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Four rods made of the same material but with different radii r and lengths l connect two heat reservoirs held at different temperatures. Which rod conducts the most heat?

1. r = 2 cm, l = 0.5 m
2. r = 2 cm, l = 2 m
3. r = 0.5 cm, l = 0.5 m
4. r = 1 cm, l = 1 m

Correct answer: r = 2 cm, l = 0.5 m

Solution

Heat current is proportional to r²/l; this is maximised by the largest radius and smallest length, r = 2 cm, l = 0.5 m.

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