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Standard XIII

Physics

Conduction Law

Two rods made...

Question

Two rods made of same material, have same thermal conductivities and area of cross-section. It is observed that to conduct same amount of heat between temperatures $T_{1}$ and $T_{2}$ , rod $1$ takes twice the time as the other. Find the ratio of their lengths.

2 : 1

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1 : 3

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1 : 1

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\sqrt{2} : 1

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Solution

The correct option is A $2 : 1$
Given,
$k_{1} = k_{2}, A_{1} = A_{2}, Q_{1} = Q_{2}$ and $t_{1} = 2 t_{2}$
We know that,
$Q = \frac{k A (T_{1} - T_{2}) t}{l}$
$∴ \frac{Q_{1}}{Q_{2}} = \frac{k_{1}}{k_{2}} \times \frac{A_{1}}{A_{2}} \times \frac{t_{1}}{t_{2}} \times \frac{l_{2}}{l_{1}}$
$\Rightarrow \frac{t_{1}}{t_{2}} = \frac{l_{1}}{l_{2}}$
$\Rightarrow \frac{l_{1}}{l_{2}} = \frac{2}{1}$
$∴$ option $(a)$ is correct.

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Conduction Law

Standard XIII Physics

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Two rods made of same material, have same thermal conductivities and area of cross-section. It is observed that to conduct same amount of heat between temperatures T1 and T2, rod 1 takes twice the time as the other. Find the ratio of their lengths.

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