Equal temperature difference exists between the ends of two metallic rods $1$ and $2$ of length. Their thermal conductivities are $K_{1}$ and $K_{2}$ and cross sectional areas represents $A_{1}$ and $A_{2}$ . The condition for equal rate of heat transfer is:

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

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

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

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

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Solution

The correct option is B $K_{1} A_{1} = K_{2} A_{2}$
Equal temperature difference exists between the two metallic rods 1 and 2.
The heat transfer $= \frac{K A Δ T}{l}$
For equal rate of heat transfer,
$\frac{K_{1} A_{1} Δ T}{l} = \frac{K_{2} A_{2} Δ T}{l}$
$K_{1} A_{1} = K_{2} A_{2}$
The correct option is B.

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