Name:
SID:
Discussion Section:
Chemical Engineering Thermodynamics 141 – Spring 2011
Thursday, March 31, 2011
Midterm II – 70 minutes – 100 total points
One one-sided 8.5”x 11” equation sheet allowed
(20 points)
1. Consider propane in vapor-liquid equilibrium.
i) (14 points)
Using data at 1 bar from the attached table, calculate the boiling point of propane
at 10 bar.
ii) (6 points)
Based on the table, what is the boiling point of propane at 10 bar? If the
calculated boiling point is different from the experimental value, state three
reasons for the error.
(45 points)
2. Consider the Linde process for liquefaction of methane shown below. Methane is compressed to
125 bar and 40°C. Then, it is cooled in a heat exchanger, HEX-1, by a vapor compression cycle
using propane as the working fluid.
After HEX-1, the methane is further cooled in heat exchanger 2 (HEX-2) using the saturated vapor
from the flash drum. The cooled methane is throttled (TV-1) to 1 bar. The mixture of liquid and
gaseous methane is sent to a flash drum, where the liquid methane (stream 9) is shipped away and
the gas (stream 7) goes through HEX-2 and is recycled to the beginning of the liquefaction process.
HEX-1 is the evaporator of a vapor compression cycle and operates at 2 bar. The condenser of this
cycle operates at 12 bar. Assume that the effluent of the evaporator (stream 11) is saturated
vapor and the effluent of the condenser is saturated liquid.
The mass flow rate of methane entering the process (stream 8) is 5 kg/s and ΔTmin = 5.45°C
between the cold and hot streams in HEX-1. The temperature of methane at 1 bar exiting HEX-2
(stream 7) is -10°C.
See attached tables for thermodynamic data for methane and propane. Consider the enthalpy of
liquid methane at 1 bar is zero. Linear interpolation is not necessary and all processes are 100%
efficient.
i) (8 points) Qualitatively draw the vapor compression cycle on an lnP-H and T-S diagram. Use
the same stream numbers from the schematic and label temperature and pressure
as provided.
ii) (13 points)
What is the coefficient of performance (COP) for the vapor compression cycle?
What would the COP be if we had a Carnot refrigerator?
iii) (14 points)
What is the mass flow rate of methane at stream 2?
iv) (5 points)
What is the circulation rate of propane in the vapor compression cycle?
v) (5 points)
What is power rating (in kW) of the compressor in the vapor compression cycle?
(20 points)
3.
Consider a container of propane at 1 bar and -42.41°C.
i) (10 points) How much would the chemical potential of the liquid and the gas change if the
temperature increased by 0.2°C and the pressure increased by 0.1 bar? What
phase(s) would be present in the final state? Entropy and volume changes over
this range may be ignored.
ii) (6 points)
What is the ratio of initial to final fugacity for the gas phase?
 o (T )   o (T  T ) .
Consider
iii) (7 points)
What is the fugacity of liquid propane at a pressure of 300 bar and -5.47oC? The
fugacity coefficient of propane is unity at the saturation pressure at this
temperature. Assume liquid propane is incompressible.
(17 points)
4.
The density (mol/mL) of a propanol-water mixture is:
  1  0.3x pr
where xpr stands for the mole fraction of propanol in solution.
i) (10 points) Calculate the partial molar volumes of propanol and water for a propanol – water
mixture with xpr = 0.4.
ii) (7 points)
On the V-xpr graph below, show the (a) molar volume of solution, (b) molar
volume of pure propanol and water, (c) and the partial molar volume of propanol
and water when xpr = 0.4.
Data on saturation curve for propane
Temperature Pressure
Density Int Energy Enthalpy Entropy
(C)
-56.97
-42.414
-32.82
-25.453
-19.384
-14.178
-9.5907
-5.4726
-1.7235
1.7265
4.9286
7.9215
10.735
13.393
15.914
18.315
20.607
22.802
24.91
26.938
28.892
30.78
32.606
34.374
(bar)
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
9.5
10
10.5
11
11.5
12
3
(kg/m )
597.73
581.27
570.06
561.21
553.75
547.21
541.33
535.96
530.97
526.31
521.91
517.72
513.73
509.9
506.21
502.64
499.18
495.82
492.54
489.35
486.22
483.15
480.15
477.19
(kJ/kg)
(kJ/kg)
66.883
66.967
99.146
99.318
120.92
121.19
137.95
138.31
152.19
152.64
164.57
165.12
175.61
176.25
185.62
186.37
194.84
195.68
203.4
204.35
211.41
212.47
218.97
220.13
226.13
227.4
232.95
234.33
239.48
240.96
245.73
247.32
251.75
253.45
257.55
259.37
263.16
265.09
268.6
270.64
273.87
276.03
279
281.28
284
286.39
288.87
291.38
(J/g*K) (J/g*K)
Phase
0.45827
2.1885 liquid
0.60269
2.2515 liquid
0.69518
2.2987 liquid
0.76498
2.3382 liquid
0.8218
2.3733 liquid
0.8701
2.4052 liquid
0.91237
2.435 liquid
0.95011
2.4631 liquid
0.98432
2.4899 liquid
1.0157
2.5158 liquid
1.0447
2.5408 liquid
1.0718
2.5652 liquid
1.0972
2.5891 liquid
1.1211
2.6126 liquid
1.1438
2.6357 liquid
1.1654
2.6586 liquid
1.186
2.6814 liquid
1.2057
2.704 liquid
1.2247
2.7266 liquid
1.2429
2.7492 liquid
1.2604
2.7717 liquid
1.2774
2.7944 liquid
1.2938
2.8172 liquid
1.3098
2.8401 liquid
Data on saturation curve for propane
Temperature Pressure
Density Int Energy Enthalpy Entropy
(C)
-56.97
-42.414
-32.82
-25.453
-19.384
-14.178
-9.5907
-5.4726
-1.7235
1.7265
4.9286
7.9215
10.735
13.393
15.914
18.315
20.607
22.802
24.91
26.938
28.892
30.78
32.606
34.374
(bar)
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
9.5
10
10.5
11
11.5
12
3
(kg/m )
1.254
2.3848
3.4787
4.5532
5.6164
6.6729
7.7259
8.7775
9.8293
10.883
11.939
12.998
14.062
15.13
16.204
17.284
18.371
19.464
20.565
21.675
22.792
23.918
25.054
26.2
Cp
Cp
(kJ/kg)
(kJ/kg) (J/g*K) (J/g*K)
Phase
468.07
507.94
2.4981
1.3613 vapor
483.62
525.55
2.45
1.4379 vapor
493.96
537.08
2.4257
1.4947 vapor
501.92
545.84
2.4103
1.5424 vapor
508.47
552.98
2.3994
1.5845 vapor
514.08
559.04
2.3912
1.623 vapor
519.01
564.31
2.3847
1.6589 vapor
523.41
568.99
2.3795
1.6929 vapor
527.41
573.19
2.3751
1.7253 vapor
531.07
577.01
2.3715
1.7566 vapor
534.45
580.52
2.3683
1.787 vapor
537.59
583.75
2.3655
1.8167 vapor
540.52
586.75
2.363
1.8459 vapor
543.27
589.54
2.3608
1.8745 vapor
545.87
592.15
2.3587
1.9029 vapor
548.32
594.6
2.3569
1.931 vapor
550.64
596.91
2.3552
1.9589 vapor
552.85
599.08
2.3536
1.9866 vapor
554.95
601.14
2.3521
2.0142 vapor
556.95
603.09
2.3507
2.0418 vapor
558.86
604.93
2.3494
2.0694 vapor
560.69
606.68
2.3481
2.0971 vapor
562.44
608.34
2.3468
2.1249 vapor
564.11
609.91
2.3456
2.153 vapor
Isobaric properties for propane
Temperature Pressure
Density
(C)
35
36
37
38
39
40
41
42
43
44
45
(bar)
12
12
12
12
12
12
12
12
12
12
12
3
(kg/m )
26.085
25.906
25.731
25.56
25.393
25.229
25.068
24.911
24.757
24.606
24.458
Isobaric properties for methane
Temperature Pressure
Density
(C)
-40
-35
-30
-25
-20
-15
-10
-5
0
5
10
15
20
25
30
35
40
(bar)
125
125
125
125
125
125
125
125
125
125
125
125
125
125
125
125
125
(kg/m3)
187.69
174.5
162.73
152.39
143.38
135.53
128.65
122.6
117.23
112.44
108.14
104.25
100.7
97.46
94.48
91.727
89.175
Isobaric properties for methane
Temperature Pressure
Density
(C)
(bar)
-40
-35
-30
-25
-20
-15
-10
-5
0
5
10
15
20
25
30
35
40
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
(kg/m3)
0.83086
0.81321
0.79629
0.78008
0.76452
0.74957
0.73519
0.72137
0.70805
0.69523
0.68286
0.67093
0.65941
0.64828
0.63752
0.62711
0.61704
Int Energy
(kJ/kg)
565.26
567.08
568.91
570.73
572.55
574.36
576.18
577.99
579.8
581.61
583.41
Int Energy
(kJ/kg)
454.06
475.34
495.39
514.17
531.76
548.29
563.9
578.74
592.92
606.56
619.74
632.54
645.01
657.21
669.18
680.96
692.58
Int Energy
(kJ/kg)
648.45
656.48
664.53
672.62
680.74
688.9
697.09
705.33
713.6
721.92
730.29
738.71
747.18
755.71
764.29
772.94
781.64
Enthalpy
Entropy
Cp
(kJ/kg)
(J/g*K) (J/g*K)
611.26
2.3499
2.1485
613.41
2.3569
2.1419
615.54
2.3638
2.1357
617.68
2.3707
2.1301
619.8
2.3775
2.1249
621.93
2.3843
2.1201
624.04
2.391
2.1158
626.16
2.3978
2.1118
628.27
2.4044
2.1082
630.38
2.4111
2.1049
632.48
2.4177
2.102
Enthalpy
Entropy
Cp
(kJ/kg)
(J/g*K) (J/g*K)
520.66
2.8506
5.353
546.98
2.9623
5.1628
572.21
3.0672
4.9243
596.2
3.1649
4.6717
618.94
3.2556
4.4287
640.52
3.34
4.2077
661.06
3.4188
4.013
680.69
3.4928
3.8444
699.55
3.5624
3.6996
717.73
3.6284
3.5756
735.33
3.6911
3.4694
752.44
3.751
3.3785
769.14
3.8085
3.3005
785.47
3.8637
3.2334
801.49
3.917
3.1757
817.24
3.9685
3.1259
832.76
4.0185
3.0831
Enthalpy
Entropy
Cp
(kJ/kg)
(J/g*K) (J/g*K)
768.8
6.1478
2.1261
779.45
6.193
2.1311
790.12
6.2373
2.1367
800.81
6.2808
2.1427
811.54
6.3237
2.1493
822.31
6.3658
2.1565
833.11
6.4072
2.1641
843.95
6.448
2.1723
854.83
6.4882
2.1809
865.76
6.5279
2.1901
876.74
6.567
2.1998
887.76
6.6056
2.2099
898.83
6.6437
2.2205
909.97
6.6813
2.2316
921.15
6.7185
2.2431
932.4
6.7553
2.2551
943.7
6.7917
2.2675