Conduction

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Question

Which of the following cylindrical rods will conduct most heat when their ends are maintained at steady temperatures ${θ_{1}}^{o} C$ and ${θ_{2}}^{o} C$ ? The rods are made of same material.

Moderate

Solution

$Thermal resistance R = \frac{l}{π r^{2} \times K} and thermal current I_{th} = \frac{∆ θ}{R}$
Now $\frac{l}{r^{2}}$ is least when $l = 1 m$ and $r = 2 c m$
Hence $I_{th}$ is maximum for option (4)

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