When designing the air-conditioning system of an airplane, the work required to is entropically compress air must be calculated. Consider the process at steady state, the inlet compressor pressure is 0.5 bar and the outlet is at 5 bar. In addition to calculating the isentropic work, determine the air outlet temperature. Should you consider the air specific heat as temperature-dependent (Appendix A.2)?

Data From Appendix A.2

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T/ h/ K 200 205 210 369.8 309.5 7.4855 215 374.8 313.1 7.5091 220 379.8 316.7 7.5322 225 384.9 320.3 7.5547 230 389.9 323.8 7.5767 235 327.4 7.5983 394.9 399.9 331.0 7.6194 240 245 404.9 334.6 7.6400 250 409.9 338.1 7.6603 341.7 7.6801 255 414.9 260 419.9 345.3 7.6996 265 348.9 7.7187 425.0 430.0 352.5 7.7375 270 275 435.0 356.0 7.7559 280 440.0 359.6 7.7739 285 445.0 363.2 7.7917 290 450.0 366.8 7.8092 295 455.1 370.4 7.8263 300 460.1 374.0 7.8432 u/ $/ kJ/kg kJ/kg kJ/(kg.K) 359.8 302.4 7.4367 364.8 306.0 7.4614 305 465.1 377.5 7.8598 310 470.1 381.1 7.8761 475.1 384.7 7.8922 315 320 480.2 388.3 7.9080 325 485.2 391.9 7.9236 $/ kJ/(kg. K) 4.2910 4.3086 4.3258 4.3427 4.3591 4.3752 4.3909 4.4063 4.4213 4.4361 4.4505 4.4647 4.4786 4.4922 4.5056 4.5187 4.5317 4.5443 4.5568 4.5690 4.5811 4.5930 4.6046 4.6161 4.6274 4.6385 Cp / kJ/(kg.K) 17.81 3224 1.002 19.41 3032 1.002 21.11 2855 1.002 22.92 2693 1.002 24.84 2543 1.002 26.86 2404 1.002 29.01 2276 1.002 31.27 2157 1.002 33.65 2047 1.002 36.17 1945 1.002 Pr V₂ 38.81 1849 1.003 41.59 1760 1.003 44.51 1677 1.003 47.57 1599 1.003 50.78 1526 1.003 54.14 1458 1.003 57.66 1394 1.003 61.34 1334 1.004 65.19 1277 1.004 69.20 1224 1.004 73.39 1173 1.004 77.76 1126 1.004 82.32 1081 1.005 87.06 1039 1.005 91.99 998.6 1.005 97.12 960.6 1.006 Cu / kJ/(kg. K) 0.715 0.715 0.715 0.715 0.715 0.715 0.715 0.715 0.715 0.715 0.715 0.716 0.716 0.716 0.716 0.716 0.716 0.716 0.717 0.717 0.717 0.717 0.718 0.718 0.718 0.718 Y 1.402 1.402 1.402 1.401 1.401 1.401 1.401 1.401 1.401 1.401 1.401 1.401 1.401 1.401 1.401 1.401 1.401 1.401 1.401 1.400 1.400 1.400 1.400 1.400 1.400 1.400