Question 11

**Setting up the cycle** From the V‑T diagram: - W → X: adiabatic (curve), volume increases 64 → 125 cm³ - X → Y: isobaric (straight line through origin, since V ∝ T at constant P), volume 125 → 250 cm³ - Y → Z: adiabatic - Z → W: isobaric **Step 1: Temperature at X (adiabatic W → X)** For a monatomic ideal gas, γ = 5/3, so TV^(γ−1) = TV^(2/3) = constant. T_X = T_W (V_W/V_X)^(2/3) = T_W (64/125)^(2/3) = T_W (4/5)² = (16/25) T_W **Step 2: Temperature at Y (isobaric X → Y)** At constant pressure, T ∝ V: T_Y = T_X (V_Y/V_X) = (16/25) T_W × 2 = (32/25) T_W **Step 3: Heat absorbed along XY** Q_XY = n C_p ΔT = (5/2) nR (T_Y − T_X) = (5/2) nR T_W (32/25 − 16/25) = (5/2)(16/25) nRT_W = (8/5)(1 J) = 1.6 J

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