metodos numericos jose gonzalez cod 2063307
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Ti 375 Vm 1.70725 b 0.0010538
Tf 378 Tc 647.1 a 1.84972488
f(t) #REF! Pc 22048.32 w 0.345
Iteraciones a g(a) b m g(m)
0 375 -0.304369209 378 376.5 0.1053521 375 -0.304369209 376.5 375.75 -0.099507
2 375.75 -0.099507106 376.5 376.125 0.002923
3 375.75 -0.099507106 376.125 375.9375 -0.048292
4 375.9375 -0.048292067 376.125 376.0313 -0.022685
5 376.03125 -0.02268462 376.125 376.0781 -0.009881
6 376.078125 -0.009880915 376.125 376.1016 -0.003479
7 376.101563 -0.003479067 376.125 376.1133 -0.000278
8 376.113281 -0.000278144 376.125 376.1191 0.001322
9 376.113281 -0.000278144 376.1191 376.1162 0.000522
10 376.113281 -0.000278144 376.1162 376.1147 0.000122
11 376.113281 -0.000278144 376.1147 376.114 -7.81E-05
12 376.114014 -7.80863E-05 376.1147 376.1144 2.19E-05
13 376.114014 -7.80863E-05 376.1144 376.1142 -2.81E-05
14 376.114197 -2.80719E-05 376.1144 376.1143 -3.06E-06
15 376.114288 -3.06469E-06 376.1144 376.1143 9.44E-06
16 376.114288 -3.06469E-06 376.1143 376.1143 3.19E-06
17 376.114288 -3.06469E-06 376.1143 376.1143 6.12E-0818 376.114288 -3.06469E-06 376.1143 376.1143 -1.5E-06
19 376.114294 -1.50174E-06 376.1143 376.1143 -7.2E-07
20 376.114297 -7.20261E-07 376.1143 376.1143 -3.3E-07
21 376.114298 -3.29523E-07 376.1143 376.1143 -1.34E-07
Ecuaciones no lineales
1. La temperatura con la ecuacin de peng robinson dado la P, Vm y las propiedades
crticas (Tc, Pc y w). R = constante de los gases (8,31451 J/molK)
METODO DE BISECCION
0.0025
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0
0.0005
0.001
0.0015
0.002
0 2 4 6 8 10 12
ERROR
ITERACIONES
Series1
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Vm^2-2bVm-b^2 2.91110325
R/(Vm-b) 0.270502302
p 100
g(a)*g(m) error
-0.03206587 0.0019960.030286899 0.000997
-0.000290837 0.0004988
0.004805404 0.0002493
0.001095487 0.0001246
0.000224145 6.232E-05
3.43764E-05 3.116E-05
9.67681E-07 1.558E-05
-3.67795E-07 7.789E-06
-1.45215E-07 3.895E-06
-3.39256E-08 1.947E-06
2.17192E-08 9.737E-07
-1.71341E-09 4.868E-07
2.19203E-09 2.434E-07
8.60315E-11 1.217E-07
-2.89273E-11 6.085E-08
-9.76751E-12 3.043E-08
-1.87604E-13 1.521E-084.60235E-12 7.607E-09
1.08164E-12 3.803E-09
2.37342E-13 1.902E-09
4.42069E-14 #DIV/0!
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ITERACION ERROR
0 0.002
1 0.001
2 0.00012
3 6.20E-05
4 3.10E-05
5 1.60E-05
6 7.80E-06
7 3.90E-06
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Ti 375 Vm 1.70725 b
Tf 378 Tc 647.1 a
f(t) -104.296 Pc 22048.32 wxi 375
f(X) -2.4622E-10
Iteraciones xi g(xi) g'(xi) xi+1 error
0 375 -0.304369209 0.294727 376.0327 0.304369
1 376.0327 -0.022284047 0.29466 376.1083 0.022284
2 376.1083 -0.00162707 0.294655 376.1139 0.001627
3 376.1139 -0.000118777 0.294655 376.1143 0.000119
4 376.1143 -8.67065E-06 0.294655 376.1143 8.67E-06
5 376.1143 -6.32952E-07 0.294655 376.1143 6.33E-07
6 376.1143 -4.62051E-08 0.294655 376.1143 4.62E-08
7 376.1143 -3.37295E-09 0.294655 376.1143 3.37E-098 376.1143 -2.46217E-10 0.294655 376.1143 2.46E-10
9 376.1143 -1.79767E-11 0.294655 376.1143 1.8E-11
10 376.1143 -1.32161E-12 0.294655 376.1143 1.32E-12
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 2 4 6 8 10 12
ERROR
ITERACIONES
Series1
METODO DE NEWTON RAPSON
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0.001054 Vm^2-2bV 2.911103
1.849725 R/(Vm-b) 0.270502
0.345 p 100
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g 9.8 c ? v 50
m 68.1 t 28
Iteracion a g(a) b m g(m)
0 13 1.091966 14 13.5 -0.7565
1 13 1.091966 13.5 13.25 0.151443
2 13.25 0.151443 13.5 13.375 -0.3065
3 13.25 0.151443 13.375 13.3125 -0.07853
4 13.25 0.151443 13.3125 13.28125 0.036202
5 13.28125 0.036202 13.3125 13.29688 -0.021236 13.28125 0.036202 13.29688 13.28906 0.007471
7 13.28906 0.007471 13.29688 13.29297 -0.00688
8 13.28906 0.007471 13.29297 13.29102 0.000293
9 13.29102 0.000293 13.29297 13.29199 -0.0033
10 13.29102 0.000293 13.29199 13.2915 -0.0015
11 13.29102 0.000293 13.2915 13.29126 -0.0006
12 13.29102 0.000293 13.29126 13.29114 -0.00016
13 13.29102 0.000293 13.29114 13.29108 6.84E-05
14 13.29108 6.84E-05 13.29114 13.29111 -4.4E-05
15 13.29108 6.84E-05 13.29111 13.29109 1.23E-05
16 13.29109 1.23E-05 13.29111 13.2911 -1.6E-05
17 13.29109 1.23E-05 13.2911 13.2911 -1.7E-06
18 13.29109 1.23E-05 13.2911 13.29109 5.3E-06
19 13.29109 5.3E-06 13.2911 13.29109 1.8E-06
20 13.29109 1.8E-06 13.2911 13.2911 4.66E-08
2. Modelo de cada libre
Un paracaidista con masa, m = 68.1 kg salta de un globo fijo y a los 28 segu
adquiere una velocidad de 50 m/s. Si la aceleracin debida a la gravedad es
m/s2, Cul es el coeficiente de resistencia (kg/s)?.
2a Ley de Newton F = m x a. Despejando a y representndola como la razn
cambio de la velocidad respecto altiempo.dv/dt = F/m ; F = FD + FU ;FD = mg ;FU = -cv ; dv/dt = (mg - cv) / m
Simplificando: dv/dt = g - cv / m
EDO que relaciona la aceleracin de un cuerpo que cae, con las fuerzas que
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21 13.2911 4.66E-08 13.2911 13.2911 -8.3E-07
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
0 5 10 15 20 25
ERROR
ITERACIONES
Series1
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-3.9E-14 #DIV/0!
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xi 15
f(X) 0
Iteraciones xi g(xi) g'(xi) xi+1 error
0 15 -5.60129 -2.934 13.0909 5.601285
1 13.0909 0.746108 -3.81589 13.28643 0.746108
2 13.28643 0.01715 -3.709 13.29105 0.017153 13.29105 0.000154 -3.70653 13.29109 0.000154
4 13.29109 1.33E-06 -3.7065 13.2911 1.33E-06
5 13.2911 1.15E-08 -3.7065 13.2911 1.15E-08
6 13.2911 9.89E-11 -3.7065 13.2911 9.89E-11
7 13.2911 8.6E-13 -3.7065 13.2911 8.6E-13
8 13.2911 0 -3.7065 13.2911 0
9 13.2911 0 -3.7065 13.2911 0
10 13.2911 0 -3.7065 13.2911 0
METODO DE NEWTON RAPSON
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AbrevaderoMtodo Secante
Datos
Longitud 160
Diametro 80
Volumen 386000
Radio 40 Iter Xi g(Xi) Xi+1 g(xi+1) xi+2 Error Iterati
1 0.1 0.2 13563.8703 0.1 -
2 0.2 13563.8703 0.1 14843.861 1.2596851 14843.861
3 0.1 14843.861 1.2596851 2.55599429 1.25988482 2.55599429
4 1.2596851 2.55599429 1.25988482 0.00080936 1.25988488 0.00080936
5 1.25988482 0.00080936 1.25988488 0 1.25988488 0
6 1.25988488 0 1.25988488 0 #DIV/0! 0
7 1.25988488 0 #DIV/0! #DIV/0! #DIV/0! #DIV/0!
8 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
9 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!10 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
11 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
12 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
13 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
14 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
15 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
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Error Abs
92.061508
0.01585247
5.0213E-06
0
#DIV/0!
#DIV/0!
#DIV/0!
#DIV/0!
#DIV/0!#DIV/0!
#DIV/0!
#DIV/0!
#DIV/0!
#DIV/0!
#DIV/0!
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AbrevaderoMtodo BiseccinDatos
Longitud 160
Diametro 80
Volumen 386000
Radio 40
Iter Xa g(Xa) Xb g(xb) m1 1 3325.19312 2 -9465.46967 1.5
2 1 3325.19312 1.5 -3071.63939 1.25
3 1.25 126.464208 1.5 -3071.63939 1.375
4 1.25 126.464208 1.375 -1472.67358 1.3125
5 1.25 126.464208 1.3125 -673.125205 1.28125
6 1.25 126.464208 1.28125 -273.335506 1.265625
7 1.25 126.464208 1.265625 -73.4368857 1.2578125
8 1.2578125 26.5133538 1.265625 -73.4368857 1.26171875
9 1.2578125 26.5133538 1.26171875 -23.461843 1.25976563
10 1.25976563 1.52573614 1.26171875 -23.461843 1.2607421911 1.25976563 1.52573614 1.26074219 -10.9680583 1.26025391
12 1.25976563 1.52573614 1.26025391 -4.72116226 1.26000977
13 1.25976563 1.52573614 1.26000977 -1.59771336 1.2598877
14 1.25976563 1.52573614 1.2598877 -0.03598868 1.25982666
15 1.25982666 0.74487371 1.2598877 -0.03598868 1.25985718
16 1.25985718 0.35444251 1.2598877 -0.03598868 1.25987244
17 1.25987244 0.15922691 1.2598877 -0.03598868 1.25988007
18 1.25988007 0.06161911 1.2598877 -0.03598868 1.25988388
19 1.25988388 0.01281521 1.2598877 -0.03598868 1.25988579
20 1.25988388 0.01281521 1.25988579 -0.01158673 1.25988483
21 1.25988483 0.00061424 1.25988579 -0.01158673 1.25988531
22 1.25988483 0.00061424 1.25988531 -0.00548625 1.25988507
23 1.25988483 0.00061424 1.25988507 -0.002436 1.25988495
24 1.25988483 0.00061424 1.25988495 -0.00091088 1.25988489
25 1.25988483 0.00061424 1.25988489 -0.00014832 1.25988486
26 1.25988486 0.00023296 1.25988489 -0.00014832 1.25988488
27 1.25988488 4.2319E-05 1.25988489 -0.00014832 1.25988489
28 1.25988488 4.2319E-05 1.25988489 -5.3001E-05 1.25988488
29 1.25988488 4.2319E-05 1.25988488 -5.3411E-06 1.25988488
30 1.25988488 1.8489E-05 1.25988488 -5.3411E-06 1.25988488
31 1.25988488 6.574E-06 1.25988488 -5.3411E-06 1.2598848832 1.25988488 6.1642E-07 1.25988488 -5.3411E-06 1.25988488
33 1.25988488 6.1642E-07 1.25988488 -2.3623E-06 1.25988488
34 1.25988488 6.1642E-07 1.25988488 -8.73E-07 1.25988488
35 1.25988488 6.1642E-07 1.25988488 -1.2817E-07 1.25988488
36 1.25988488 2.4412E-07 1.25988488 -1.2817E-07 1.25988488
37 1.25988488 5.7917E-08 1.25988488 -1.2817E-07 1.25988488
38 1.25988488 5.7917E-08 1.25988488 -3.5157E-08 1.25988488
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g(m) g(Xa)*g(m)Error Itera Error Abs-3071.63939 -10213794.2 - 20
126.464208 420517.913 20 9.09090909
-1472.67358 -186240.498 9.09090909 4.76190476
-673.125205 -85126.2458 4.76190476 2.43902439
-273.335506 -34567.1582 2.43902439 1.2345679
-73.4368857 -9287.13758 1.2345679 0.62111801
26.5133538 3352.99028 0.62111801 0.30959752
-23.461843 -622.052144 0.30959752 0.15503876
1.52573614 40.4523821 0.15503876 0.07745933
-10.9680583 -16.7343629 0.07745933 0.03874467-4.72116226 -7.20324789 0.03874467 0.01937609
-1.59771336 -2.43768902 0.01937609 0.00968898
-0.03598868 -0.05490924 0.00968898 0.00484473
0.74487371 1.13648074 0.00484473 0.0024223
0.35444251 0.26401491 0.0024223 0.00121114
0.15922691 0.05643679 0.00121114 0.00060557
0.06161911 0.00981142 0.00060557 0.00030278
0.01281521 0.00078966 0.00030278 0.00015139
-0.01158673 -0.00014849 0.00015139 7.5695E-05
0.00061424 7.8716E-06 7.5695E-05 3.7848E-05
-0.00548625 -3.3699E-06 3.7848E-05 1.8924E-05
-0.002436 -1.4963E-06 1.8924E-05 9.4619E-06
-0.00091088 -5.595E-07 9.4619E-06 4.731E-06
-0.00014832 -9.1105E-08 4.731E-06 2.3655E-06
0.00023296 1.4309E-07 2.3655E-06 1.1827E-06
4.2319E-05 9.8586E-09 1.1827E-06 5.9137E-07
-5.3001E-05 -2.243E-09 5.9137E-07 2.9568E-07
-5.3411E-06 -2.2603E-10 2.9568E-07 1.4784E-07
1.8489E-05 7.8243E-10 1.4784E-07 7.3921E-08
6.574E-06 1.2155E-10 7.3921E-08 3.6961E-08
6.1642E-07 4.0523E-12 3.6961E-08 1.848E-08-2.3623E-06 -1.4562E-12 1.848E-08 9.2402E-09
-8.73E-07 -5.3813E-13 9.2402E-09 4.6201E-09
-1.2817E-07 -7.9008E-14 4.6201E-09 2.31E-09
2.4412E-07 1.5048E-13 2.31E-09 1.155E-09
5.7917E-08 1.4139E-14 1.155E-09 5.7751E-10
-3.5157E-08 -2.0362E-15 5.7751E-10 2.8875E-10
1.135E-08 6.5738E-16 2.8875E-10 #DIV/0!
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metodo de newton para sistemas no lineales
0.4 2 -0.48952 0.979048
1.2214 1 0.597905 -0.19581
-0.4895 0.97905 2.96 -2.644732
0.5979 -0.1958 -1.2214 2.008934
1.
( + ) = ;
+ =
2.
+ = ;
+ =
,
,
= ,
y=1
=A =
( = , , = ) = + = , ; = , , = = + = ,
= = =
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ITERACION
1
X 0.2 Y 1
PASO 1 0.4 2 PASO 2 -0.48952 0.979046 2.961.221403 1 0.597905 -0.195809 -1.2214
PASO 3 2.96 -0.48952 0.979046 -2.644797
-1.2214 0.597905 -0.19581 2.008959
PASO 4 0.2 -2.6448 -2.444797
1 2.008959 3.008959
2
X -2.4448 Y 3.008959
PASO 1 -4.88959 6.017919 PASO 2 -0.18479 1 .112038 -11.0309
0.086744 1 0.016029 0.903538 -2.0957
PASO 3 -11.0309 -0.18479 1.112038 -0.292132
-2.0957 0.016029 0.903538 -2.070363
=
+ =
=
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PASO 4 -2.4448 -0.29213 -2.736929
3.008959 -2.07036 0.938597
3
X -2.73693 Y 0.938597
PASO 1 -5.47386 1.877194 PASO 2 -0.17872 0 .335486 -4.37174
0.064769 1 0.011575 0.978271 -0.00337
PASO 3 -4.37174 -0.17872 0.335486 0.780175
-0.00337 0.011575 0.978271 -0.053897
PASO 4 -2.73693 0.780175 -1.956753
0.938597 -0.0539 0.8847
4X -1.95675 Y 0.8847
PASO 1 -3.91351 1.7694 PASO 2 -0.24018 0.424974 -0.61158
0.141316 1 0.033941 0.939944 -0.02602
PASO 3 -0.61158 -0.24018 0.424974 0.135832
-0.02602 0.033941 0.939944 -0.045212
+ =
=
+ =
=
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PASO 4 -1.95675 0.135832 -1.820921
0.8847 -0.04521 0.839488
5
X -1.82092 Y 0.839488
PASO 1 -3.64184 1.678976 PASO 2 -0.25552 0 .429008 -0.02049
0.161877 1 0.041362 0.930554 -0.00136
PASO 3 -0.02049 -0.25552 0.429008 0.004651
-0.00136 0.041362 0.930554 -0.002118
PASO 4 -1.82092 0.004651 -1.81627
0.839488 -0.00212 0.837371
6X -1.81627 Y 0.837371
PASO 1 -3.63254 1.674741 PASO 2 -0.25609 0 .428881 -2.6E-05
0.162631 1 0.041648 0.93025 -1.8E-06
PASO 3 -2.6E-05 -0.25609 0.428881 5.94E-06
-1.8E-06 0.041648 0.93025 -2.72E-06
+ =
=
+ =
=
=
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PASO 4 -1.81627 5.94E-06 -1.816264
0.837371 -2.7E-06 0.837368
+ =+ = = ,
= ,
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con x=1con y=1
con z=1
X 1 Y 1 z 1
-1 3 1 0.21844565 0.2815543 0.34466305 0.34
1.
+ , = ;
+ , = + ;
, = ;
, = ;
, =
3.
+ , = ;
+ , = ;
+ ,
+
1 3 11 1 2
1
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PASO 1 1 1 -2 PASO 2 0.31692081 0.1830792 0.04923758 0.09
2.718282 -2.71828 1 0.26768323 -0.2676832 0.19695031 -0.59
norma
0.34 0.2184457 0.2815543 0.34466305 -0.1037398 0.115228
PASO 3 0.09 0.3169208 0.1830792 0.04923758 0.09518003
-0.59 0.2676832 -0.2676832 0.19695031 -0.0492799
1 -0.1037398 0.89626
PASO 4 1 0.09518 1.09518
1 -0.0492799 0.95072
X 0.89626 Y 1.09518 z 0.95072
-0.75131 3.042453 0.981566 0.2389304 0.3048389 0.3451069 0.07301
PASO 1 1.09518 1 -1.90144 PASO 2 0.29348846 0.1609893 0.01803313 0.012302
2.450422 -2.98972 1 0.29196829 -0.2656709 0.20825651 -0.00142
norma
0.0730105 0.2389304 0.3048389 0.3451069 0.02070425 0.021566
PASO 3 0.0123025 0.2934885 0.1609893 0.01803313 0.02338267
-0.001421 0.2919683 -0.2656709 0.20825651 0.01775238
0.89626 0.0207042 0.916964
=
+ =
=
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PASO 4 1.09518 0.0233827 1.118563
0.95072 0.0177524 0.968473
X 0.89626 Y 1.09518 z 0.95072
-0.75131 3.042453 0.981566 0.2389304 0.3048389 0.3451069 0.07301PASO 1 1.09518 1 -1.90144 PASO 2 0.29348846 0.1609893 0.01803313 0.012302
2.450422 -2.98972 1 0.29196829 -0.2656709 0.20825651 -0.00142
norma
0.0730105 0.2389304 0.3048389 0.3451069 0.02070425 0.021566
PASO 3 0.0123025 0.2934885 0.1609893 0.01803313 0.02338267
-0.001421 0.2919683 -0.2656709 0.20825651 0.01775238
0.89626 0.0207042 0.916964
PASO 4 1.09518 0.0233827 1.118563
0.95072 0.0177524 0.968473
X 0.89626 Y 1.09518 z 0.95072
-0.75131 3.042453 0.981566 0.2389304 0.3048389 0.3451069 0.07301
PASO 1 1.09518 1 -1.90144 PASO 2 0.29348846 0.1609893 0.01803313 0.012302
2.450422 -2.98972 1 0.29196829 -0.2656709 0.20825651 -0.00142
=
=
+ =
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norma
0.0730105 0.2389304 0.3048389 0.3451069 0.02070425 0.021566
PASO 3 0.0123025 0.2934885 0.1609893 0.01803313 0.02338267
-0.001421 0.2919683 -0.2656709 0.20825651 0.01775238
0.89626 0.0207042 0.916964
PASO 4 1.09518 0.0233827 1.1185630.95072 0.0177524 0.968473
X 0.916964 Y 1.118563 z 0.968473
-0.75063 3.12518 1.025682 0.23447044 0.2980517 0.33681757 -0.05709
PASO 1 1.118563 1 -1.93695 PASO 2 0.28377567 0.1578019 0.01459002 0.002257
2.501685 -3.06045 1 0.28191072 -0.2626861 0.20204064 0.000295
norma
-0.057093 0.2344704 0.2980517 0.33681757 -0.0126147 0.013142
PASO 3 0.0022567 0.2837757 0.1578019 0.01459002 -0.0158412
0.0002949 0.2819107 -0.2626861 0.20204064 -0.0166284
0.916964 -0.0126147 0.90435
PASO 4 1.118563 -0.0158412 1.102721
0.968473 -0.0166284 0.951844
=
+ =
=
+ =
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, = 2 .
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D3 B3 D4 B4 D5
Propano 11.57094 8.56238 6.76773 5.81176 3.95255
n-butano 30.69344 25.17339 20.84461 17.81885 11.70061
i-butano 33.819624 32.02329 29.91337 23.71197 15.83681
Pentano 22.735882 32.53703 37.8993 46.49406 53.23297Hexano 0.974395 0.89049 2.27396 3.25458 8.51728
Heptano 0.202999 0.68499 1.42122 1.45294 3.0609
C8+ 0.002598 0.10275 0.75799 1.15073 2.98105
Agua 0.000122 0.02569 0.12182 0.30512 0.71785
caudal D3 B3 D4 B4 D5
100 100.00001 100 100.00001 100.00002
1 0 0 0 0
2.65263151 1 0 0 0
2.92280696 2.84371508 1 0 0
1.96491227 6.3858478 3.21407061 1 0
0.08421053 0.06886565 0.78884605 0.13368086 1
0.01754386 0.19588742 0.34159458 0.0406318 0.33049586
0.00022453 0.04070308 0.33426273 0.05409246 0.27389834
1.0544E-05 0.01039117 0.04803926 0.01420393 0.06064294
BALANCE GENERAL
MATRIZ L
11.57094 8.56238 6.76773 5.81176 3.95255 1.25631
0 2.46055104 2.89231618 2.40239232 1.21595134 0.11617251
0 6.99710612 10.1326016 6.7253174 4.28426934 1.98145838
0 15.7127045 24.6013043 35.0744615 45.466556 66.5054711
0 0.16944743 1.70404586 2.76516861 8.18443367 11.3241855
0 0.481991 1.218221 1.249941 2.857901 5.339561
0 0.100152 0.755392 1.148132 2.978452 2.953432
0 0.025568 0.121698 0.304998 0.717728 0.738888
11.57094 8.56238 6.76773 5.81176 3.95255 1.25631
0 2.46055104 2.89231618 2.40239232 1.21595134 0.11617251
0 0 1.9076785 -0.10640186 0.82645017 1.65109686
0 0 6.13141339 19.7331498 37.7016758 65.7636111
0 0 1.50486464 2.59972631 8.10069639 11.3161852
0 0 0.65165264 0.77934256 2.61971143 5.31680427
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0 0 0.63766583 1.05034724 2.92895904 2.94870342
0 0 0.09164346 0.28003434 0.70509284 0.73768083
11.57094 8.56238 6.76773 5.81176 3.95255 1.25631
0 2.46055104 2.89231618 2.40239232 1.21595134 0.11617251
0 0 1.9076785 -0.10640186 0.82645017 1.651096860 0 0 20.0751329 35.0454066 60.4568692
0 0 0 2.683661 7.44875444 10.0137239
0 0 0 0.81568886 2.33740052 4.75279852
0 0 0 1.08591342 2.65270754 2.39680327
0 0 0 0.2851458 0.66539079 0.65836337
11.57094 8.56238 6.76773 5.81176 3.95255 1.25631
0 2.46055104 2.89231618 2.40239232 1.21595134 0.11617251
0 0 1.9076785 -0.10640186 0.82645017 1.65109686
0 0 0 20.0751329 35.0454066 60.4568692
0 0 0 0 2.7638544 1.93179776
0 0 0 0 0.91344243 2.29632687
0 0 0 0 0.75701512 -0.87345779
0 0 0 0 0.16760825 -0.20036184
11.57094 8.56238 6.76773 5.81176 3.95255 1.25631
0 2.46055104 2.89231618 2.40239232 1.21595134 0.11617251
0 0 1.9076785 -0.10640186 0.82645017 1.65109686
0 0 0 20.0751329 35.0454066 60.45686920 0 0 0 2.7638544 1.93179776
0 0 0 0 0 1.6578757
0 0 0 0 0 -1.40257399
0 0 0 0 0 -0.31751173
11.57094 8.56238 6.76773 5.81176 3.95255 1.25631
0 2.46055104 2.89231618 2.40239232 1.21595134 0.11617251
0 0 1.9076785 -0.10640186 0.82645017 1.65109686
0 0 0 20.0751329 35.0454066 60.45686920 0 0 0 2.7638544 1.93179776
0 0 0 0 0 1.6578757
0 0 0 0 0 0
0 0 0 0 0 0
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B5 D6 B6 A
1.25631 0.65309 0.00147 500 11.57094 8.56238
3.4487 1.84694 0.03712 1400 30.69344 25.17339
5.65341 2.99769 0.10016 1700 33.819624 32.02329
68.97401 49.63492 47.13193 4000 22.735882 32.5370311.42998 17.76408 15.08222 800 0.974395 0.89049
5.54256 10.776 10.31011 500 0.202999 0.63220823
2.95603 13.58429 19.38348 800 0.002598 0.10207449
0.73901 2.74298 7.95351 300 0.000122 0.02565828
B5 D6 B6 100
100.00001 99.99999 100
0 0 0 11.57094 8.56238 6.76773
0 0 0 0 2.46055104 2.89231618
0 0 0 0 0 1.9076785
0 0 0 0 0 0
0 0 0 0 0 0
1 0 0 0 0 0
-0.84600672 1 0 0 0 0
-0.19151721 0.19411757 1 0 0 0
50073.6842469
29.0595142
0.65309 0.00147 -746.391852
0.11453289 0.03322063 829.675242
1.088834 0.09586347 222.990693
48.3516554 47.1290416 788.954179
17.7090829 15.0820962 147.677509
10.573001 10.107111
13.581692 19.380882
2.742858 7.953388
0.65309 0.00147
0.11453289 0.03322063
0.76313509 0.00139346
47.6202658 46.9168997
17.7011956 15.0798085
10.5505654 10.1006035
SUSTITUCION
HACIA
ADEL
ANTE
-
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13.5770302 19.3795298
2.74166787 7.9530428
0.65309 0.00147
0.11453289 0.03322063
0.76313509 0.0013934645.1674958 46.912421
17.0991995 15.0787092
10.2898826 10.1001275
13.3219425 19.379064
2.70500743 7.95297586
0.65309 0.00147
0.11453289 0.03322063
0.76313509 0.00139346
45.1674958 46.912421
11.0611698 8.80741651
8.4546458 8.1939912
10.8787214 16.8414556
2.06345143 7.28663506
0.65309 0.00147
0.11453289 0.03322063
0.76313509 0.00139346
45.1674958 46.91242111.0611698 8.80741651
4.79897496 5.28317652
7.84908534 14.4291188
1.39266958 6.75252744
0.65309 0.00147
0.11453289 0.03322063
0.76313509 0.00139346
45.1674958 46.91242111.0611698 8.80741651
4.79897496 5.28317652
11.9090504 18.8987217
2.31175588 7.76434667
AL OBSERVAR EST
YA QUE NO ES MUY
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6.76773 5.81176 3.95255 1.25631 0.65309 0.00147
20.84461 17.81885 11.70061 3.4487 1.84694 0.03712
29.91337 23.71197 15.83681 5.65341 2.99769 0.10016
37.8993 46.49406 53.23297 68.97401 49.63492 47.131932.27396 3.25458 8.51728 11.42998 17.76408 15.08222
1.33695314 1.35190173 2.927244 5.36160153 10.5844587 10.1071368
0.75691154 1.1494369 2.97933946 2.95371408 13.5818386 19.3808823
0.12176936 0.30505928 0.71776967 0.73890125 2.74286489 7.95338802
5.81176 3.95255 1.25631 0.65309 0.00147
2.40239232 1.21595134 0.11617251 0.11453289 0.03322063
-0.10640186 0.82645017 1.65109686 0.76313509 0.00139346
20.0751329 35.0454066 60.4568692 45.1674958 46.912421
0 2.7638544 1.93179776 11.0611698 8.80741651
0 0 1.6578757 4.79897496 5.28317652
0 0 0 11.9090504 18.8987217
0 0 0 0 4.09577282
(L x U)
MATRIZ U
SUSTITUCION
HACIA
ATRS
-80.8529036418.174893
-71.1195379
-390.420602
153.718681
-6.53568043
9.03013842
36.0560792
SUSTITUCION
HACIA
ATRS
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METODO, NO ES MUY FACTIBLE UTILIZARLO
CERTADO PARA LA SOLUCION DE EL PROBLEMA
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Compuesto CH4
Datos
Presion 850
Vol Molar 7.31382327
ratura Critica 342.7
resion Critica 667.8tor Acentrico 0.011
R 10.7314
a 9260.50201
b 0.42843183
Iteraciones xi Tr(Xi) (Xi) g(Xi) Xi+1 Tr(Xi+1) (Xi+1) g(Xi+1) Xi+2 Error
0 500 1.45900204 0.84381758 -201.876858 500.1 1.45929384 0.8437307 -201.707495 619.197329 201.7074946
1 500.1 1.45929384 0.8437307 -201.707495 619.197329 1.80682033 0.74862055 -1.30127615 619.97065 1.3012762
2 619.197329 1.80682033 0.74862055 -1.30127615 619.97065 1.80907689 0.74805208 -0.00763075 619.975212 0.0076308
3 619.97065 1.80907689 0.74805208 -0.00763075 619.975212 1.8090902 0.74804872 -2.6309E-07 619.975212 0.0000003
4 619.975212 1.8090902 0.74804872 -2.6309E-07 619.975212 1.8090902 0.74804872 0 619.975212 0.0000000
3. En un laboratorio se realizaron pruebas a un gas a una determinada presin,
temperatura y volumen molar. Se desea ajustar estos datos con la ecuacin de vander
Waals para obtener las constantes crticas.
Los datos reportados fueron:Calcular la Tc y Pc del gas y determinar cul gas es con el cual estaban
trabajando. Para todos los ejercicios calcular la norma de los deltas y los residuos
.
= , = , = , = ,
.
= , = , = , = ,
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Compuesto CH4
850
7.31382327
342.7667.8
0.011
10.7314
9260.50201
0.42843183
Iteraciones a Tr(a) (a) F(a) b Tr(b)
0 600 1.75080245 0.76291861 -33.444269 700 2.04260286
1 600 1.75080245 0.76291861 -33.444269 650 1.89670266
2 600 1.75080245 0.76291861 -33.444269 625 1.82375255
3 612.5 1.7872775 0.75356785 -12.5085816 625 1.82375255
4 618.75 1.80551503 0.74894965 -2.04962673 625 1.82375255
5 618.75 1.80551503 0.74894965 -2.04962673 621.875 1.81463379
6 618.75 1.80551503 0.74894965 -2.04962673 620.3125 1.81007441
7 619.53125 1.80779472 0.74837501 -0.74266742 620.3125 1.81007441
8 619.921875 1.80893456 0.74808791 -0.08922174 620.3125 1.81007441
9 619.921875 1.80893456 0.74808791 -0.08922174 620.117188 1.80950449
10 619.921875 1.80893456 0.74808791 -0.08922174 620.019531 1.80921953
11 619.970703 1.80907704 0.74805204 -0.00754262 620.019531 1.80921953
12 619.970703 1.80907704 0.74805204 -0.00754262 619.995117 1.80914828
13 619.970703 1.80907704 0.74805204 -0.00754262 619.98291 1.80911266
14 619.970703 1.80907704 0.74805204 -0.00754262 619.976807 1.8090948515 619.973755 1.80908595 0.74804979 -0.00243769 619.976807 1.80909485
16 619.973755 1.80908595 0.74804979 -0.00243769 619.975281 1.8090904
17 619.974518 1.80908818 0.74804923 -0.00116145 619.975281 1.8090904
18 619.974899 1.80908929 0.74804895 -0.00052334 619.975281 1.8090904
19 619.97509 1.80908985 0.74804881 -0.00020428 619.975281 1.8090904
20 619.975185 1.80909012 0.74804874 -4.475E-05 619.975281 1.8090904
21 619.975185 1.80909012 0.74804874 -4.475E-05 619.975233 1.80909026
22 619.975209 1.80909019 0.74804873 -4.8678E-06 619.975233 1.80909026
23 619.975209 1.80909019 0.74804873 -4.8678E-06 619.975221 1.80909023
24 619.975209 1.80909019 0.74804873 -4.8678E-06 619.975215 1.80909021
25 619.975209 1.80909019 0.74804873 -4.8678E-06 619.975212 1.8090902
26 619.975211 1.8090902 0.74804872 -2.3752E-06 619.975212 1.8090902
27 619.975211 1.8090902 0.74804872 -1.1289E-06 619.975212 1.8090902
28 619.975212 1.8090902 0.74804872 -5.0569E-07 619.975212 1.8090902
29 619.975212 1.8090902 0.74804872 -1.9411E-07 619.975212 1.8090902
30 619.975212 1.8090902 0.74804872 -3.8325E-08 619.975212 1.8090902
b
Datos
Presion
Vol Molar
Temperatura CriticaPresion Critica
Factor Acentrico
R
a
3. En un laboratorio se realizaron pruebas a un gas a un
temperatura y volumen molar. Se desea ajustar estos d
Waals para obtener las constantes crticas.
Los datos reportados fueron:
Calcular la Tc y Pc del gas y determinar cul gas es con
trabajando. Para todos los ejercicios calcular la norma
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(b) F(b) M Tr(M) (M) F(M) F(a)*F(M)
0.69212175 133.418029 650 1.89670266 0.726408 50.1597591 -1677.55647
0.726408 50.1597591 625 1.82375255 0.74436881 8.40352185 -281.049645
0.74436881 8.40352185 612.5 1.7872775 0.75356785 -12.5085816 418.340367
0.74436881 8.40352185 618.75 1.80551503 0.74894965 -2.04962673 25.6379232
0.74436881 8.40352185 621.875 1.81463379 0.74665459 3.17766787 -6.51303299
0.74665459 3.17766787 620.3125 1.81007441 0.74780096 0.56420133 -1.15640212
0.74780096 0.56420133 619.53125 1.80779472 0.74837501 -0.74266742 1.522191
0.74780096 0.56420133 619.921875 1.80893456 0.74808791 -0.08922174 0.06626208
0.74780096 0.56420133 620.117188 1.80950449 0.74794442 0.23749262 -0.0211895
0.74794442 0.23749262 620.019531 1.80921953 0.74801616 0.07413615 -0.00661456
0.74801616 0.07413615 619.970703 1.80907704 0.74805204 -0.00754262 0.00067297
0.74801616 0.07413615 619.995117 1.80914828 0.7480341 0.03329681 -0.00025115
0.7480341 0.03329681 619.98291 1.80911266 0.74804307 0.0128771 -9.7127E-05
0.74804307 0.0128771 619.976807 1.80909485 0.74804755 0.00266724 -2.0118E-05
0.74804755 0.00266724 619.973755 1.80908595 0.74804979 -0.00243769 1.8387E-050.74804755 0.00266724 619.975281 1.8090904 0.74804867 0.00011478 -2.798E-07
0.74804867 0.00011478 619.974518 1.80908818 0.74804923 -0.00116145 2.8313E-06
0.74804867 0.00011478 619.974899 1.80908929 0.74804895 -0.00052334 6.0783E-07
0.74804867 0.00011478 619.97509 1.80908985 0.74804881 -0.00020428 1.0691E-07
0.74804867 0.00011478 619.975185 1.80909012 0.74804874 -4.475E-05 9.1415E-09
0.74804867 0.00011478 619.975233 1.80909026 0.74804871 3.5014E-05 -1.5669E-09
0.74804871 3.5014E-05 619.975209 1.80909019 0.74804873 -4.8678E-06 2.1784E-10
0.74804871 3.5014E-05 619.975221 1.80909023 0.74804872 1.5073E-05 -7.3374E-11
0.74804872 1.5073E-05 619.975215 1.80909021 0.74804872 5.1028E-06 -2.4839E-11
0.74804872 5.1028E-06 619.975212 1.8090902 0.74804872 1.1747E-07 -5.718E-13
0.74804872 1.1747E-07 619.975211 1.8090902 0.74804872 -2.3752E-06 1.1562E-11
0.74804872 1.1747E-07 619.975211 1.8090902 0.74804872 -1.1289E-06 2.6812E-12
0.74804872 1.1747E-07 619.975212 1.8090902 0.74804872 -5.0569E-07 5.7086E-13
0.74804872 1.1747E-07 619.975212 1.8090902 0.74804872 -1.9411E-07 9.8163E-14
0.74804872 1.1747E-07 619.975212 1.8090902 0.74804872 -3.8325E-08 7.4394E-15
0.74804872 1.1747E-07 619.975212 1.8090902 0.74804872 3.9571E-08 -1.5165E-15
a determinada presin,
atos con la ecuacin de vander
l cual estaban
de los deltas y los residuos
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Error
50.1597591
8.4035219
12.5085816
2.0496267
3.1776679
0.5642013
0.7426674
0.0892217
0.2374926
0.0741361
0.0075426
0.0332968
0.0128771
0.0026672
0.00243770.0001148
0.0011615
0.0005233
0.0002043
0.0000448
0.0000350
0.0000049
0.0000151
0.0000051
0.0000001
0.0000024
0.0000011
0.0000005
0.0000002
0.0000000
0.0000000
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