In the following p-V diagram the equation of state along the curved path is given by (V - 2)² = 4ap where a is a constant. The total work done in the closed path is

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G1 Physics · Accepted Answer

The curved path satisfies (V-2)² = 4ap. Therefore, p = (V-2)²/(4a). At points A and C, V = 1 m³ and V = 3 m³, respectively. For either endpoint, (V-2)² = 1. Hence the top pressure is P₀ = 1/(4a). The cycle follows the curved path from A to C and returns from C to A along the top horizontal line. Work along the curved path is W(curve) = ∫ from 1 to 3 [(V-2)²/(4a)]dV. Let u = V-2. Then the limits are -1 to +1: W(curve) = (1/4a)∫ from -1 to 1 u²du = (1/4a)(2/3) = 1/(6a). Along the top horizontal p…