3. (60 points) For jet aircraft flying out of Houston on a summer afternoon (T = 95 OF, 70% relative humidity) and Palm Springs on a winter morning (T = 40 OF, 55% relative humidity), determine for both locations: a) the mass of water vapor in 1 m3 of air b) the thermal efficiency of an ideal Brayton cycle with a pressure ratio of 9. Assume that both cities are at sea level and both air and H20 can be treated as ideal gases with constant specific heats evaluated at 300 K.914 PROPERTY TABLES AND CHARTS TABLE A-4 Saturated water-Temperature table Specific volume, Internal energy, Enthalpy, Entropy, KJ/kg-K ms/kg KJ/kg KJ/kg Sat. Sat. Sat. Sat. Sat. Sat. Sat. Sat. Sat. Temp., press., liquid, vapor, liquid, Evap., vapor, liquid, Evap., vapor, liquid, Evap., vapor, T OC Psat kPa 0.000 2374.9 2374.9 2500.9 0.0000 9.1556 9.1556 0.01 0.6117 0.001000 206.00 0.001 2500.9 2510.1 0.0763 8.9487 9.0249 5 0.8725 0.001000 147.03 21.019 2360.8 2381.8 21.020 2489.1 2519.2 0.1511 8.7488 8.8999 10 1.2281 0.001000 106.32 42.020 2346.6 2388.7 42.022 2477.2 15 1.7057 0.001001 77.885 62.980 2332.5 2395.5 62.982 2465.4 2528.3 0.2245 8.5559 8.7803 0.2965 8.3696 8.6661 20 2.3392 0.001002 57.762 83.913 2318.4 2402.3 83.915 2453.5 2537.4 43.340 2304.3 2409.1 104.83 2441.7 2546.5 25 3.1698 0.001003 104.83 0.3672 8.1895 8.5567 30 4.2469 0.001004 32.879 125.73 2290.2 2415.9 125.74 2429.8 2555.6 0.4368 8.0152 8.4520 35 5.6291 0.001006 25.205 146.63 2276.0 2422.7 146.64 2417.9 2564.6 0.5051 7.8466 8.3517 40 7.3851 0.001008 19.515 167.53 2261.9 2429.4 167.53 2406.0 2573.5 0.5724 7.6832 8.2556 45 9.5953 0.001010 15.25 188.43 2247.7 2436.1 188.44 2394.0 2582.4 0.6386 7.5247 8.1633 50 12.352 0.001012 12.026 209.33 2233.4 2442.7 209.34 2382.0 2591.3 0.7038 7.3710 8.0748 55 15.763 0.001015 9.5639 230.24 2219.1 2449.3 230.26 2369.8 2600.1 0.7680 7.2218 7.9898 60 19.947 0.001017 7.6670 251.16 2204.7 2455.9 251.18 2357.7 2608.8 0.8313 7.0769 7.9082 65 25.043 0.001020 6.1935 272.09 2190.3 2462.4 272.12 2345.4 2617.5 0.8937 6.9360 7. 70 31.202 0.001023 5.0396 293.04 2175.8 2468.9 293.07 2333.0 2626.1 0.9551 6.7989 7.7540 75 38.597 0.001026 4.1291 313.99 2161.3 2475.3 314.03 2320.6 2634.6 1.0158 6.6655 7.6812 80 47.416 0.001029 3.4053 334.97 2146.6 2481.6 335.02 2308.0 2643.0 1.0756 6.5355 7.6111 85 57.868 0.001032 2.8261 355.96 2131.9 2487.8 356.02 2295.3 2651.4 1.1346 6.4089 7.5435 90 70.183 0.001036 2.3593 376.97 2117.0 2494.0 377.04 2282.5 2659.6 1.1929 6.2853 7.4782 95 84.609 0.001040 1.9808 398.00 2102.0 2500.1 398.09 2269.6 2667.6 1.2504 6.1647 7.4151 100 101.42 0.001043 1.6720 419.06 2087.0 2506.0 419.17 2256.4 2675.6 1.3072 6.0470 7.3542 105 120.90 0.001047 .4186 440.15 2071.8 2511.9 440.28 2243.1 2683.4 1.3634 5.9319 7.2952 110 143.38 0.001052 1.2094 461.27 2056.4 2517.7 461.42 2229.7 2691.1 1.4188 5.8193 7.2382 115 169.18 0.001056 1.0360 482.42 2040.9 2523.3 482.59 2216.0 2698.6 1.4737 5.7092 7.1829 120 198.67 0.001060 0.89133 503.60 2025.3 2528.9 503.81 2202.1 2706.0 1.5279 5.6013 7.1292 125 232.23 0.001065 0.77012 524.83 2009.5 2534.3 525.07 2188.1 2713.1 1.5816 5.4956 7.0771 130 270.28 0.001070 0.66808 546.10 1993.4 2539.5 546.38 2173.7 2720.1 1.6346 5.3919 7.0265 135 313.22 0.001075 0.58179 567.41 1977.3 2544.7 567.75 2159.1 2726.9 1.6872 5.2901 6.9773 140 361.53 0.001080 0.50850 588.77 1960.9 2549.6 589.16 2144.3 2733.5 1.7392 5.1901 6.9294 145 415.68 0.001085 0.44600 610.19 1944.2 2554.4 610.64 2129.2 2739.8 1.7908 5.0919 6.8827 150 476.16 0.001091 0.39248 631.66 1927.4 2559.1 632.18 2113.8 2745.9 1.8418 4.9953 6.8371 155 543.49 0.001096 .34648 653.19 1910.3 2563.5 653.79 2098.0 2751.8 1.8924 4.9002 6.7927 160 618.23 0.001102 0.30680 674.79 1893.0 2567.8 675.47 2082.0 2757.5 1.9426 4.8066 6.7492 165 700.93 0.001108 0.27244 696.46 1875.4 2571.9 697.24 2065.6 2762.8 1.9923 4.7143 6.7067 170 792.18 0.001114 0.24260 718.20 1857.5 2575.7 719.08 2048.8 2767.9 2.0417 4.6233 6.6650 175 892.60 0.001121 0.21659 740.02 1839.4 4 2579.4 741.02 2031.7 2772.7 2.0906 4.5335 6.6242 180 1002.8 0.001127 0.19384 761.92 1820.9 2582.8 763.05 2014.2 2777.2 2.1392 4.4448 6.5841 185 1123.5 0.001134 0.17390 783.91 1802.1 2586.0 785.19 1996.2 2781.4 2.1875 4.3572 6.5447 190 1255.2 0.001 141 .15636 806,00 1783.0 2589.0 807.43 1977.9 2785.3 2.2355 4.2705 6.5059 195 1398.8 0.001149 0.14089 828.18 1763.6 2591.7 829.78 1959.0 2788.8 2.2831 4.1847 6.4678 200 1554.9 0.001157 0.12721 850,46 1743.7 2594.2 852.26 1939.8 2792.0 2.3305 4.0997 6.4302 909 APPENDIX 1 TABLE A-2 Ideal-gas specific heats of various common gases (a) At 300 K Gas constant, R KB/kB - K K J / kg . K Formula kJ/kg.K Gas 1.005 0.718 1.400 0.2870 Air 0.5203 0.3122 1.667 0.2081 1.091 Argon Ar 1.7164 1.5734 0.1433 Butane CAH 10 0.1889 0.846 0.657 1.289 Carbon dioxide CO2 1.040 0.744 1.400 0.2968 Carbon monoxide CO 1.7662 1.4897 1.186 C2 6 0.2765 1.237 Ethane 0.2964 1.5482 1.2518 CoH, 1.667 Ethylene 2.0769 5.1926 3.1156 Helium He 1.405 4.1240 14.307 10.183 1.299 Hydrogen H 2 0.5182 2.2537 1.7354 Methane CHA 1.0299 0.6179 1.667 0.4119 Neon Ne 0.2968 1.039 0.743 1.400 N2 0.0729 1.6385 1.044 Nitrogen 1.7113 Octane C8H 18 0.658 1.395 0.2598 0.918 1.126 Oxygen 1.6794 1.4909 Propane C3 H8 0.1885 1.4108 1.327 0.4615 1.8723 Steam HO Note: The unit kJ/kg.K is equivalent to kJ/kg. C. Source: Chemical and Process Thermodynamics 3/E by Kyle, B. G., @ 2000. Adapted by permission of Pearson Education, Inc., Upper Saddle River, NJ