第三章 习题解答(2)

2019-02-17 17:35

S2RR??1.2?0.19?5?(0.4?5)?1.288

R-1?H2??2.198?8.314?425??7766.5 kJ?kmol

R-1-1S2??1.288?8.314??10.708 kJ?kmol?K

1故 ?V?V2?V1??2.882?9.8813??10?4??6.999 m3?mol?

?H= H1??HT??Hp?(?H2)?11769.7 kJ?kmolRididRRididR-1-1

-1?S= S1??ST??Sp?(?S2)?14.0378 kJ?kmol?K

6?4?U??H??(pV)?11769.7?(12.67?10?2.882?10 ?10618.3 kJ?kmol-16?4?2.53?10?9.8813?10)

6 解:(1)设计过程如下:

273.15K0.43MPa饱和液氨①273.15K0.43MPa气氨②273.15K0.43MPa理想气氨③300K1.013MPa理想气氨 ④300K1.013MPa气氨

① 273K,0.43MPa下液氨汽化

?HV?21432 kJ?kmol-1 ?SV?78.462 kJ?kmol-1?K-1

② 273K,0.43MPa下真实气体转变成理想气体

查表知,Tc=405.6K, Pc=11.28MPa,ω=0.250

Tr?273.15405.6?0.673

pr?0.43 1?0.03811.28查图知用普遍化维利系数法计算。

B=0.083?00.422T1.6r=?0.712

B=0.139?dB010.172Tr4.2=?0.769

dTrdB1? 0.675?1.892.6Tr0.772Tr5.2

dTr??5.66

01??dB0?dB1 B?B??? ??pr?Tr????????????0.119RTcTr?Tr???dTr??dTrH1RS11 ?dB0dB???pr??????0.126RdTr??dTrR故

H1??0.119?RTC??0.119?8.314?405.6??401.287 kJ?kmolR-1

6

S1??0.126?R??0.126?8.314??1.048 kJ?kmol?kR-1-1

③ 273K,0.43MPa下理想气体变化为300K,1.013MPa的理想气体 查表已知

?Hp? 13idCp?27.31?0.02383T?1.707?10T?1.185?10TT2id?52?83

2?T1CpdT?27.31??300?273.15??id?512?0.02383??300?273.152?84??4

?1.707?10??300?273.153-13??4?1.185?10300273.151??300?273.15?

?961.585 kJ?kmol?Sidp??300273.15CpTiddT?Rln?51.0130.432?27.31?ln2?0.02383??300?273.15??8 ?1.707?10 ?8.314?ln?12??300?273.15??1.185?10?13??300?273.1533?1.0130.43-1-1 ??3.766 kJ?kmol?K④ 300K,1.013MPa的理想气体变化为300K,1.013MPa的真实气体

Tr?300405.6?0.740

Pr? 1.013?0.089811.28查图知用普遍化维利系数法计算。

B?0.083?00.422Tr1.6??0.6

B?0.139?dB0'0.172??4.2Tr?0.6750.742.60.47dTr?0.675Tr2.6?1.477

dB'dTrH2?R0.722Tr5.2?0.7220.745.2?3.456011?dB0BdBB???prTr?(?)??(?)?RTcTrdTrTr??dTr

??0.6??0.898?0.74???1.477?0.74????0.2190.47??????0.25??13.456???0.74????S21 ?dB0dB???Pr?????0.898?(1.477?0.25?3.456)??0.210?RdTr??dTrR? H2??0.219?8.314?405.6??738.5 kJ?kmolS2??0.210?8.314??1.746 kJ?kmol?KR-1-1R-1

-1又因

H0?418.6?17?7116.2 kJ?kmol-1-1S0=4.186?17=71.162 kJ?kmol?K

?28370 kJ?kmol

-1故

H= H0?(?H1)?(H2)??HV??HRRidRRidS= S0?(?S1)?(S2)??SV??S?143.1 kJ?kmol?K

-1-1(2) 同理可求出30.4MPa,500 K气氨的焓和熵。 过程①和②的结果与上述相同

7

过程③的焓变和熵变为:

?Hidp??500273.15CpdT?27.31??500?273.15??0.02383?id?512??500?273.1522?4 ?1.707?10?13??500?273.153-13??1.185?10?8?14??500?273.154? ?3080.56 kJ?kmol?Sidp??500273.15CpTiddT?Rln?5p2p1?27.31?ln2500273.152?0.02383??300?273.15??8

3 ?1.707?10 ?8.314?ln?12??500?273.15??1.185?10-1-1?13??500?273.153?30.40.43??11.578 kJ?kmol?K过程④的焓变和熵变计算如下为:

Tr?500405.6?1.23

pr??2.711.2830.4

查图用普遍化压缩因子法。 查图可知

(H)RTc(S)RR0R0??2.9 ,

(H)RTcR'??1.1'

??1.7

R0(S)RR??1.2(H2)RTcRR?(H)RTc??(H)RTcR'??3.175

RS2R??1.7?0.25??(1.2?)?

2-1?H2??3.715?8.314?405.6??10706.6 kJ?kmol

S2??2?8.314??16.628 kJ?kmol?KRRid故 H= H??(H1?)H(2?)?HV??H?0RRidR-1-1

-121323? kJ kmol-1-1S= S0?(?S1)?(S2)??SV??S?122.466 kJ?kmol?K

7解:

Tr1? 477.4?1.14420 p?6.89?1.71

r14.02用普遍化压缩因子法查图得:

z?z0??z1?0.477?0.187?0.136?0.502

zRT0.502?8.314?477.43-1V?p?6.89?289 cm?mol查得T=273.15K时,pS?1.27?10Pa

5 8

?H273.15K0.127MPa饱和液①273.15K0.127MPa饱和气②?S273.15K0.127MPa理想气③477.4K6.89MPa理想气体 ④477.4K6.89MPa真实气体

① 273.15K饱和液体丁烯-1的汽化 查得

?HV?21754 kJ?kmol-1

?SV??HVT?217354273?79.68 kJ?kmol?1?K?1

② 273.15K,0.127MPa的真实气体转变为273.15K,0.127MPa的理想气体

Tr2?273420?0.65

Pr2?0.127?0.031 64.02用普遍化压缩因子法:

H1R ??0.0316?0.65?[(0.06?0.756)?0.187?(16.73?0.904) ??0.0872RTc??prTr[(dB0dTr?B0Tr)??(dB1dTr?B1Tr)]S1RR??Pr(dB0dTr??dB1dTr)

??0.0316?(2.06?0.187?6.73)??0.1049H1??0.0872RTc??0.0872?8.314?420??305.5 kJ?kmolS1??1.049?8.314??8.721 kJ?kmolR?1R?1

?K?1

③ 273.15K,0.127MPa的理想气体转变为477.4K,6.89MPa的理想气体

477.4?Hid??273CpdT?3id?16.363?(477.4?273)?263.082?10?23.418 kJ?kmolCpTid?0.5?(477.4?273)?82.117?1022?6?13?(477.4?273)22

?1?K?1?Sid??477.4273dT?Rln6.890.127?3?16.363?ln6.890.127?263.082?10?1?(477.4?273)?82.117?10?6?(477.4?273)?8.314?ln226.890.127

?23.418 kJ?kmol?K?1④ 477.4K,6.89MPa的理想气体转变为477.4K,6.89MPa的真实气体

Tr2?1.14

H2R pr2?1.71用普遍化压缩因子法,查得

0RTc?(H2)RTcR??(H2)RTcR'??2.35?1.87?(?0.68)??2.48

R-1?H2??2.48?8.314?420??8659.9 kJ?kmol

S2RRR?(S2)RR0??(S2)RR'??1.64?0.187?(?0.56)??1.74-1-1

?S2??1.74?8.314??14.47 kJ?kmol?K

-1故

?H= (?H1)?(H2)??HV??H?24499 kJ?kmolRR?

9

?S= (?S1)?(S2)??SV??S?89.5 kJ?kmol?K

RR?-1-1?u?H?pV?34499?6.89?10?289?10?32508 kJ?kmol66-1

8解:设计过程

?H315K8.053MPa实际气体①315K8.053MPa理想气体②?S?U?V③415K15.792MPa实际气体415K15.792MPa理想气体

查表

Tc?304.2 K pc?7.376MP a ?=0.225

?1.04Tr1?315.15304.2 ,

pr1?8.0537.376?1.09

用普遍化压缩因子法 查图

z1?0.50 5

0 z1'?0.04 z1?z10??z1'?0.5125

?166.74 cm?mol3?1?V1?z1RTp1

又 ?T?397.15?1.31

r2304.2pr2?' 15.792?2.147.376

0用普遍化压缩因子法得 z2?0.67 5 z2?0.20 0?z2?z2??z2?0.675?0.225?0.2?0.720

0'?V2?z2RTp2?149.9 cm?mol3?1

3-1故 ?V=V2?V1=149.9?166.74=?16.84 cm?mol

过程①

用普遍化压缩因子法查图得

H1R(H1)RTcR0??2.34 (H1)RTcR'??0.89

?RTc=(H1)RTcR0+?(H1)RTcR'??2.54

R-1?H1=?2.54?8.314?304.2=?6424 kJ?kmol

R0R'查图得:(S1)??1.40 (S1)??0.82

RRRS1RR?(S1)R0??(S1)RR'??1.58

R-1-1? S1??1.58?8.314??13.14kJ?kmol?K

过程②

10


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