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Standard XIII

Physics

Thermal Resistance

Two metal rod...

Question

Two metal rods $1$ and $2$ of same lengths have the same temperature difference between their ends. Their thermal conductivities are $K_{1}$ and $K_{2}$ , and cross-sectional areas $A_{1}$ and $A_{2}$ respectively. If the rate of heat conduction in $1$ is four times that in $2$ , then

K_{1} A_{1} = K_{2} A_{2}

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K_{1} A_{1} = 4 K_{2} A_{2}

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K_{1} A_{1} = 2 K_{2} A_{2}

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4 K_{1} A_{1} = K_{2} A_{2}

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Solution

The correct option is B $K_{1} A_{1} = 4 K_{2} A_{2}$
We know, rate of heat flow $H = \frac{K A Δ T}{Δ x}$
$∵ Δ T$ is the same for both the rods and lengths ( $Δ x$ ) are also same, we can say that $\frac{H}{K A} =$ constant.
i.e $\frac{H_{1}}{K_{1} A_{1}} = \frac{H_{2}}{K_{2} A_{2}}$
$\Rightarrow \frac{H_{1}}{H_{2}} = \frac{K_{1} A_{1}}{K_{2} A_{2}}$
From the data given in the question, $\frac{H_{1}}{H_{2}} = 4$
$\Rightarrow 4 K_{2} A_{2} = K_{1} A_{1}$
Thus, option (b) is the correct answer.

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Thermal Resistance

Standard XIII Physics

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