For an ideal gas subjected to different processes as shown in the graphs, select the graph which will involve greatest amount of heat exchange if the initial and final temperatures are same in all?

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Each graph is a straight line through the origin, so P ∝ V k , i.e. PV n = constant with n = -k: (a) n = -1, (b) n = -2, (c) n = 2, (d) n = 3. Molar heat capacity C = C V + R/(1-n): (a) C V + R/2, (b) C V + R/3, (c) C V - R, (d) C V - R/2. With Δ T the same, Q = nCΔ T. Since C V ≥ 1.5R, the largest magnitude is C V + R/2, for graph (a). Matches (a).

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