化工热力学：第2 章 流体的p –V -T 关系

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1

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 3Bté￥ p –V –T1"b
2

g?? úZ?￥+?? T#? ú" ?￥t ?ilb
3

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4

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5

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6

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7

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8

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9

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10

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11

? 3A8￥ pVT1"b
12

g?
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?t￥?=? ú" ?? ?Z ? ?Z?￥
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 ? ì31 ?¨ @8￥ p –V –T ? ?￡ ?D'1" Té? w ?byN
 @8￥ p –V –T1"￥ù? ^B[×1￥$yTb 2.1 Bté￥ p –V –T1" Btéü? ?/￥ p –V –T1"
 V[V U1??w ?
?m 2
 1b 2 m 2
 1 Bté￥ p –V –Tm w ? s?Mu# MiubwL AC? BC}VAi￥H?L
 ? ìM??? C
 C? ^Bté￥ "??
 ? ??￥?aa ?? :8sY?1 "?? T c a "? a ? p c ? "?8 V c b | p –V –T w ?g??ü ? 
5 V[¤?=?m?bm 2
 2 ? 2
 3 sY1m 2
 1 g?￥ p –Tm? p –Vmb m 2
 3 Bté￥ p –Vm m 2
 2 Bté￥ p –Tm m 2
 2 ?￥?HMü?wL
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 3 ? V[ A
 "???L "??  ^B? ￡ü.?
| q?w q??? ,
 3 ?D V U1
 0= ? ? ? ? ? ? ? ? = C TT V p
2
 1
 0 2 2 = ? ? ? ? ? ? ? ? ? ? = C TT V p
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 2
 T
2
 1
?
2
 2
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 ? ì ?Z??￥ù?il×vb 2.2 8￥ ?Z? í ? @8 p –V -T1"￥f ? T1
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2
 3
 T
2
 3
?1 ?Z?
Equation of Satate
 EOS

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 ?Z? μdè×1￥N′
 ??? V U?<W￥S?= paVaT -W￥f ?1"
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1

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2

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? ú
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3

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4

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? L8 V[?T ?X8) ?
[e?ù5b ?X8 ?Z? ^Ke?￥ ?Z?
 RTpV =
2
 4
 μ H
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 V[¨ ?X8 ?Z?é?í ?￥ ?b 6?
 ? V[T1? ? L8 ?Z? ^???￥S-B
? →p 0? ∞→V H
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 μ?T L￥ ? ?$bZ?￥? T1
 "+′+′+′+== 32 1 pDpCpB RT pV Z
2
 5
 "++++= 32 1 V D V C V B
2
 6
 "++++= 32 1 ρρρ DCB
2
 7
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 )(BB ′ a )(CC ′ a )(DD ′ llsY?1?=a??a? 1ll? ú
virial
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2
 5
j
2
 7
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?]? T￥ virial" ?-Wi"/ ?1"
 RT B B =′
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 8a
 () 2 2 RT BC C ? =′
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 8b
 () 3 3 23 RT BBCD D +? =′
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 8c
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2
 5
j
2
 7
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 V B Z +=1
2
 9
 pB′+=1
2
 10a
 RT Bp +=1
2
 10b
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???? "??aa ??ú? 1.5MPa H
¨=¨ [￥? úZ? V[ ?ú?1V U8￥ p –V -T1"
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1

van der Waals  ?Z? 2 V a bV RT p ? ? =
2
 11
 ?Z? ^?B? a¨? L=8￥ ?Z?
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 ? ìsYV?s0W￥? ??s0' &8￥?Y
 V[V @8￥ p-V-T L ?  E?¤?
9 V[?Bté￥ "? ? 9 ?¤?b
2

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 )( 5.0 bVVT a bV RT p + ? ? =
2
 12
 T? a
 b1 RK? ?
D @8￥+?μ1
 V[¨/ T9 ?
 5 cc pTRa /42748.0 5.22 =
2
 13a
 cc pRTb /08664.0=
2
 13b
 RKZ?￥9 ??1 van der WaalsZ?μ?v￥4ú
 V[1??1¨?d? ?D???t
??<?#cμ_o￥??tˉ?á 3?v￥êμb1 éB?4ú RKZ?￥ú
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3

Soave-Redlish-Kwang Z?
1972M
 1 4ú RKZ??té#?A8 p –V –T9 ?￥?b Soave RKZ?é ? ?é
?1 RKS
 SRK
 Soave
Z?bZ?? T1
 ( ) ()bVV Ta bV RT p + ? ? =
2
 14
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 () ( ) ( )TpTRTaTa cc αα ?=?= /4278.0 22
2
 15a
 cc pRTb /08664.0=
2
 15b
 [ ] 2 5.0 )1(1)( r TmT ?+=α
2
 15c
 2 176.0574.1480.0 ωω ?+=m
2
 15d
 T?
 ω1ê?y0b RKSZ?4ú ?té#cμ_oté￥ p –V –T9 ?úb ÷?1￥ ^?Z? ?A8 á￥9 ??÷?b 1 L? ?¨9 ?p3
 RKZ?? RKSZ?9 V[V U?/ ? T
 ? ? ? ? ? ? + ? ? = h h B A h Z 11 1
2
 16a
 Z B V b h m ==
2
 16b
 T?
 RT bp B =
2
 16c
 5.22 TR ap A =
RKZ?

 22 TR ap A = (RKSZ? )
2
 16d
 ?¨  ?Z? V[é?Y}9 ?b
4

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 RobinsonZ? RKZ?? RKSZ?9 ? "?a êy0 Zc?A8 á H??C?v￥êμ
1  ???B üA￥?@
 Peng
 Robinson? 1976M4  e ì￥Z?
e? PRZ?b ( ) ()()bVbbVV Ta bV RT p ?++ ? ? =
2
 17
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 () () ( )TpTRTaTa cc αα ?=?= /45724.0 22
2
 18a
 cc pRTb /07780.0=
2
 18b
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2
 18c
 2 26992.054226.13746.0 ωω?+=k
2
 18d
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5

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 V[|V U1?/￥? T
 ))(( )( bVbV Ta bV RT p σε ++ ? ? =
2
 19
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 Webb
 RubinZ?
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 ?Z?9 ??1 ó^Q#
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2
 20
 T?
 ρ1 á
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2

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 ?Z? ^ 1955 M Martin ? q?áSD??? *4￥
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 b1 4ú?Z?ú áu￥ú?
 1981M?? *? q??|?Z?￥ a¨S? ?Z?AMu
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 7 ∑ = ? = 5 1 )( )( i i i bV Tf p
2
 21
 T? )/475.5exp()( ciiii TTCTBATf ?++=
52 ≤≤ i
 RTTf =)( 1
)1=i T?
 bCBA iii ,,, ￥1Z?￥è ?
 VVBté "?? ?#??awL ￥B? ? p¤b MH
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 rrrr TVVp 8)13)(/3( 2 =?+
2
 22
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 ??]￥ @8
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 ^dè?￥b?ü ^=? ?a ê y0m￥G b oμò?8￥ "?a êy0 Z c M?￥Hq/
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o a¨?o?d?￥e?s0b? z1 ?e ?￥?¨S? ?4ú9 ?ú￥μrZE ^e?1 ?e ?
=? ?1 ?e ?
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 ),,( crr ZpTfZ =
2
 24
 Lydersen ?|?  ?Qa?a ?a
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 )27.0( ' ?+= c ZDZZ
2
 25
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 Z1 27.0= c Z H @8￥a êy0b D1 27.0≠ c Z H￥n?" ?
 ? ì? ^ r T a r p ￥f ?
 V[VM?￥m?°b ?e ??ZE??¨? @8a êy0￥9 ?
] H? V¨?A81 á￥9 ?
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 )27.0( ?+=′ c ZDρρ
2
 26
 =a[ê?y0 ωT1??? ?￥? ?e ? " [ c Z T1??? ??
 Pitzer?|4￥ê?y0 ω¤? dè<W￥ P¨b Bté￥ê?y0 ^? té￥?a ??l￥b L?C
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' ? ? ? ? ? ? ? ? ?= r s r T p 1 1log α
2
 27
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 c s s r p p p = ??]￥ @8
 α μ?]￥′b?e? @8
bada_
￥ ?μ?a ?  ? ]BH°L 
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 1log ?= s r p ?B?b?ó? @81?a wL￥ê?
¨ r T =0.7￥ @8Dbada_
e?o?s0
￥ s r plog ′-μ ?V?b Pitzerü?Bμ′?l1ê?y0 ω
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2
 28
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 )1()0( ZZZ ω+=
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 29
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 )0( Z a )1( Z ? ^ r T a r p ￥f ?b V?M?￥m°b Pitzer 1" T?d?D?￥8?4 V L￥2T
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 P¨ H??÷F?ib 2.3.3 ?R? ?Z? ?ì?R? ?Z? ^·¨1? ? r T a r p a r V }9M  TapaV
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2
 30
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 31
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 32a
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 32b
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2
 29
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2
 30
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 11
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 36
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 37
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 45
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 46
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