A piston-cylinder assembly contains 1.23 kg of air at T1 = 748 K and P1 = 200 kP

Question

A piston-cylinder assembly contains 1.23 kg of air at T1 = 748 K and P1 = 200 kPa. The air is compressed to a final temperature and pressure of T2 = 946 K and P2 = 818 kPa During the process. 53.4 kJ of energy is transferred to the surroundings by heat transfer. Determine the work (kJ) done during the process. Note: Use the ideal gas tables for your calculations. Ideal Gas Properties of Air T(K) Cp(kJ/kg.K) h (kJ/kg) u (kJ/kg) s degree (kJ/kg.K) Pr Vr 200 1.00424 199.97 142.56 1.29559 0.3363 1707.1 300 1.00371 300.26 214.15 1.70226 1.3867 621.02 400 1.01358 401.06 286.23 1.99215 3.8069 301.62 500 1.03039 503.21 359.68 2.22003 8.4205 170.45 600 1.05137 607.27 435.04 2.40970 16.304 105.64 700 1.07431 713.55 512.61 2.57348 28.846 69.661 800 1.09755 822.14 592.50 2.71846 47.799 48.044 900 1.11988 933.03 674.68 2.84903 75.330 34.296 1000 1.14053 1046.06 759.01 2.96811 114.06 25.168 1100 1.15904 1161.06 845.30 3.07770 167.08 18.899 1200 1.17526 1277.80 933.33 3.17926 23

Explanation / Answer

From table, by interpolation between 700 and 800 K we get u(T1) = u(748) = 552.55 kJ/kg

Similarly by interpolating between 900 and 1000 K, u(T2) = u(946) = 802.1 kJ/kg

Q - W = m(u2 - u1)

-53.4 - W = 1.23*(802.1 - 552.55)

W = -360.4 kJ

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