2. (40 points) An adiabatic compressor receives Ar gas at 1 atm and 21 C and...

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2. (40 points) An adiabatic compressor receives Ar gas at 1 atm and 21 C and delivers pressurized Ar gas at 15 atm while operating at an isentropic efficiency of 87%. Neglecting changes in kinetic energy and assuming ideal gas behavior with constant specific heats evaluated at 300 K, determine the Ar gas temperature at the compressor outlet. Hint: For isentropic processes, k-1 T2 T k 914 PROPERTY TABLES AND CHARTS TABLE A-4 Saturated water-Temperature table Specific volume, Internal energy, m/kg kJ/kg Enthalpy, kJ/kg Entropy, kJ/kg.K Sat. Sat. Sat. Sat. Sat. Sat. Sat. Sat. Sat. Temp., press., liquid, vapor, liquid, Evap., vapor, liquid, Evap., vapor, liquid, Evap., vapor, TC Psat kPa vt Vg U Ufg Ug ht hfg hg St Sfg Sg 0.01 0.6117 0.001000 206.00 0.000 2374.9 2374.9 5 10 0.8725 0.001000 147.03 1.2281 0.001000 106.32 21.019 15 1.7057 0.001001 20 2.3392 0.001002 77.885 57.762 25 3.1698 0.001003 43.340 30 4.2469 0.001004 32.879 35 5.6291 0.001006 25.205 40 7.3851 0.001008 19.515 45 9.5953 0.001010 15.251 146.63 167.53 188.43 50 12.352 0.001012 12.026 55 15.763 0.001015 60 19.947 0.001017 65 25.043 70 31.202 0.001020 0.001023 0.001 2500.9 2500.9 2360.8 2381.8 21.020 2489.1 2510.1 42.020 2346.6 2388.7 42.022 2477.2 2519.2 62.980 2332.5 2395.5 62.982 2465.4 2528.3 83.913 2318.4 2402.3 83.915 2453.5 2537.4 104.83 2304.3 2409.1 104.83 2441.7 2546.5 125.73 2290.2 2415.9 125.74 2429.8 2555.6 2276.0 2422.7 146.64 2417.9 2564.6 2261.9 2429.4 2247.7 2436.1 209.33 2233.4 2442.7 9.5639 230.24 2219.1 2449.3 7.6670 251.16 2204.7 2455.9 6.1935 272.09 2190.3 2462.4 5.0396 293.04 2175.8 2468.9 2374.9 0.0000 9.1556 9.1556 0.0763 8.9487 9.0249 0.1511 8.7488 8.8999 0.2245 8.5559 8.7803 0.2965 8.3696 8.6661 75 38.597 0.001026 4.1291 313.99 80 47.416 0.001029 3.4053 334.97 85 57.868 0.001032 2.8261 90 70.183 95 84.609 100 101.42 105 120.90 0.001036 0.001040 0.001043 0.001047 110 143.38 0.001052 115 169.18 120 198.67 125 232.23 130 270.28 135 313.22 140 361.53 145 415.68 150 476.16 155 543.49 160 165 170 618.23 700.93 792.18 175 892.60 180 1002.8 0.001056 0.001060 0.001065 0.001070 0.001075 0.001080 0.001085 0.001091 0.001096 0.001102 0.001108 0.001114 0.001121 0.001127 185 1123.5 190 1255.2 195 1398.8 200 1554.9 0.001134 355.96 2.3593 376.97 1.9808 398.00 1.6720 419.06 1.4186 440.15 1.2094 461.27 1.0360 482.42 0.89133 503.60 0.77012 524.83 0.66808 546.10 0.58179 567.41 0.50850 588.77 0.44600 610.19 0.39248 631.66 0.34648 653.19 0.30680 674.79 0.27244 696.46 0.24260 718.20 0.21659 740.02 0.19384 761.92 0.17390 783.91 167.53 2406.0 2573.5 188.44 2394.0 2582.4 209.34 2382.0 2591.3 230.26 2369.8 2600.1 251.18 2357.7 2608.8 272.12 2345.4 2617.5 293.07 2333.0 2626.1 2161.3 2475.3 314.03 2320.6 2634.6 2146.6 2481.6 335.02 2308.0 2643.0 2131.9 2487.8 356.02 2295.3 2651.4 2117.0 2494.0 377.04 2282.5 2659.6 2102.0 2500.1 398.09 2269.6 2667.6 0.3672 8.1895 8.5567 0.4368 8.0152 8.4520 0.5051 7.8466 8.3517 0.5724 7.6832 8.2556 0.6386 7.5247 8.1633 0.7038 7.3710 8.0748 0.7680 7.2218 7.9898 0.8313 7.0769 7.9082 0.8937 6.9360 7.8296 0.9551 6.7989 7.7540 1.0158 6.6655 7.6812 1.0756 6.5355 7.6111 1.1346 6.4089 7.5435 1.1929 6.2853 7.4782 1.2504 6.1647 7.4151 0.001141 0.15636 806.00 0.001149 0.001157 0.14089 828.18 0.12721 850.46 1927.4 2559.1 632.18 1910.3 2563.5 653.79 1893.0 2567.8 675.47 1875.4 2571.9 697.24 1857.5 2575.7 719.08 1839.4 2579.4 741.02 1820.9 2582.8 763.05 1802.1 2586.0 785.19 1783.0 2589.0 1763.6 2591.7 829.78 1743.7 2594.2 852.26 2087.0 2506.0 419.17 2256.4 2675.6 2071.8 2511.9 440.28 2243.1 2683.4 2056.4 2517.7 461.42 2229.7 2691.1 2040.9 2523.3 482.59 2216.0 2698.6 2025.3 2528.9 503.81 2202.1 2706.0 2009.5 2534.3 525.07 2188.1 2713.1 1993.4 2539.5 546.38 2173.7 2720.1 1977.3 2544.7 567.75 2159.1 2726.9 1960.9 2549.6 589.16 2144.3 2733.5 1944.2 2554.4 610.64 2129.2 2739.8 2113.8 2745.9 2098.0 2751.8 2082.0 2757.5 2065.6 2762.8 2048.8 2767.9 1.3072 6.0470 7.3542 2031.7 2772.7 2014.2 2777.2 1996.2 2781.4 1.3634 5.9319 7.2952 1.4188 5.8193 7.2382 1.4737 5.7092 7.1829 1.5279 5.6013 7.1292 1.5816 5.4956 7.0771 1.6346 5.3919 7.0265 1.6872 5.2901 6.9773 1.7392 5.1901 6.9294 1.7908 5.0919 6.8827 1.8418 4.9953 6.8371 1.8924 4.9002 6.7927 1.9426 4.8066 6.7492 1.9923 4.7143 6.7067 2.0417 4.6233 6.6650 2.0906 4.5335 6.6242 2.1392 4.4448 6.5841 2.1875 4.3572 6.5447 807.43 1977.9 2785.3 1959.0 2788.8 1939.8 2792.0 2.2355 4.2705 6.5059 2.2831 4.1847 6.4678 2.3305 4.0997 6.4302 TABLE A-2 Ideal-gas specific heats of various common gases (a) At 300 K 909 APPENDIX 1 Gas Air Formula Gas constant, R kJ/kg.K Cp kJ/kg.K Cv kJ/kg.K k 0.2870 1.005 0.718 1.400 Argon Ar 0.2081 0.5203 0.3122 1.667 Butane C4H10 0.1433 1.7164 1.5734 1.091 Carbon dioxide CO2 0.1889 0.846 0.657 1.289 Carbon monoxide CO 0.2968 1.040 0.744 1.400 Ethane C2H6 0.2765 1.7662 1.4897 1.186 Ethylene CH4 0.2964 1.5482 1.2518 1.237 Helium He 2.0769 5.1926 3.1156 1.667 Hydrogen H 4.1240 14.307 10.183 1.405 Methane CHA 0.5182 2.2537 1.7354 1.299 Neon Ne 0.4119 1.0299 0.6179 1.667 Nitrogen N 0.2968 1.039 0.743 1.400 Octane C8H18 0.0729 1.7113 1.6385 1.044 Oxygen 02 0.2598 0.918 0.658 1.395 Propane C3H8 0.1885 1.6794 1.4909 1.126 Steam HO 0.4615 1.8723 1.4108 1.327 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. 2. (40 points) An adiabatic compressor receives Ar gas at 1 atm and 21 C and delivers pressurized Ar gas at 15 atm while operating at an isentropic efficiency of 87%. Neglecting changes in kinetic energy and assuming ideal gas behavior with constant specific heats evaluated at 300 K, determine the Ar gas temperature at the compressor outlet. Hint: For isentropic processes, k-1 T2 T k 914 PROPERTY TABLES AND CHARTS TABLE A-4 Saturated water-Temperature table Specific volume, Internal energy, m/kg kJ/kg Enthalpy, kJ/kg Entropy, kJ/kg.K Sat. Sat. Sat. Sat. Sat. Sat. Sat. Sat. Sat. Temp., press., liquid, vapor, liquid, Evap., vapor, liquid, Evap., vapor, liquid, Evap., vapor, TC Psat kPa vt Vg U Ufg Ug ht hfg hg St Sfg Sg 0.01 0.6117 0.001000 206.00 0.000 2374.9 2374.9 5 10 0.8725 0.001000 147.03 1.2281 0.001000 106.32 21.019 15 1.7057 0.001001 20 2.3392 0.001002 77.885 57.762 25 3.1698 0.001003 43.340 30 4.2469 0.001004 32.879 35 5.6291 0.001006 25.205 40 7.3851 0.001008 19.515 45 9.5953 0.001010 15.251 146.63 167.53 188.43 50 12.352 0.001012 12.026 55 15.763 0.001015 60 19.947 0.001017 65 25.043 70 31.202 0.001020 0.001023 0.001 2500.9 2500.9 2360.8 2381.8 21.020 2489.1 2510.1 42.020 2346.6 2388.7 42.022 2477.2 2519.2 62.980 2332.5 2395.5 62.982 2465.4 2528.3 83.913 2318.4 2402.3 83.915 2453.5 2537.4 104.83 2304.3 2409.1 104.83 2441.7 2546.5 125.73 2290.2 2415.9 125.74 2429.8 2555.6 2276.0 2422.7 146.64 2417.9 2564.6 2261.9 2429.4 2247.7 2436.1 209.33 2233.4 2442.7 9.5639 230.24 2219.1 2449.3 7.6670 251.16 2204.7 2455.9 6.1935 272.09 2190.3 2462.4 5.0396 293.04 2175.8 2468.9 2374.9 0.0000 9.1556 9.1556 0.0763 8.9487 9.0249 0.1511 8.7488 8.8999 0.2245 8.5559 8.7803 0.2965 8.3696 8.6661 75 38.597 0.001026 4.1291 313.99 80 47.416 0.001029 3.4053 334.97 85 57.868 0.001032 2.8261 90 70.183 95 84.609 100 101.42 105 120.90 0.001036 0.001040 0.001043 0.001047 110 143.38 0.001052 115 169.18 120 198.67 125 232.23 130 270.28 135 313.22 140 361.53 145 415.68 150 476.16 155 543.49 160 165 170 618.23 700.93 792.18 175 892.60 180 1002.8 0.001056 0.001060 0.001065 0.001070 0.001075 0.001080 0.001085 0.001091 0.001096 0.001102 0.001108 0.001114 0.001121 0.001127 185 1123.5 190 1255.2 195 1398.8 200 1554.9 0.001134 355.96 2.3593 376.97 1.9808 398.00 1.6720 419.06 1.4186 440.15 1.2094 461.27 1.0360 482.42 0.89133 503.60 0.77012 524.83 0.66808 546.10 0.58179 567.41 0.50850 588.77 0.44600 610.19 0.39248 631.66 0.34648 653.19 0.30680 674.79 0.27244 696.46 0.24260 718.20 0.21659 740.02 0.19384 761.92 0.17390 783.91 167.53 2406.0 2573.5 188.44 2394.0 2582.4 209.34 2382.0 2591.3 230.26 2369.8 2600.1 251.18 2357.7 2608.8 272.12 2345.4 2617.5 293.07 2333.0 2626.1 2161.3 2475.3 314.03 2320.6 2634.6 2146.6 2481.6 335.02 2308.0 2643.0 2131.9 2487.8 356.02 2295.3 2651.4 2117.0 2494.0 377.04 2282.5 2659.6 2102.0 2500.1 398.09 2269.6 2667.6 0.3672 8.1895 8.5567 0.4368 8.0152 8.4520 0.5051 7.8466 8.3517 0.5724 7.6832 8.2556 0.6386 7.5247 8.1633 0.7038 7.3710 8.0748 0.7680 7.2218 7.9898 0.8313 7.0769 7.9082 0.8937 6.9360 7.8296 0.9551 6.7989 7.7540 1.0158 6.6655 7.6812 1.0756 6.5355 7.6111 1.1346 6.4089 7.5435 1.1929 6.2853 7.4782 1.2504 6.1647 7.4151 0.001141 0.15636 806.00 0.001149 0.001157 0.14089 828.18 0.12721 850.46 1927.4 2559.1 632.18 1910.3 2563.5 653.79 1893.0 2567.8 675.47 1875.4 2571.9 697.24 1857.5 2575.7 719.08 1839.4 2579.4 741.02 1820.9 2582.8 763.05 1802.1 2586.0 785.19 1783.0 2589.0 1763.6 2591.7 829.78 1743.7 2594.2 852.26 2087.0 2506.0 419.17 2256.4 2675.6 2071.8 2511.9 440.28 2243.1 2683.4 2056.4 2517.7 461.42 2229.7 2691.1 2040.9 2523.3 482.59 2216.0 2698.6 2025.3 2528.9 503.81 2202.1 2706.0 2009.5 2534.3 525.07 2188.1 2713.1 1993.4 2539.5 546.38 2173.7 2720.1 1977.3 2544.7 567.75 2159.1 2726.9 1960.9 2549.6 589.16 2144.3 2733.5 1944.2 2554.4 610.64 2129.2 2739.8 2113.8 2745.9 2098.0 2751.8 2082.0 2757.5 2065.6 2762.8 2048.8 2767.9 1.3072 6.0470 7.3542 2031.7 2772.7 2014.2 2777.2 1996.2 2781.4 1.3634 5.9319 7.2952 1.4188 5.8193 7.2382 1.4737 5.7092 7.1829 1.5279 5.6013 7.1292 1.5816 5.4956 7.0771 1.6346 5.3919 7.0265 1.6872 5.2901 6.9773 1.7392 5.1901 6.9294 1.7908 5.0919 6.8827 1.8418 4.9953 6.8371 1.8924 4.9002 6.7927 1.9426 4.8066 6.7492 1.9923 4.7143 6.7067 2.0417 4.6233 6.6650 2.0906 4.5335 6.6242 2.1392 4.4448 6.5841 2.1875 4.3572 6.5447 807.43 1977.9 2785.3 1959.0 2788.8 1939.8 2792.0 2.2355 4.2705 6.5059 2.2831 4.1847 6.4678 2.3305 4.0997 6.4302 TABLE A-2 Ideal-gas specific heats of various common gases (a) At 300 K 909 APPENDIX 1 Gas Air Formula Gas constant, R kJ/kg.K Cp kJ/kg.K Cv kJ/kg.K k 0.2870 1.005 0.718 1.400 Argon Ar 0.2081 0.5203 0.3122 1.667 Butane C4H10 0.1433 1.7164 1.5734 1.091 Carbon dioxide CO2 0.1889 0.846 0.657 1.289 Carbon monoxide CO 0.2968 1.040 0.744 1.400 Ethane C2H6 0.2765 1.7662 1.4897 1.186 Ethylene CH4 0.2964 1.5482 1.2518 1.237 Helium He 2.0769 5.1926 3.1156 1.667 Hydrogen H 4.1240 14.307 10.183 1.405 Methane CHA 0.5182 2.2537 1.7354 1.299 Neon Ne 0.4119 1.0299 0.6179 1.667 Nitrogen N 0.2968 1.039 0.743 1.400 Octane C8H18 0.0729 1.7113 1.6385 1.044 Oxygen 02 0.2598 0.918 0.658 1.395 Propane C3H8 0.1885 1.6794 1.4909 1.126 Steam HO 0.4615 1.8723 1.4108 1.327 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.