝⎭12707362.8344.2 kJ/kg w q q =+=-=1344.248.68%707w q η=== 5-4 12,1100030070%1000t c T T T η--=== ,10.7707495 kJ/kg t c w q η==⨯= 5-5 ⑴221126310000089765 kJ/h 293T Q Q T ==⨯= ⑵12,122939.77293263c T T T ε===-- 12,1000002.84 kW 9.773600cQ P ε===⨯⑶100000100000 kJ/h 27.78 kW 3600P ===5-6 ⑴12,1229314.65293273c T T T ε===-- 12,2010000.455 kW 9.773600cQ P ε⨯===⨯由()1221212003600T T T PT T -⨯=-220t =℃ 得1313 K 40T ==℃5-7 2,10.351000015000 kJ/h t c Q Q ηε==⨯⨯= 5-8 ()()2111000010.37000 kJ/h t Q Q η=-=⨯-=215000700022000 kJ/h Q Q Q =+=+=总 5-9 可逆绝热压缩终态温度2T1 1.411.422110.3300410.60.1p T T p κκ--⎛⎫⎛⎫==⨯= ⎪⎪⎝⎭⎝⎭K可逆过程0Q U W =∆+=，不可逆过程0Q U W ''=∆+= 且 1.1W W '=，则 1.1U U '∆=∆()()21211.1v v mc T T mc T T '-=-()()21211.1300 1.1410.6300421.7T T T T '=+-=+⨯-=K 2211421.70.3ln ln 0.1 1.01ln 0.287ln 3000.1p T p S m c R T p '⎛⎫⎛⎫∆=-=⨯- ⎪ ⎪⎝⎭⎝⎭=0.00286 kJ/kg.K5-10 理论制冷系数：21,122587.37293258c T T T ε===-- 制冷机理论功率：21,1257004.74 kW 7.373600cQ P ε===⨯散热量：12125700 4.743600142756 kJ/h Q Q P =+=+⨯=冷却水量：21H O 1427564867.2 kg/h 4.197Q mc t ===∆⨯5-11 ⑴ 1111003070 kJ W Q U =-∆=-=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：120.0261006000.026115.6 kJ Q Q T T ⎛⎫=+=+⨯= ⎪⎝⎭工质向热源放热：()22115.63085.6 kJ W Q U =-∆=---=- 5-12 可逆定温压缩过程熵变：211ln0.287ln 0.66 kJ/kg K 0.1p s R p ∆=-=-⨯=-⋅ 可逆过程耗功：1120.1ln0.287400ln 264 kJ/kg 1p w RT p ==⨯⨯=- 实际耗功：()1.25 1.25264330 kJ/kg w w '==⨯-=- 因不可逆性引起的耗散损失：()33026466 kJ/kg q w w ''=-=---=- 总熵变：0660.660.44 kJ/kg K 300q s s T ''∆=∆+=-+=-⋅ 5-13 ()121v q c T T =-，()231p q c T T =-()()31313121121212111111111p v c T T T T v v q wq q c T T T T p p ηκκ---==-=-=-=---- 5-14 1112lnp q RT p =，()421223ln v pq c T T RT p =-+ ()412412223321111122lnln 1111lnlnv p T T pc T T RT T p p q p p q RT T p p κη--++-=-=-=-5-15 ⑴11940 K T '=，2660 K T '=216601166%1940T T η'=-=-=' ⑵01100066%660 kJ W Q η==⨯=20,max11600110001700 kJ 2000T W Q T ⎛⎫⎛⎫=-=⨯-= ⎪ ⎪⎝⎭⎝⎭0,max 0700660 kJ 40 kJ W W W δ=-=-=5-16 11114000.10.445 kg 0.287313p V m RT ⨯===⨯ 22222000.10.238 kg 0.287293p V m RT ⨯===⨯ ()()11220v v U m c T T m c T T ∆=-+-=1122120.4453130.238293306 K 0.4450.238m T m T T m m +⨯+⨯===++()()12120.4450.2380.2873060.3 MPa 0.10.1m m RT p V V ++⨯⨯===++ 1122121122 ln ln ln ln 3060.3 0.4451.01ln 0.287ln 3130.43060.3 0.2381.01ln 0.287ln 0.0093 kJ/K2930.2p p S m s m s T p T p m c R m c R T p T p ∆=∆+∆⎛⎫⎛⎫=-+- ⎪ ⎪⎝⎭⎝⎭⎛⎫=⋅-⋅ ⎪⎝⎭⎛⎫+-⋅= ⎪⎝⎭5-17 ⑴2211400 2.51000 K pT T p ==⨯=()()1210.7231000400433.8 kJ/kg v q c T T =-=⨯-=12331ln 0.287400ln 264.3 kJ/kg 10v q RT v ==⨯=-⑵12433.8264.3169.5 kJ/kg w q q =-=-=21264.31139.0%433.8q q η=-=-=5-18 ⑴()12201s R T T W m w m κκκ'-===- ()()21201201.41298258.2 K 0.5 1.40.287T T m R κκ'--=-=-=⨯⨯⑵1 1.412 1.42112980.4229.4 K p T T p κκ--⎛⎫==⨯= ⎪⎝⎭()()120.287298229.40.5 1.41 1.4134.5 kWs R T T W m w m κκκ-⨯-===⨯⨯--= 5-19 1 1.311.322111303515.5 K 0.1n np T T p --⎛⎫⎛⎫==⨯= ⎪ ⎪⎝⎭⎝⎭()()21 1.3 1.40.287515.53031 1.31 1.4150.8 kJ/kgv n q c T T n κ--=-=⨯⨯----=- 环境熵变：1050.80.175 kJ/kg K 290q s T ∆===⋅空气熵变：22211ln ln p T ps c R T p ∆=-515.511.005ln 0.287ln 0.127 kJ/kg K 3030.1=⨯-=-⋅孤立系统熵变：120.1750.1270.048 kJ/kg K iso s s s ∆=∆+∆=-=⋅ 5-20 1 1.411.422110.2800505.1 K 1p T T p κκ--⎛⎫⎛⎫==⨯= ⎪ ⎪⎝⎭⎝⎭()()120.2968800505.1218.8 kJ/kg 1 1.41R T T w κ-⨯-===--()()()12120210212112021 505.1800 218.81000.2968167.6 kJ/kg2001000u u v ex ex u u p v v T s s RT RT c T T p p p -=---+-⎛⎫=--- ⎪⎝⎭⎛⎫=-⨯⨯-= ⎪⎝⎭排开环境所作的功为作功能力损失（51.2kJ/kg ）5-21 1 1.211.222110.2800611.8 K 1n np T T p --⎛⎫⎛⎫==⨯= ⎪⎪⎝⎭⎝⎭()()120.2968800611.8279.3 kJ/kg 1 1.21R T T w n -⨯-===--31110.29688000.237 m /kg 1000RT v p ⨯=== 32220.2968611.80.908 m /kg 200RT v p ⨯=== 22221111ln ln ln ln 11.40.2968611.80.2ln 0.2968ln 0.20 kJ/kg K1.418000.1p T p T p R s c R R T p T p κκ∆=-=--⨯=-=⋅-()()()()()()1212021021120210 10.2968 800611.81000.9080.2373000.21.41 132.5 kJ/kg u u ex ex u u p v v T s s RT T p v v T s κ-=---+-=---+∆-=⨯--⨯-+⨯-= 5-22 1112001013.94 kg 0.287500pV m RT ⨯===⨯ ()()2113.94 1.0056005001400.7 kJ p Q mc T T =-=⨯⨯-=21600ln1.005ln 0.1832 kJ/kg K 500p T s c T ∆==⨯=⋅ 01400.730013.940.1832634.6 kJ q Ex Q T m s =-⋅∆=-⨯⨯= 030013.940.1832766.1 kJ q An T m s =⋅∆=⨯⨯=5-23 ()()12 1.40.287500320180.74 kJ/kg 1 1.41s R T T w κκ-⨯⨯-===--22113200.1lnln 1.005ln 0.287ln 5000.5 0.0134 kJ/kg Kp T p s c R T p ∆=-=⨯-⨯=⋅()()()1212021120 1.0055003203000.0134184.92 kJ/kgh h p ex ex h h T s s c T T T s -=-+-=-+∆=⨯-+⨯=12180.7497.7%184.92s ex h h w ex ex η===-5-24 ⑴21300201167.3%100020T T η'+=-=-='- ⑵013001170%1000t T T η=-=-= ()()110000.70.67327 kJ t L Q ηη=-=⨯-= ⑶()()211100010.673327 kJ Q Q η=-=⨯-=12110211111111 10003270.09 kJ/K9801000300320S Q Q T T T T ⎛⎫⎛⎫∆=-+- ⎪⎪''⎝⎭⎝⎭⎛⎫⎛⎫=-+-= ⎪ ⎪⎝⎭⎝⎭0iso 3000.0927 kJ L T S =∆=⨯= 符合！。
