Two gases A and B are in separate cylinders with frictionless movable pistons of radii rₐ and rᵦ. Both begin at equal pressure. Equal heat is supplied reversibly at constant pressure; internal-energy changes are equal. Pistons move 16 cm and 9 cm. Find rₐ/rᵦ.
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Question

Two gases A and B are in separate cylinders with frictionless movable pistons of radii rₐ and rᵦ. Both begin at equal pressure. Equal heat is supplied reversibly at constant pressure; internal-energy changes are equal. Pistons move 16 cm and 9 cm. Find rₐ/rᵦ.

Options

G1 Physics · Accepted Answer

Step 1: First law: Q = ΔU + W for each gas. Step 2: Equal Q and equal ΔU imply equal work Wₐ = Wᵦ. Step 3: At constant equal pressure, W = PΔV, so ΔVₐ = ΔVᵦ. Step 4: A piston’s displacement x changes volume by ΔV = πr²x. Step 5: Hence πrₐ²(16) = πrᵦ²(9), giving (rₐ/rᵦ)² = 9/16. Step 6: Take the positive root: rₐ/rᵦ = 3/4. Final answer: 3/4, Option B.