Nothing Special   »   [go: up one dir, main page]

Tarea XI Termo

Descargar como xlsx, pdf o txt
Descargar como xlsx, pdf o txt
Está en la página 1de 42

Para el sistema etano (1)/propano (2) como gas calcule 𝑓 ̂_1,𝑓 ̂_2,∅ ̂_1,∅ ̂_2 a 50°C, P=30 bar y Y1=0.

35
a) Aplicando la ecuacion (11.63)
b) Suponiendo que la mezcla es una solucion ideal, estipule que todos los Kij = 0

DATOS Propieades Criticas


T (°C)P 50 T (°K) 323.15 Componente Tc (°K) Pc (bar)
P (bar) 30 P (bar) 30 Etano 305.3 48.72
K 0 Y1 0.35 Propano 369.8 42.48
Y2 0.65 R(cc*bar/(mol*K)) 83.14

Solucion
IJ Tcij (°K) Zcij Vcij (cc/mol) Pcij (bar) Wij Trij
11 305.30 0.279 145 48.8397 0.1 1.0585
22 369.80 0.276 200 42.4283 0.152 0.8739
12 336.01 0.278 171.028891 45.3263 0.126 0.9617

lnφ1 φ1 lnφ2 φ2 f1 f2
-0.15965373 0.85243891 -0.37217815 0.6892314422 8.95060861 13.4400131

Solucion ideal
φ1 φ2 f1 f2
1.0000 1.0000 10.5 19.5
, P=30 bar y Y1=0.35

Propieades Criticas
Vc/10-6 cc/mol Zc W
145 0.279 0.1
200 0.276 0.152

Bo Bl Bij δ12 (delta)


-0.3023 0.0035 -156.940197 33.0444646
-0.4406 -0.1640 -337.354462
-0.3662 -0.0636 -230.625098
DATOS
T(°C) 25 T(°K) 298.15 Componentes Xi
P(bar) 1 P(bar) 1 Co2 0.7
R (bar cm3/(mol K) 83.14 N2 0.3
R (bar m3/(mol K) 8.314E-05 1
1 bar m3 = 10^5 J

Vi (m3) n lnxi xi*lnxi As (bar m3/K) As(J/K)


0.7 40.341790169 -0.35667494 -0.24967246 0.0020488489 204.884891
0.3 -1.2039728 -0.36119184
-0.6108643
R (bar cc/mol*K) 83.14
Componente n (mol) Xi T (°C) T(°K) P (bar)
Nitrogeno 4 0.615 75 348.15 30
Argon 2.5 0.385 130 403.15 20
6.5

T N2 Ar2 diferencia
363.15 12471 12471 0

P Ec. Izquierda Ec. Derecha diferencia


24.381608998 8049.09518 8049.09518 6.30492E-06

Calculando entropia
1 (bar cc/mol*K) = 10^-1 J
(bar cc/K) (J/K)
AS --- N2 118.06119126 11.8061191
AS --- Ar2 -95.47146357 -9.54714636
AS mix 360.06353307 36.0063533
AS 382.65326075 38.2653261
Cv Cp Xi*LnXi
207.85 290.99 -0.29877404
124.71 207.85 -0.3675044
-0.66627844
R (bar cc/mol*K) 83.14
Componente Flujo (Kg/s) Flujo (g/s) Pm (g/mol) flujo molar Yi
(mol/s)
Nitrogeno 2 2000 28.014 71.392875 0.224
Hidrogeno 0.5 500 2.016 248.015873 0.776
319.408748 1
1 (bar cc/mol*K) = 10^-1 J

Yi*lnYi AS (bar AS (J/K)


cc/K)
-0.33488769 14109.5924 1410.959
-0.19643412
-0.53132181
4.¿Cuál es el trabajo ideal que se requiere para separar una mezcla equimolar de metano etano a ⟨𝐶_𝑃^𝑖𝑔 ⟩_𝑠/𝑅=
175°C y 3 bar en un proceso de flujo uniforme en dos corrientes de gases puros a 35°C y 1 bar si ((𝜏+1)/2)]((𝜏−
Talfa = 300 K?

∆𝑆=𝑅∗⟨𝐶_𝑃^𝑖𝑔 ⟩_𝑠/
datos
T(°K) 308.15 R(J/mol°k) 8.3145
To(°K) 448.15
P1 (bar) 1
P2 (bar) 1

comp compcicion A B C D τ
metano 0.5 1.702 0.009081 -2.164E-06 0 0.6876046
etano 0.5 1.131 0.019225 -5.561E-06 0

por lo tanto el trabajo ideal es -2429 J/mol


⟨𝐶_𝑃^𝑖𝑔 ⟩_𝑠/𝑅=𝐴+[𝐵𝑇_𝑂+(𝐶𝑇_0^2+𝐷/(𝜏^2 𝑇_0^2 )) ⟨𝐶_𝑃^𝑖𝑔 ⟩_𝐻/𝑅=𝐴+𝐵/2 𝑇_𝑂 (𝜏+1)+𝐶/3 𝑇_0^2
((𝜏+1)/2)]((𝜏−1)/(ln⁡(𝜏))) (𝜏^2+𝜏+1)+(𝐷/(𝜏𝑇_0^2 ))

∆𝑆=𝑅∗⟨𝐶_𝑃^𝑖𝑔 ⟩_𝑠/𝑅∗𝑙𝑛 𝑇/𝑇_0 −𝑃/𝑃_0


∆𝐻=𝑅∗(𝐶𝑃)𝐻(𝑇−𝑇_𝑂)

𝑤_𝑖𝑑𝑒𝑎𝑙=∆𝐻−𝑇_𝜎 ∆𝑆

Cp S CpH ΔS ΔH w ideal
3.75617414 4.82299919 -15.9987405 -7228.41754 -2428.79538
6.07361702 7.59664212
4.91 6.21
𝑂 (𝜏+1)+𝐶/3 𝑇_0^2
))
𝐵^𝑜=0.083−0.422⁄( 〖𝑇𝑟〗 ^1.6

DATOS Propieades Criticas


T (°C) 150 Componente Tc (°K) Pc (bar) W Tr
T(°K) 423.15 CO2 304.2 73.83 0.224 1.39102564

P (bar) Z Fi= (Z-1)/P Ai Lnφi φi fi


0 1 0 0 1 0
10 0.985 -0.0015 -0.0075 -0.0075 0.993 9.925
20 0.970 -0.0015 -0.0150 -0.0225 0.978 19.555
40 0.942 -0.00145 -0.0295 -0.0520 0.949 37.973
60 0.913 -0.00145 -0.0290 -0.0810 0.922 55.332
80 0.885 -0.0014375 -0.0289 -0.1099 0.896 71.676
100 0.869 -0.00131 -0.0275 -0.1374 0.872 87.167
200 0.765 -0.001175 -0.1243 -0.2616 0.770 153.964
300 0.762 -0.00079333 -0.0984 -0.3600 0.698 209.299
400 0.824 -0.00044 -0.0617 -0.4217 0.656 262.377
500 0.910 -0.00018 -0.0310 -0.4527 0.636 317.960
-0.4527

0.8
φi , φG(Pi)

φi
φG(Pi)
0.6
φi , φG(
φi
φG(Pi)
0.6

0.4
0 100 200 300 400 500 600
Pi (bar)
ln⁡〖∅ =∫1▒ 〖 (𝑧−1) 𝑑𝑃/𝑃=𝑃𝑟/𝑇𝑟 (𝐵^𝑜+𝜔𝐵^𝑙 ) 〗〗

^𝑜=0.083−0.422⁄( 〖𝑇𝑟〗 ^1.6 ) ; 𝐵^𝑙=0.139−0.172⁄( 〖𝑇𝑟〗 ^4.2 ) ; 𝑇𝑟=𝑇⁄𝑇𝑐 ; 𝑃𝑟=𝑃⁄𝑃𝑐

Bo Bl
-0.16587211 0.09599481

P (bar) Z Pr Lnφ φG(Pi) fG(Pi)


0 1 0 0 1 0
10 0.985 0.1354463 -0.01405746 0.98604089 9.86040887
20 0.970 0.27089259 -0.02811491 0.97227663 19.4455326
40 0.942 0.54178518 -0.05622983 0.94532185 37.8128739
60 0.913 0.81267777 -0.08434474 0.91911434 55.1468606
80 0.885 1.08357036 -0.11245966 0.8936334 71.4906718
100 0.869 1.35446296 -0.14057457 0.86885887 86.8858869
200 0.765 2.70892591 -0.28114915 0.75491573 150.983147
300 0.762 4.06338887 -0.42172372 0.65591523 196.77457
400 0.824 5.41785182 -0.56229829 0.56989777 227.959107
500 0.910 6.77231478 -0.70287286 0.49516073 247.580365

400

300
fi , fG(Pi)

200
fi
fG(Pi)

100
200

fi , fG(
fi
fG(Pi)

100

0
0 100 200 300 400 500 600
Pi (bar)
ln⁡〖∅ =∫1▒ 〖 (𝑧−1) 𝑑𝑃/𝑃=
DATOS
T (°K) 600
P (bar) 300

Propieades Criticas
Componente Tc (°K) Pc (bar) W Tr Pr
SO2 430.8 78.84 0.245 1.39275766 3.80517504

completar con tabla E15 y E16


Pr φ0 0.67216
Tr 3 3.80517504 5
1.3 0.6383 0.5383
1.39275766 φ0
1.4 0.7145 0.6237

Pr φ1 1.35424724
Tr 3 3.80517504 5
1.3 1.2853 1.3868
1.39275766 φ1
1.4 1.2942 1.4488
⁡〖∅ =∫1▒ 〖 (𝑧−1) 𝑑𝑃/𝑃=𝑃𝑟/𝑇𝑟 (𝐵^𝑜+𝜔𝐵^𝑙 ) 〗〗

∅=∅^0 〖 (∅^1) 〗 ^𝜔

φ fi GR/RT
0.72399817 217.199451 -0.32296642
ln⁡〖∅ =∫1▒ 〖

A) DATOS
T (°C)P 280 T (°K) 553.15
P (bar) 20 P (bar) 20 𝐵^𝑜=0.083−0.422⁄( 〖𝑇𝑟〗

Propieades Criticas
Componente Tc (°K) Pc (bar) W Tr Pr
isubutileno 417.9 40 0.194 1.32364202 0.5

B) DATOS
T (°C) 280 T (°K) 553.15
P (bar) 100 P (bar) 100

Propieades Criticas
Componente Tc (°K) Pc (bar) W Tr Pr
isubutileno 417.9 40 0.194 1.32364202 2.5

completar con tabla E15 y E16


Pr φ0 = 0.70226
Tr 2 2.5 3
1.3 0.7345 0.6383
1.3236420196 M
1.4 0.7925 0.7145

Pr φ1 = 1.46193447
Tr 2 2.5 3
1.3 1.776 1.2853
1.3236420196 M
1.4 1.1858 1.2942
ln⁡〖∅ =∫1▒ 〖 (𝑧−1) 𝑑𝑃/𝑃=𝑃𝑟/𝑇𝑟 (𝐵^𝑜+𝜔𝐵^𝑙 ) 〗〗

^𝑜=0.083−0.422⁄( 〖𝑇𝑟〗 ^1.6 ) ; 𝐵^𝑙=0.139−0.172⁄( 〖𝑇𝑟〗 ^4.2 ) ; 𝑇𝑟=𝑇⁄𝑇𝑐 ; 𝑃𝑟=𝑃⁄𝑃𝑐

Bo Bl lnφ φ fi
-0.18645086 0.08602242 -0.06412705 0.93788583 18.7577167

Según el profe
Bo Bl lnφ φ fi
-0.18645086 0.08602242 -0.32063525 0.7256879 72.56879

∅=∅^0 〖 (∅^1) 〗 ^𝜔

φ fi
0.75595561 75.5955608
𝐵^𝑜=0.083−0.422⁄( 〖𝑇𝑟〗 ^1.6 ) ; 𝐵^𝑙=0.139−0.172⁄( 〖𝑇𝑟〗

Pr,sat = Pi,sat/Pc
A) DATOS PV (bar) = presion de vap
T (°C) 110 T (°K) 383.15 PV (bar) R
P (bar) 275 P (bar) 275 5.267 83.14

Propieades Criticas
Componente Tc (°K) Pc (bar) Vc Zc W Tr
Ciclopentano 511.8 45.02 258 0.273 0.196 0.74863228

Pi,sat = 5.267
lnφi,sat -0.10534662
φi,sat 0.90001251
fi 11.7841834

B) DATOS PV (bar) = presion de vapor


V
T (°C) 120 T (°K) 393.15 P (bar) R
P (bar) 34 P (bar) 34 25.83 83.14 ln⁡〖∅ (𝑚𝑜𝑑)=∫1▒ 〖

Propieades Criticas
Componente Tc (°K) Pc (bar) Vc Zc W Tr
isubutileno 420 40.43 239.3 0.277 0.191 0.93607143

Pi,sat = 25.83
lnφi,sat -0.27495583
φi,sat 0.75960567
fi 20.28535
𝑉_𝑖^𝑠𝑎𝑡=𝑉_𝑐
〖𝑍𝑐〗 ^((1−𝑇𝑟)^(2

𝐵^𝑙=0.139−0.172⁄( 〖𝑇𝑟〗 ^4.2 ) ; 𝑇𝑟=𝑇⁄𝑇𝑐 ; 𝑃𝑟=𝑃⁄𝑃𝑐

ln⁡〖∅ (𝑚𝑜𝑑)=∫1▒ 〖 (𝑧−1) 𝑑𝑃/𝑃=(𝑃𝑟,𝑠𝑎𝑡)/𝑇𝑟 (𝐵^𝑜+𝜔𝐵^𝑙 ) 〗〗


Pr,sat = Pi,sat/Pc
PV (bar) = presion de vapor

Pr,sat Vi,sat Bo Bl
0.11699245 107.545777 -0.58762969 -0.44123049

V (bar) = presion de vapor

ln⁡〖∅ (𝑚𝑜𝑑)=∫1▒ 〖 (𝑧−1) 𝑑𝑃/𝑃=(𝑃𝑟,𝑠𝑎𝑟)/𝑇𝑟 (𝐵^𝑜+𝜔𝐵^𝑙 ) 〗〗

Pr,sat Vi,sat Bo Bl
0.63888202 133.299189 -0.38604884 -0.08800253
𝑉_𝑖^𝑠𝑎𝑡=𝑉_𝑐
〖𝑍𝑐〗 ^((1−𝑇𝑟)^(2⁄7) )
A) DATOS
T (°C)P 100 T (°K) 373.15
P (bar) 35 P (bar) 35
K 0 Y1 0.21
Y2 0.43
R(cc*bar/(mol*K)) 83.14 Y3 0.36

Solucion
IJ Tcij (°K) Zcij Vcij (cc/mol)
11 190.60 0.286 98.6
12 241.23 0.2825 120.5334969683
13 265.49 0.281 143.3784693222
21 241.23 0.283 120.5334969683
22 305.30 0.279 145.5
23 336.01 0.278 171.3078099766
31 265.49 0.281 143.3784693222
32 336.01 0.278 171.3078099766
33 369.80 0.276 200

Bpara Bpara 2 B para 3


0.5∑B para φ1 0.5∑B para φ3 0.5∑B para φ2
5.6287781377302 1.3425046829308 4.754396171954
4.7124654176346 2.3014365993099 9.735192161621
-3.635067270033 -8.150393437636 -2.748938160287
16.688900848493 1.7752654109463 2.120455907519
13.972103035947 3.0433121330509 4.341885905873
37.367180169772 0.312125388602 18.20299198668

B) DATOS
T (°C)P 100 T (°K) 373.15
P (bar) 35 P (bar) 35
K 0 Y1 0.21
Y2 0.43
R(cc*bar/(mol*K)) 83.14 Y3 0.36

Solucion
IJ Tcij (°K) Zcij Vcij (cc/mol)
11 190.60 0.286 98.6
12 241.23 0.2825 120.5334969683
13 265.49 0.281 143.3784693222
21 241.23 0.283 120.5334969683
22 305.30 0.279 145.5
23 336.01 0.278 171.3078099766
31 265.49 0.281 143.3784693222
32 336.01 0.278 171.3078099766
33 369.80 0.276 200
Propieades Criticas
Componente Tc (°K) Pc (bar) Vc/10-6 cc/mol Zc W
Metano 190.6 45.99 98.6 0.286 0.012
Etano 305.3 48.72 145.5 0.279 0.1
Propano 369.8 42.48 200 0.276 0.152

Pcij (bar) Wij Trij Bo Bl Bij δij (delta)


45.9644 0.012 1.9578 -0.061044 0.1287639 -20.5125803 0
47.0052 0.056 1.5469 -0.1270 0.1115 -51.5149657 30.4422831
43.2591 0.082 1.4055 -0.1618 0.0978 -78.4526352 107.809437
47.0052 0.056 1.5469 -0.1270 0.1115 -51.5149657 30.4422831
48.6719 0.1 1.2222 -0.2231 0.0650 -112.959634 0
45.2525 0.126 1.1105 -0.2738 0.0283 -166.839707 23.4823467
43.2591 0.082 1.4055 -0.1618 0.0978 -78.4526352 107.809437
45.2525 0.126 1.1105 -0.2738 0.0283 -166.839707 23.4823467
42.4283 0.152 1.0091 -0.3330 -0.0266 -244.202127 0

Lnφ1 Lnφ2 Lnφ3


0.01901486 -0.12708555 -0.2549654627

φ1 φ2 φ3
1.01919679 0.88065833 0.774943262

f1 f2 f3
7.4910964 13.2539079 9.7642851008

Propieades Criticas
Componente Tc (°K) Pc (bar) Vc/10-6 cc/mol Zc W
Metano 190.6 45.99 98.6 0.286 0.012
Etano 305.3 48.72 145.5 0.279 0.1
Propano 369.8 42.48 200 0.276 0.152

Pcij (bar) Wij Trij Bo Bl Bij δij (delta) Prk


45.9644 0.012 1.9578 -0.061044 0.1287639 -20.5125803 0 0.7614581
47.0052 0.056 1.5469 -0.1270 0.1115 -51.5149657 30.4422831
43.2591 0.082 1.4055 -0.1618 0.0978 -78.4526352 107.809437
47.0052 0.056 1.5469 -0.1270 0.1115 -51.5149657 30.4422831
48.6719 0.1 1.2222 -0.2231 0.0650 -112.959634 0 0.71910119
45.2525 0.126 1.1105 -0.2738 0.0283 -166.839707 23.4823467
43.2591 0.082 1.4055 -0.1618 0.0978 -78.4526352 107.809437
45.2525 0.126 1.1105 -0.2738 0.0283 -166.839707 23.4823467
42.4283 0.152 1.0091 -0.3330 -0.0266 -244.202127 0 0.82492038
Lnφ1 Lnφ2 Lnφ3
-0.02314168 -0.12743768 -0.27550153

φ1 φ2 φ3
0.97712404 0.88034828 0.75919127

f1 f2 f3
7.18186166 13.2492416 9.56580997
A) 𝐺^𝐸∕𝑅𝑇=( 〖− 2.6𝑥 〗 _1− 〖 1.8𝑥 〗 _2 ) 𝑥_1 𝑥_2
𝑥_2=1−𝑥_1

𝐺^𝐸∕𝑅𝑇=( 〖− 2.6𝑥 〗 _1−1.8(1−𝑥_1 )) 𝑥_1 (1−𝑥_1 )

𝐺^𝐸/𝑅𝑇=−1.8𝑥_1+ 〖𝑥 _1 〗 ^2+0.8 〖𝑥 _1 〗𝑀⁡〖


^3 =𝐺^𝐸/𝑅𝑇 〗
𝐺^𝐸/𝑅𝑇=𝑥_1 (−1.8+2𝑥

𝐺^𝐸/𝑅𝑇=−1.8𝑥_1+2 〖𝑥 _1 〗 ^2+
ln⁡〖𝛾 _1=𝐺^𝐸/𝑅𝑇+ 〗 (1−𝑥_1 ) ln⁡〖𝛾
(𝑑 𝐺^𝐸/𝑅𝑇)/(𝑑𝑥_1 )
_2=𝐺^𝐸/𝑅𝑇−𝑥_1 (𝑑 𝐺^𝐸/𝑅𝑇)/(𝑑𝑥_1 ) 〗

(𝑑 𝐺^𝐸/𝑅𝑇)/(𝑑𝑥_1 )=−1.8+2𝑥_1+2.4 〖𝑥 _1 〗 ^2

ln⁡〖𝛾 _1= 〗− 1.8+2𝑥_1+ 〖 1.4𝑥_1 〗 ^2−1.6 〖𝑥 _1 〗 ^3

ln⁡〖𝛾 _2= 〗−〖𝑥 _1 〗 ^2−1.6 〖𝑥 _1 〗 ^3


B)

𝐺^𝐸/𝑅𝑇=𝑥_1 (−1.8+2𝑥_1+ 〖 1.4𝑥_1 〗 ^2−1.6 〖𝑥 _1 〗 ^3 )+(1−𝑥_1 )(− 〖𝑥 _1 〗 ^2−1.6 〖𝑥 _1 〗 ^3)

/𝑅𝑇=−1.8𝑥_1+2 〖𝑥 _1 〗 ^2+1.4 〖𝑥 _1 〗 ^3−1.6 〖𝑥 _1 〗 ^4+− 〖𝑥 _1 〗 ^2−1.6 〖𝑥 _1 〗 ^3+ 〖𝑥 _1 〗 ^3+1.6 〖𝑥 _1 〗 ^4

𝐺^𝐸/𝑅𝑇=−1.8𝑥_1+ 〖𝑥 _1 〗 ^2+0.8 〖𝑥 _1 〗 ^3
𝑥 _1 〗 ^3+1.6 〖𝑥 _1 〗 ^4
DATOS
T (°C) 75 T (°K) 348.15 Componente Yi
P (bar) 2 P (bar) 2 propano 0.5
R 83.14 n-pentano 0.5

T (°C) T (°K) B11 B22 B12


50 323.15 -331 -980 -558
75 348.15 -276 -809 -466
100 373.15 -235 -684 -399

ij Bij B Z dBij/dT dB/dT


11 -276 -504.25 0.96515829 1.92 3.55
22 -809 5.92
12 -466 3.18

〖𝑑𝐵〗 _𝑖𝑗/𝑑𝑇=[■8(−276&−466@−466&−809)]
HR (bar SR (bar
HR/RT SRR cc/(mol ) cc/(mol k)) HR (J/mol) SR (J/mol K)
-0.12023984 -0.08539812 -3480.365 -7.1 -348.0365 -0.71
^ = 𝑃(𝐵_11+𝑦_2^2
ln⁡〖∅ ̂ _1=𝑃/𝑅𝑇
ln ∅ 1 ( 𝐵 + 𝑦 2 𝛿 )𝛿_12 𝑑𝑜𝑛𝑑𝑒
11 2 12
)𝑑𝑜𝑛𝑑𝑒
〗 𝛿 =2 𝐵 − 𝐵
𝛿_12=2𝐵_12−𝐵_
12 12
𝜔𝑖 +𝜔 𝑗
𝜔_𝑖𝑗=(𝜔_𝑖+𝜔_𝑗)/2 𝑅𝑇
𝜔𝑖𝑗 = 〖𝑇𝑐〗 _𝑖𝑗=( 〖𝑇𝑐〗 _𝑖 〖) 𝑇𝑐〗 _𝑗 )^(1∕2) (1−𝐾_𝑖𝑗) ∅ ̂_1=𝑓 ̂_1/(𝑌_1𝑓^𝑃) , ∅ ̂_2=𝑓 ̂
2 𝑓^ _
ln⁡〖∅ ̂ ln ^ 2= 𝑃(𝐵_22+𝑦_1^2
_2=𝑃/𝑅𝑇
∅ ( 𝐵22+ 𝑦 1 𝛿 12)𝛿_12 ) 〗 ∅
2 ^ 1= 1 , ∅ ^ 2= 2
𝑅𝑇 𝑌1𝑃 𝑌2𝑃
〖𝑍𝑐〗 _𝑖𝑗=(
𝑍𝑐〖 𝑍𝑐𝑍𝑐 + 𝑍𝑐〖𝑗 𝑍𝑐〖𝑇𝑐〗
〗𝐵_𝑖𝑗=(𝑅
𝑖_𝑖+ 〗 _𝑗)/2 𝑅 𝑇𝑐
_𝑖𝑗)/ 〖𝑖𝑗𝑃𝑐〗𝑜 _𝑖𝑗 (𝐵^𝑜+𝜔_𝑖𝑗
𝑙 𝐵^𝑙 )
𝑖𝑗 =
2 𝐵 𝑖𝑗 = ( 𝐵 + 𝜔𝑖𝑗 𝐵 )
𝑃𝑐 𝑖𝑗
_𝑖𝑗)/𝑉𝑐 𝑉𝑐〗 _𝑗 〗 ^(1∕3))/2)^3
3
〖𝑉𝑐〗
〖𝑃𝑐〗 _𝑖𝑗=( 〖𝑍𝑐〗 _𝑖𝑗𝑍𝑐 𝑅 𝑇𝑐 𝑖𝑗〖〖
_𝑖𝑗=((
𝑅 𝑖𝑗〖𝑇𝑐〗 〗 _𝑖 〗
〖𝑉𝑐〗 𝑉𝑐
1/3
_𝑖𝑗^(1∕3)+ 〖〖
+𝑉𝑐
1 /3

𝑃𝑐𝑖𝑗 =
𝑉𝑐 𝑖𝑗
𝑉𝑐 𝑖𝑗 =( 𝑖
2
𝑗
)
𝐵^𝑜=0.083−0.422⁄( 〖𝑇𝑟〗 _𝑖𝑗^1.6 ) ; 𝐵^𝑙=0.139−0.172⁄( 〖𝑇

𝑇=𝑇𝑐∗𝑇𝑟
𝑃=𝑃𝑐∗𝑃𝑟
𝑑𝑜𝑛𝑑𝑒
𝑑𝑜𝑛𝑑𝑒 𝛿 12=2 𝐵 12 − 𝐵11 − 𝐵 12
𝛿_12=2𝐵_12−𝐵_11−𝐵_12
∅ ̂_1=𝑓 ̂_1/(𝑌_1𝑓^𝑃) , ∅ ̂_2=𝑓 ̂
𝑓^ _2/(𝑌_2 𝑃)
∅^ 1= 1 , ∅ ^ 2= 2
𝑌1𝑃 𝑌2𝑃

6 ) ; 𝐵^𝑙=0.139−0.172⁄( 〖𝑇𝑟〗 _𝑖𝑗^4.2 ) ; 〖𝑇𝑟〗 _𝑖𝑗=𝑇⁄ 〖𝑇𝑐〗 _𝑖𝑗 ; 〖𝑃𝑟〗 _𝑖𝑗=𝑃⁄ 〖𝑃𝑐〗 _𝑖𝑗

=𝑇𝑐∗𝑇𝑟
=𝑃𝑐∗𝑃𝑟

También podría gustarte