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A thermodynamic system undergoes a cyclic process ABCDA on a P-V diagram. The cycle consists of two isobaric and two isochoric processes forming a rectangle. If the pressure changes between P0 and 2*P0 and the volume changes between V0 and 2*V0, the net work done by the system per cycle equals k times P0 * V0. Find k.
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Correct answer: 1
Solution
For any closed cyclic process on a P-V diagram, the net work done equals the area enclosed. For a rectangle with pressure varying from P0 to 2*P0 (delta_P = P0) and volume varying from V0 to 2*V0 (delta_V = V0), the area = delta_P * delta_V = P0 * V0. Hence work = 1 * P0 * V0, so k = 1.
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