Solve Problem 10.19 with variable specific heats using Table A.7.
Problem 10.19
In a Brayton cycle the inlet is at 300 K, 100 kPa, and the combustion adds 800 kJ/kg. The maximum temperature is 1400 K due to material considerations. Find the maximum permissible compression ratio and, for that ratio, the cycle efficiency using cold air properties.
Table A.7
Ideal Gas Properties of Air, Standard Entropy at 0.1-MPa (1-Bar) Pressure
T | u | h | ST0 | T | u | h | ST0 |
(K) | (kJ/kg) | (kJ/kg) | (kJ/kg-K) | (K) | (kJ/kg) | (kJ/kg) | (kJ/kg-K) |
200 | 142.77 | 200.17 | 6.46260 | 1100 | 845.45 | 1161.18 | 8.24449 |
220 | 157.07 | 220.22 | 6.55812 | 1150 | 889.21 | 1219.30 | 8.29616 |
240 | 171.38 | 240.27 | 6.64535 | 1200 | 933.37 | 1277.81 | 8.34596 |
260 | 185.70 | 260.32 | 6.72562 | 1250 | 977.89 | 1336.68 | 8.39402 |
280 | 200.02 | 280.39 | 6.79998 | 1300 | 1022.75 | 1395.89 | 8.44046 |
290 | 207.19 | 290.43 | 6.83521 | 1350 | 1067.94 | 1455.43 | 8.48539 |
298.15 | 213.04 | 298.62 | 6.86305 | 1400 | 1113.43 | 1515.27 | 8.52891 |
300 | 214.36 | 300.47 | 6.86926 | 1450 | 1159.20 | 1575.40 | 8.57111 |
320 | 228.73 | 320.58 | 6.93413 | 1500 | 1205.25 | 1635.80 | 8.61208 |
340 | 243.11 | 340.70 | 6.99515 | 1550 | 1251.55 | 1696.45 | 8.65185 |
360 | 257.53 | 360.86 | 7.05276 | 1600 | 1298.08 | 1757.33 | 8.69051 |
380 | 271.99 | 381.06 | 7.10735 | 1650 | 1344.83 | 1818.44 | 8.72811 |
400 | 286.49 | 401.30 | 7.15926 | 1700 | 1391.80 | 1879.76 | 8.76472 |
420 | 301.04 | 421.59 | 7.20875 | 1750 | 1438.97 | 1941.28 | 8.80039 |
440 | 315.64 | 441.93 | 7.25607 | 1800 | 1486.33 | 2002.99 | 8.83516 |
460 | 330.31 | 462.34 | 7.30142 | 1850 | 1533.87 | 2064.88 | 8.86908 |
480 | 345.04 | 482.81 | 7.34499 | 1900 | 1581.59 | 2126.95 | 8.90219 |
500 | 359.84 | 503.36 | 7.38692 | 1950 | 1629.47 | 2189.19 | 8.93452 |
520 | 374.73 | 523.98 | 7.42736 | 2000 | 1677.52 | 2251.58 | 8.96611 |
540 | 389.69 | 544.69 | 7.46642 | 2050 | 1725.71 | 2314.13 | 8.99699 |
560 | 404.74 | 565.47 | 7.50422 | 2100 | 1774.06 | 2376.82 | 9.02721 |
580 | 419.87 | 586.35 | 7.54084 | 2150 | 1822.54 | 2439.66 | 9.05678 |
600 | 435.10 | 607.32 | 7.57638 | 2200 | 1871.16 | 2502.63 | 9.08573 |
620 | 450.42 | 628.38 | 7.61090 | 2250 | 1919.91 | 2565.73 | 9.11409 |
640 | 465.83 | 649.53 | 7.64448 | 2300 | 1968.79 | 2628.96 | 9.14189 |
660 | 481.34 | 670.78 | 7.67717 | 2350 | 2017.79 | 2692.31 | 9.16913 |
680 | 496.94 | 692.12 | 7.70903 | 2400 | 2066.91 | 2755.78 | 9.19586 |
700 | 512.64 | 713.56 | 7.74010 | 2450 | 2116.14 | 2819.37 | 9.22208 |
720 | 528.44 | 735.10 | 7.77044 | 2500 | 2165.48 | 2883.06 | 9.24781 |
740 | 544.33 | 756.73 | 7.80008 | 2550 | 2214.93 | 2946.86 | 9.27308 |
760 | 560.32 | 778.46 | 7.82905 | 2600 | 2264.48 | 3010.76 | 9.29790 |
780 | 576.40 | 800.28 | 7.85740 | 2650 | 2314.13 | 3074.77 | 9.32228 |
800 | 592.58 | 822.20 | 7.88514 | 2700 | 2363.88 | 3138.87 | 9.34625 |
850 | 633.42 | 877.40 | 7.95207 | 2750 | 2413.73 | 3203.06 | 9.36980 |
900 | 674.82 | 933.15 | 8.01581 | 2800 | 2463.66 | 3267.35 | 9.39297 |
950 | 716.76 | 989.44 | 8.07667 | 2850 | 2513.69 | 3331.73 | 9.41576 |
1000 | 759.19 | 1046.22 | 8.13493 | 2900 | 2563.80 | 3396.19 | 9.43818 |
1050 | 802.10 | 1103.48 | 8.19081 | 2950 | 2613.99 | 3460.73 | 9.46025 |
1100 | 845.45 | 1161.18 | 8.24449 | 3000 | 2664.27 | 3525.36 | 9.48198 |
TABLE A.7.1 The Isentropic Relative Pressure and Relative Volume Functions
T[K] | Pr | vr | T[K] | Pr | vr | T[K] | Pr | vr |
200 | 0.2703 | 493.47 | 700 | 23.160 | 20.155 | 1900 | 1327.5 | 0.95445 |
220 | 0.3770 | 389.15 | 720 | 25.742 | 18.652 | 1950 | 1485.8 | 0.87521 |
240 | 0.5109 | 313.27 | 740 | 28.542 | 17.289 | 2000 | 1658.6 | 0.80410 |
260 | 0.6757 | 256.58 | 760 | 31.573 | 16.052 | 2050 | 1847.1 | 0.74012 |
280 | 0.8756 | 213.26 | 780 | 34.851 | 14.925 | 2100 | 2052.1 | 0.68242 |
290 | 0.9899 | 195.36 | 800 | 38.388 | 13.897 | 2150 | 2274.8 | 0.63027 |
298.15 | 1.0907 | 182.29 | 850 | 48.468 | 11.695 | 2200 | 2516.2 | 0.58305 |
300 | 1.1146 | 179.49 | 900 | 60.520 | 9.9169 | 2250 | 2777.5 | 0.54020 |
320 | 1.3972 | 152.73 | 950 | 74.815 | 8.4677 | 2300 | 3059.9 | 0.50124 |
340 | 1.7281 | 131.20 | 1000 | 91.651 | 7.2760 | 2350 | 3364.6 | 0.46576 |
360 | 2.1123 | 113.65 | 1050 | 111.35 | 6.2885 | 2400 | 3693.0 | 0.43338 |
380 | 2.5548 | 99.188 | 1100 | 134.25 | 5.4641 | 2450 | 4046.2 | 0.40378 |
400 | 3.0612 | 87.137 | 1150 | 160.73 | 4.7714 | 2500 | 4425.8 | 0.37669 |
420 | 3.6373 | 77.003 | 1200 | 191.17 | 4.1859 | 2550 | 4833.0 | 0.35185 |
440 | 4.2892 | 68.409 | 1250 | 226.02 | 3.6880 | 2600 | 5269.5 | 0.32903 |
460 | 5.0233 | 61.066 | 1300 | 265.72 | 3.2626 | 2650 | 5736.7 | 0.30805 |
480 | 5.8466 | 54.748 | 1350 | 310.74 | 2.8971 | 2700 | 6236.2 | 0.28872 |
500 | 6.7663 | 49.278 | 1400 | 361.62 | 2.5817 | 2750 | 6769.7 | 0.27089 |
520 | 7.7900 | 44.514 | 1450 | 418.89 | 2.3083 | 2800 | 7338.7 | 0.25443 |
540 | 8.9257 | 40.344 | 1500 | 483.16 | 2.0703 | 2850 | 7945.1 | 0.23921 |
560 | 10.182 | 36.676 | 1550 | 554.96 | 1.8625 | 2900 | 8590.7 | 0.22511 |
580 | 11.568 | 33.436 | 1600 | 634.97 | 1.6804 | 2950 | 9277.2 | 0.21205 |
600 | 13.092 | 30.561 | 1650 | 723.86 | 1.52007 | 3000 | 10007 | 0.19992 |
620 | 14.766 | 28.001 | 1700 | 822.33 | 1.37858 |
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640 | 16.598 | 25.713 | 1750 | 931.14 | 1.25330 |
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660 | 18.600 | 23.662 | 1800 | 1051.05 | 1.14204 |
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680 | 20.784 | 21.818 | 1850 | 1182.9 | 1.04294 |
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700 | 23.160 | 20.155 | 1900 | 1327.5 | 0.95445 |
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