topic 8 property cet

8/19/2019 Topic 8 Property CET

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The Advanced ChemicalEngineering Thermodynamics

The thermodynamics properties offluids (II)

Q&A_-10- 11/17/2005(10)

Ji-Sheng Chang


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Property relations

The residual Gibbs ree energ! The deini"i#n # residual $r#$er"ies

%& (T') %(T') - %*G(T')

+ esidual $r#$er"!

*G + *deal gas beha,i#r $r#$er"!

%&

(T') %(T') - %*G

(T')'% are "he $r#$er"ies as ' G' .' S'


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Property relations

The residual $r#$er"ies & (T') (T') - *G(T') - T/

asi "her3#d!na3is rela"i#nshi$ #ralula"i#ns

G& (T') G(T') - G*G(T')%#re i3$#r"an" in "radi"i#nal Che3ial4ngineering Ther3#d!na3is

.& (T') .(T') - .*G(T')


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Property relations

eri,ing "he residual $r#$er"ies in"er3s # "he T $r#$er"ies6

r#3 "he genera"ing un"i#n # Gibbsree energ!' & /T 8∂(G& /T)/∂9T'

Then d(G& /T) (& /T)d'

"# in"egra"e r#3 0 "# a" #ns"an" T6


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Property relations

The in"egra"ed resul" in "er3s # T$r#$er"! as "he #r3ula (:6;5)

T)(constant,)1(0∫ −= P

R

P

dP Z

RT

G

T)(constant,)1

(0∫ −=

P R

dP P RT

V

RT

G


6/28

Property relations

The residual en"hal$!' .& /T - T8∂(G& /T)/∂T9'The in"egra"ed resul" in "er3s # T$r#$er"! as "he #r3ula (:6;:)

T)(constant,0∫

∂∂−= P

P

R

P

dP

T

Z T RT

H


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Property relations

*n $re,i#us se"i#n S ./T - G/T'"hen "he residual en"r#$! S& / .& /T - G& /TThe resul" in "er3s # T $r#$er"!as "he #r3ula (:6;


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Property relations

=sing "he inde$enden" $r#$er"! # Tand

%#re #33#nl! as "he #r3 ('T) #"he T e>ua"i#ns # s"a"e' es$eiall!"he ubi e>ua"i#ns # s"a"e6

?T/' ?ρT as ρ 1/

dTd(?ρ)T(?dρ@ρd?)a" #ns"an" T


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Property relations

d/dρ /ρ@d?/?' as "he #r3ula (:65


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Property relations

Calula"ing "he residual $r#$er"ies The T da"a'

=sing gra$hial in"egra"i#n 3e"h#d "#

alula"e "he residual Gibbs ree energ! r#3s"ea3 da"a6

T)(constant,1

0∫

−

= P

R

dP P

Z

RT

G


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Phase diagram

0 2 0 0 4 0 0 0 0 ! 0 0 " 0 0 0

T #$

0

" 0 0

2 0 0

% 0 0

4 0 0

& 0 0

P

# '

a

r

S#lidi>uid

Gas

C'TC

16 T $hase diagra3 # Ba"er

26 The S#lid/i>uid e>uilibriu3 ur,e

#r Ba"er

#r 3#s" #3$#nen"

200C $a"h

Cri"ial $r#$er"ies

C220655 bar

TC:;761 D

TTri27E61: D


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apor#i*uid e*uili'rium curve

The An"#ine e>ua"i#n The #ns"an" # An"#ine

e>ua"i#n #r Ba"er A1:6E


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Property

Cri"ial $r#$er"ies # Ba"er

C220655 bar

TC:;761 D

Tri06:11 a

TTri27E61: D TnE7E615 D

a" 1601E25 bar 1 a"3


14/28

Property relations

r#ble3s

Calula"e "he residual Gibbs

energ! # "he 200°C su$erhea"s"ea3 a" 10 bar' using "he Tda"a r#3 s"ea3 "ables


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Properties

P/kPa P/bar V/cm3g-

1

V/cm3mol-1

Z (Z-1)/P

1 0.01 218350 3933575 0.999951 -0.00493

50 0.5 4356.0 78473.34 0.997432 -0.00514100 1 2172.3 39133.98 0.994822 -0.00518

200 2 1080.4 19463.41 0.989555 -0.00522

300 3 716.35 12905.05 0.984174 -0.00528

400 4 534.26 9624.694 0.978674 -0.00533500 5 424.96 7655.654 0.973069 -0.00539

600 6 352.04 6342.001 0.967317 -0.00545

700 7 299.92 5403.059 0.961455 -0.00551

800 8 260.79 4698.132 0.955446 -0.00557


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Properties

P/kPa P/bar V/cm3g-

1

V/cm3mol-1

Z (Z-1)/P

900 9 230.32 4149.215 0.949291 -0.00563

1000 10 205.92 3709.649 0.943027 -0.0057

1100 11 185.92 3349.349 0.936579 -0.00577

1200 12 169.23 3048.678 0.930002 -0.00583

1300 13 155.09 2793.946 0.923321 -0.0059

1400 14 142.94 2575.064 0.916447 -0.005971500 15 132.38 2384.826 0.909367 -0.00604

1550 15.5 127.61 2298.894 0.90582 -0.00608

1554.9 15.55 127.20 2291.508 0.905764 -0.00606


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+esidual ,i''s free energy

properties

0 4 ! " 2 " 2 0P - ' a r .

/ 0 0 0 !

/ 0 0 0

/ 0 0 0 4

/ 0 0 0 2

0

( 1

/ "

) # P

-

'

a

r /

"

.

, + # + T o f s u p e r h e a t s te a m

2 0 0 C


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E3ample "

Calula"ing "he residual $r#$er"ies The T e>ua"i#ns # s"a"e

=sing "he "B# "er3 ,irial e>ua"i#n #s"a"es' es"i3a"e "he 3#lar ,#lu3e'residual en"hal$!' residual en"r#$!' andresidual Gibbs ree energ! # "hecarbon dioxide a" "he s"a"es #

"e3$era"ure # 25°C and $ressure # 1bar6


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eriving the

formulas

The e>ua"i#ns #residual Gibbs reeenerg!

Three "!$e # "he

"B# "er3 ,iriale>ua"i#n

The residual Gibbsree energ! #r a gasa" eah and T


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eriving the

formulas

Se#nd ,irial#eiien" r#3 T da"a

r#3 generaliHed

#rrela"i#ne>ua"i#ns

ased 3#leular

"her3#d!na3i' i"is in"egra"ed r#3$#"en"ial un"i#n


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E3ample 2


=sing "he "B# "er3 ,irial e>ua"i#n #s"a"es' es"i3a"e "he 3#lar ,#lu3e'residual en"hal$!' residual en"r#$!' andresidual Gibbs ree energ! # "hemethane a" "he s"a"es # "e3$era"ure

# 25°C and $ressure # 1 bar6


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E3ample %


(？ )=sing "he "B# "er3 ,irial e>ua"i#n #s"a"es' es"i3a"e "he 3#lar ,#lu3e'residual en"hal$!' residual en"r#$!' andresidual Gibbs ree energ! # "he

benzene a" "he s"a"es # "e3$era"ure# 25°C and $ressure # 1 bar6


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Theorem of

corresponding states

TB#-$ara3e"er "he#re3 ##rres$#nding s"a"es

Gi,en T and inding T'

Calula"e Tr' r

=sing Tr' r "# inding "he redued$r#$er"ies r#3 Table 461 "# 461:


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Theorem of


Three-$ara3e"er "he#re3 ##rres$#nding s"a"es

Gi,en T and inding T' ' ω Calula"e Tr' r

=sing Tr' r' ω "# inding "heredued $r#$er"ies r#3 Table 461 "#461:


25/28

Theorem of


ased #n "he #rres$#nding s"a"es$rini$les The ee/Desler generaliHed #rrela"i#n

"ables' A$$endiI 4 a" "eI" b##s # $agesr#3 :F5 "# 7116

The $r#$er"ies # s#3e $ure s$eies"ables' A$$endiI a" "eI" b##s # $agesr#3 :7F "# :


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E3ample 4

A$$lia"i#n # "he "he#re3 ##rres$#nding s"a"es "# es"i3a"e "he"her3#d!na3is $r#$er"ies # "he

$ure #3$#nen"s6 A" "e3$era"ure # 25°C and $ressure # 1

bar' es"i3a"e "he 3#lar ,#lu3e' residualen"hal$!' residual en"r#$!' and residual

Gibbs ree energ! # "he carbon dioxide6


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E3ample &


$ure #3$#nen"s6 A" "e3$era"ure # 25°C and $ressure # 1

bar' es"i3a"e "he 3#lar ,#lu3e' residualen"hal$!' residual en"r#$!' and residual

Gibbs ree energ! # "he methane6


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E3ample


$ure #3$#nen"s6 (？ )

A" "e3$era"ure # 25°C and $ressure # 1bar' es"i3a"e "he 3#lar ,#lu3e' residualen"hal$!' residual en"r#$!' and residualGibbs ree energ! # "he benzene6

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