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A piston cylinder contains 0.5 kg of air at 500 kPa and 500 K. The air expands in a process so pressure is linearly decreasing with volume to a final state of 100 kPa and 300 K. Find the work in the process.

A piston cylinder contains 0.5 kg of air at 500 kPa and 500 K. The air expands in a process so pressure is linearly decreasing with volume to a final state of 100 kPa and 300 K. Find the work in the process. Correct Answer 86.1 kJ

Work = ⌠ PdV = (1/2)(P1 + P2)(V2 – V1) V1 = mR T1/ P1 = 0.5 × 0.287 × (500/500) = 0.1435 m^3 V2 = mR T2/ P2 = 0.5 × 0.287 × (300/100) = 0.4305 m^3 W = (1/2)(500 + 100)(0.4305 – 0.1435) = 86.1 kJ.

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