Two ends of roads of length L and radius r of same material are kept at same temperature which of fo

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10-2.Transmission of Heat

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Two ends of roads of length $L$ and radius $r$ of the same material are kept at the same temperature which of the following rod conducts most heat?

A

$L = 50 \,cm;\,\, r = 1\, cm$

B

$L = 100\,cm;\,\, r = 2\, cm$

C

$L = 25 \,cm;\,\,r = 0.5\, cm$

D

$L = 75\, cm;\,\, r = 1.5\, cm$

Solution

Heat flow rate $(\mathrm{Q})=\frac{\mathrm{KA} \Delta \mathrm{T}}{\Delta \mathrm{x}}$

$\mathrm{Q} \propto \frac{\mathrm{A}}{\Delta \mathrm{x}} \alpha \frac{\pi \mathrm{r}^{2}}{\mathrm{L}}$

For maximum, by checking $\left(Q \propto \frac{r^{2}}{L}\right)$ for all

options, we can conclude : $\mathrm{L}=100 \mathrm{cm}: \mathrm{r}=2 \mathrm{cm}$

gives maximum value.

Standard 11

Physics

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