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5) Evaluating Changes in Entropy for an Ideal Gas Air enters a turbine at 427 °C and 1 MPa and exits at 127 °C. The outlet prTABLE A-2 Ideal-gas specific heats of various common gases (Concluded) (c) As a function of temperature (Tin K, C in kJ/kmol-TABLE A-17 Ideal-gas properties of air K kJ/kg 200 199.97 0.3363 142.56 1707.0 1.29559 210 209.97 0.3987 149.69 1512.0 1.3444TABLE A-17 Ideal-gas properties of air (Concluded) s° kJ/kg- K kJ/kg kJ/kgv 1260 1348.55 290.8 986.90 12.435 3.23638 1600 175

5) Evaluating Changes in Entropy for an Ideal Gas Air enters a turbine at 427 °C and 1 MPa and exits at 127 °C. The outlet pressure can be tuned by the operator in the range from 300 - 800 kPa. Determine the change in specific entropy of the air, se -si, as it flows through this turbine 3 ways a) Assuming constant specific heats. b) Integrating an appropriate formula from Table A-2(c) from the text, which gives a polynomial for Cp(T) on a molar basis. c Using Table A-17 from the text, for ideal-gas properties of air. For all three approaches, plot the change in specific entropy as a function of the turbine outlet pressure (d) For all values of the outlet pressure, note that the change in specific entropy is negative. Does this indicate that this process is actually impossible? You must briefly justify your answer.
TABLE A-2 Ideal-gas specific heats of various common gases (Concluded) (c) As a function of temperature (Tin K, C in kJ/kmol-K) Temperature-o error range, K Max. Avg 2.873×10-9 273-1800 0.59 0.34 1.312 x 10-9 273-1800 1.19 0.28 1.966 x 10-9 273-1800 0.72 0.33 Substance Formula a Nitrogen Oxygen 28.90 -0.1571 x 102 25.48 28.11 0.1967 x 10-2 0.8081 x 10-5 -0.7155 x 10-5 0.4802 x 10-5 0 1.520 x 10-2 ir
TABLE A-17 Ideal-gas properties of air K kJ/kg 200 199.97 0.3363 142.56 1707.0 1.29559 210 209.97 0.3987 149.69 1512.0 1.34444 220 219.970.4690 156.82 1346.0 1.39105 230 230.02 0.5477 164.00 1205.0 1.43557 240 240.02 0.6355 171.13 1084.0 1.47824 250 250.05 0.7329 178.28 979.0 1.51917 260 260.09 0.8405 185.45 887.8 1.55848 270 270.11 0.9590 192.60 808.0 1.59634 280 280.13 1.0889 199.75 738.0 1.63279 285 285.14 1.1584 203.33 706.1 1.65055 290 290.16 1.2311 206.91 676.1 1.66802 295 295.171.3068 210.49 647.9 1.68515 298 298.18 1.3543 212.64 631.9 1.69528 300 300.19 1.3860 214.07 621.2 1.70203 305 305.22 1.4686 217.67 596.0 1.71865 310 310.241.5546 221.25 572.3 1.73498 315 315.271.6442 224.85 549.8 1.75106 320 320.29 1.7375 228.42 528.6 1.76690 325 325.31 1.8345 232.02 508.4 1.78249 330 330.341.9352 235.61 489.4 1.79783 340 340.42 2.149 242.82 454.1 1.82790 350 350.49 2.379 250.02 422.2 1.85708 360 360.58 2.626 257.24 393.4 1.88543 370 370.672.892 264.46 367.2 1.91313 380 380.773.176 271.69 343.4 1.94001 390 390.88 3.481 278.93 321.5 1.96633 400 400.98 3.806 286.16 301.6 1.99194 410 411.12 4.153 293.43 283.3 2.01699 420 421.26 4.522 300.69 266.6 2.04142 430 431.43 4.915 307.99 251.1 2.06533 440 441.61 5.332 315.30 236.8 2.08870 1000 450 451.80 5.775 322.62 223.6 2.11161 1020 1068.89 123.4 776.10 23.72 2.99034 460 462.02 6.245 329.97 211.4 2.134071040 1091.85 133.3 793.36 23.29 3.01260 470 472.24 6.742 337.32 200.1 2.156041060 1114.86 143.9 810.62 21.14 3.03449 480 482.49 7.268 344.70 189.5 2.177601080 1137.89 155.2 827.88 19.98 3.05608 490 492.747.824 352.08 179.7 2.19876 1100 1161.07 167.1 845.33 18.896 3.07732 500 503.028.411359.49 170.6 2.21952 1120 1184.28 179.7 862.79 17.886 3.09825 510 513.32 9.031 366.92 162.1 2.23993 1140 1207.57 193.1 880.35 16.946 3.11883 520 523.63 9.684374.36 154.1 2.25997 1160 1230.92 207.2 897.91 16.064 3.13916 530 533.98 10.37 381.84 146.7 2.27967 1180 1254.34 222.2 915.57 15.241 3.15916 540 544.35 11.10 389.34 139.7 2.29906 1200 1277.79 238.0 933.33 14.470 3.17888 550 555.74 11.86 396.86 133.1 2.31809 1220 1301.31 254.7 951.09 13.747 3.19834 560 565.17 12.66 404.42 127.0 2.33685 1240 1324.93 272.3 968.95 13.069 3.21751 570 575.59 13.50 411.97 121.2 2.35531 kJ/kg.K kJ/kg kJ/kg-K 580 586.04 14.38 419.55 115.7 2.37348 590 596.52 15.31 427.15 110.6 2.39140 600 607.02 16.28 434.78 105.8 2.40902 610 617.5317.30 442.42 101.2 2.42644 620 628.0718.36 450.09 96.92 2.44356 630 638.63 19.84 457.78 92.84 2.46048 640 649.22 20.64 465.50 88.99 2.47716 650 659.8421.86 473.25 85.34 2.49364 660 670.4723.13 481.01 81.89 2.50985 670 681.14 24.46 488.81 78.61 2.52589 680 691.82 25.85 496.62 75.50 2.54175 690 702.52 27.29 504.45 72.56 2.55731 700 713.2728.80 512.33 69.76 2.57277 710 724.04 30.38 520.23 67.07 2.58810 720 734.82 32.02 528.14 64.53 2.60319 730 745.62 33.72 536.07 62.13 2.61803 740 756.4435.50 544.02 59.82 2.63280 750 767.2937.35 551.99 57.63 2.64737 760 778.18 39.27 560.01 55.54 2.66176 780 800.03 43.35 576.12 51.64 2.69013 800 821.95 47.75 592.30 48.08 2.71787 820 843.98 52.59 608.59 44.84 2.74504 840 866.08 57.60 624.95 41.85 2.77170 860 888.2763.09 641.40 39.12 2.79783 880 910.56 68.98 657.95 36.61 2.82344 900 932.93 75.29 674.58 34.31 2.84856 920 955.38 82.05 691.28 32.18 2.87324 940 977.92 89.28 708.08 30.22 2.89748 960 1000.55 97.00 725.02 28.40 2.92128 980 1023.25 105.2 741.98 26.73 2.94468 1046.04 114.0 758.94 25.17 2.96770
TABLE A-17 Ideal-gas properties of air (Concluded) s° kJ/kg- K kJ/kg kJ/kgv 1260 1348.55 290.8 986.90 12.435 3.23638 1600 1757.57 791.2 1298.30 5.804 3.52364 1280 1372.24 310.4 1004.76 11.835 3.25510 1620 1782.00 834.1 1316.96 5.574 3.53879 1300 1395.97 330.9 1022.82 11.275 3.27345 1640 1806.46 878.9 1335.72 5.355 3.55381 1320 1419.76 352.5 1040.88 10.747 3.29160 1660 1830.96 925.6 1354.48 5.147 3.56867 1340 1443.60 375.3 1058.94 10.247 3.30959 1680 1855.50 974.2 1373.24 4.949 3.58335 1360 1467.49 399.1 1077.10 9.780 3.32724 1700 1880.1 1025 1392.7 4.761 3.5979 1380 1491.44 424.2 1095.269.337 3.34474 1750 1941.61161 1439.8 4.328 3.6336 1400 1515.42 450.5 1113.52 8.919 3.36200 1800 2003.3 1310 1487.2 3.994 3.6684 1420 1539.44 478.0 1131.778.526 3.37901 1850 2065.3 1475 1534.9 3.601 3.7023 1440 1563.51 506.9 1150.13 8.153 3.39586 1900 2127.4 1655 1582.6 3.295 3.7354 1460 1587.63 537.1 1168.49 7.801 3.41247 1950 2189.71852 1630.6 3.022 3.7677 1480 1611.79 568.8 1186.957.468 3.42892 2000 2252.1 2068 1678.7 2.776 3.7994 1500 1635.97 601.9 1205.41 7.152 3.44516 2050 2314.6 2303 1726.8 2.555 3.8303 1520 1660.23 636.5 1223.87 6.854 3.46120 2100 2377.7 2559 1775.3 2.356 3.8605 1540 1684.51 672.8 1242.43 6.569 3.47712 2150 2440.3 2837 1823.8 2.175 3.8901 1560 1708.82 710.5 1260.99 6.301 3.49276 2200 2503.2 3138 1872.4 2.012 3.9191 1580 1733.17 750.0 1279.65 6.046 3.50829 2250 2566.434641921.3 1.864 3.9474
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