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A cylindrical metallic rod in thermal contact with two reservoirs of heat at its two ends conducts an amount of heat Q in time t. The metallic rod is melted and the material is formed into a rod of half the radius of the original rod. What is the amount of heat conducted by the new rod, when placed in thermal contact with the two reservoirs in time t?

1. Q/4
2. Q/16
3. 2Q
4. Q/2

Correct answer: Q/16

Solution

The rate of heat conduction is proportional to the cross-sectional area of the rod, which depends on the square of the radius. Halving the radius reduces the area by a factor of 4, and thus the heat conducted is reduced by a factor of 16.

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