Which of the following rods, (given radius $r$ and length $l$) each made of the same material and whose ends…
Which of the following rods, (given radius $r$ and length $l$) each made of the same material and whose ends are maintained at the same temperature will conduct most heat?
$r=r_0 \quad l=l_0$
$r=2 r_0 \quad l=l_0$
$r=r_0 \quad l=2 l_0$
$r=2 r_0 \quad l=2 l_0$
Solution
Heat conducted
$=\frac{K A\left(T_1-T_2\right) t}{l}=\frac{K \pi r^2\left(T_1-T_2\right) t}{l}$
The rod with maximum ratio of $\frac{A}{l}$ will conduct most. Here the rod $r=2 r_0$ and $l=l_0$ will conduct most.
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