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A cylinder/piston contains 100L of air at 25°C, 110 kPa. The air is compressed in a reversible polytropic process to a final state of 200°C, 800 kPa. Assume the heat transfer is with the ambient at 25°C. Find the work done by the air.

A cylinder/piston contains 100L of air at 25°C, 110 kPa. The air is compressed in a reversible polytropic process to a final state of 200°C, 800 kPa. Assume the heat transfer is with the ambient at 25°C. Find the work done by the air. Correct Answer -21.28 kJ

m = P1V1 /(RT1) = 110 × 0.1/(0.287 × 298.15) = 0.1286 kg T2/T1 = (P2/P1)^ => 473.15/298.15 = (800/110)^ ⇒ (n-1)/n = 0.2328 hence n = 1.3034 V2 = V1(P1/P2)^(1/n) = 0.1(110/800)^(0.7672) = 0.02182 m^3 Work = ⌠PdV = (P2V2 – P1V1)/(1-n) = (800 × 0.02182 – 110 × 0.1)/(1 – 1.3034) = -21.28 kJ.

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