Name: SID: Discussion Section
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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.
Transcript of Name: SID: Discussion Section
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? Consider
)()( TTT oo .
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:
prx3.01
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 Cp
(C) (bar) (kg/m3) (kJ/kg) (kJ/kg) (J/g*K) (J/g*K) Phase
-56.97 0.5 597.73 66.883 66.967 0.45827 2.1885 liquid
-42.414 1 581.27 99.146 99.318 0.60269 2.2515 liquid
-32.82 1.5 570.06 120.92 121.19 0.69518 2.2987 liquid
-25.453 2 561.21 137.95 138.31 0.76498 2.3382 liquid
-19.384 2.5 553.75 152.19 152.64 0.8218 2.3733 liquid
-14.178 3 547.21 164.57 165.12 0.8701 2.4052 liquid
-9.5907 3.5 541.33 175.61 176.25 0.91237 2.435 liquid
-5.4726 4 535.96 185.62 186.37 0.95011 2.4631 liquid
-1.7235 4.5 530.97 194.84 195.68 0.98432 2.4899 liquid
1.7265 5 526.31 203.4 204.35 1.0157 2.5158 liquid
4.9286 5.5 521.91 211.41 212.47 1.0447 2.5408 liquid
7.9215 6 517.72 218.97 220.13 1.0718 2.5652 liquid
10.735 6.5 513.73 226.13 227.4 1.0972 2.5891 liquid
13.393 7 509.9 232.95 234.33 1.1211 2.6126 liquid
15.914 7.5 506.21 239.48 240.96 1.1438 2.6357 liquid
18.315 8 502.64 245.73 247.32 1.1654 2.6586 liquid
20.607 8.5 499.18 251.75 253.45 1.186 2.6814 liquid
22.802 9 495.82 257.55 259.37 1.2057 2.704 liquid
24.91 9.5 492.54 263.16 265.09 1.2247 2.7266 liquid
26.938 10 489.35 268.6 270.64 1.2429 2.7492 liquid
28.892 10.5 486.22 273.87 276.03 1.2604 2.7717 liquid
30.78 11 483.15 279 281.28 1.2774 2.7944 liquid
32.606 11.5 480.15 284 286.39 1.2938 2.8172 liquid
34.374 12 477.19 288.87 291.38 1.3098 2.8401 liquid
Data on saturation curve for propane
Temperature Pressure Density Int Energy Enthalpy Entropy Cp
(C) (bar) (kg/m3) (kJ/kg) (kJ/kg) (J/g*K) (J/g*K) Phase
-56.97 0.5 1.254 468.07 507.94 2.4981 1.3613 vapor
-42.414 1 2.3848 483.62 525.55 2.45 1.4379 vapor
-32.82 1.5 3.4787 493.96 537.08 2.4257 1.4947 vapor
-25.453 2 4.5532 501.92 545.84 2.4103 1.5424 vapor
-19.384 2.5 5.6164 508.47 552.98 2.3994 1.5845 vapor
-14.178 3 6.6729 514.08 559.04 2.3912 1.623 vapor
-9.5907 3.5 7.7259 519.01 564.31 2.3847 1.6589 vapor
-5.4726 4 8.7775 523.41 568.99 2.3795 1.6929 vapor
-1.7235 4.5 9.8293 527.41 573.19 2.3751 1.7253 vapor
1.7265 5 10.883 531.07 577.01 2.3715 1.7566 vapor
4.9286 5.5 11.939 534.45 580.52 2.3683 1.787 vapor
7.9215 6 12.998 537.59 583.75 2.3655 1.8167 vapor
10.735 6.5 14.062 540.52 586.75 2.363 1.8459 vapor
13.393 7 15.13 543.27 589.54 2.3608 1.8745 vapor
15.914 7.5 16.204 545.87 592.15 2.3587 1.9029 vapor
18.315 8 17.284 548.32 594.6 2.3569 1.931 vapor
20.607 8.5 18.371 550.64 596.91 2.3552 1.9589 vapor
22.802 9 19.464 552.85 599.08 2.3536 1.9866 vapor
24.91 9.5 20.565 554.95 601.14 2.3521 2.0142 vapor
26.938 10 21.675 556.95 603.09 2.3507 2.0418 vapor
28.892 10.5 22.792 558.86 604.93 2.3494 2.0694 vapor
30.78 11 23.918 560.69 606.68 2.3481 2.0971 vapor
32.606 11.5 25.054 562.44 608.34 2.3468 2.1249 vapor
34.374 12 26.2 564.11 609.91 2.3456 2.153 vapor
Isobaric properties for propane
Temperature Pressure Density Int Energy Enthalpy Entropy Cp
(C) (bar) (kg/m3) (kJ/kg) (kJ/kg) (J/g*K) (J/g*K)
35 12 26.085 565.26 611.26 2.3499 2.1485
36 12 25.906 567.08 613.41 2.3569 2.1419
37 12 25.731 568.91 615.54 2.3638 2.1357
38 12 25.56 570.73 617.68 2.3707 2.1301
39 12 25.393 572.55 619.8 2.3775 2.1249
40 12 25.229 574.36 621.93 2.3843 2.1201
41 12 25.068 576.18 624.04 2.391 2.1158
42 12 24.911 577.99 626.16 2.3978 2.1118
43 12 24.757 579.8 628.27 2.4044 2.1082
44 12 24.606 581.61 630.38 2.4111 2.1049
45 12 24.458 583.41 632.48 2.4177 2.102
Isobaric properties for methane
Temperature Pressure Density Int Energy Enthalpy Entropy Cp
(C) (bar) (kg/m3) (kJ/kg) (kJ/kg) (J/g*K) (J/g*K)
-40 125 187.69 454.06 520.66 2.8506 5.353
-35 125 174.5 475.34 546.98 2.9623 5.1628
-30 125 162.73 495.39 572.21 3.0672 4.9243
-25 125 152.39 514.17 596.2 3.1649 4.6717
-20 125 143.38 531.76 618.94 3.2556 4.4287
-15 125 135.53 548.29 640.52 3.34 4.2077
-10 125 128.65 563.9 661.06 3.4188 4.013
-5 125 122.6 578.74 680.69 3.4928 3.8444
0 125 117.23 592.92 699.55 3.5624 3.6996
5 125 112.44 606.56 717.73 3.6284 3.5756
10 125 108.14 619.74 735.33 3.6911 3.4694
15 125 104.25 632.54 752.44 3.751 3.3785
20 125 100.7 645.01 769.14 3.8085 3.3005
25 125 97.46 657.21 785.47 3.8637 3.2334
30 125 94.48 669.18 801.49 3.917 3.1757
35 125 91.727 680.96 817.24 3.9685 3.1259
40 125 89.175 692.58 832.76 4.0185 3.0831
Isobaric properties for methane
Temperature Pressure Density Int Energy Enthalpy Entropy Cp
(C) (bar) (kg/m3) (kJ/kg) (kJ/kg) (J/g*K) (J/g*K)
-40 1 0.83086 648.45 768.8 6.1478 2.1261
-35 1 0.81321 656.48 779.45 6.193 2.1311
-30 1 0.79629 664.53 790.12 6.2373 2.1367
-25 1 0.78008 672.62 800.81 6.2808 2.1427
-20 1 0.76452 680.74 811.54 6.3237 2.1493
-15 1 0.74957 688.9 822.31 6.3658 2.1565
-10 1 0.73519 697.09 833.11 6.4072 2.1641
-5 1 0.72137 705.33 843.95 6.448 2.1723
0 1 0.70805 713.6 854.83 6.4882 2.1809
5 1 0.69523 721.92 865.76 6.5279 2.1901
10 1 0.68286 730.29 876.74 6.567 2.1998
15 1 0.67093 738.71 887.76 6.6056 2.2099
20 1 0.65941 747.18 898.83 6.6437 2.2205
25 1 0.64828 755.71 909.97 6.6813 2.2316
30 1 0.63752 764.29 921.15 6.7185 2.2431
35 1 0.62711 772.94 932.4 6.7553 2.2551
40 1 0.61704 781.64 943.7 6.7917 2.2675
