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Standard VII

Physics

Conduction

Two metal rod...

Question

Two metal rods of same length and areas $A_{1}$ and $A_{2}$ are arranged in parallel. If the thermal conductivities of the materials are $k_{1}$ and $k_{2}$ , the effective thermal conductivity of the combination is :

\frac{2 k_{1} k_{2}}{k_{1} + k_{2}}

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\frac{k_{1} + k_{2}}{2}

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\frac{k_{1} A_{1} + k_{2} A_{2}}{A_{1} + A_{2}}

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\frac{k_{1} k_{2} (A_{1} + A_{2})}{k_{1} A_{2} + k_{2} A_{1}}

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Solution

The correct option is B $\frac{k_{1} A_{1} + k_{2} A_{2}}{A_{1} + A_{2}}$
As we know that for a plate, $Q = \frac{K A (T_{1} - T_{2})}{L}$
where, $R_{t h} = \frac{L}{K A}$
So we can solve it same as we solve the resistance in circuit.
$K (A_{1} + A_{2}) = K_{1} A_{1} + K_{2} A_{2}$
so equivalent thermal conductivity will be given as $K = \frac{K_{1} A_{1} + K_{2} A_{2}}{A_{1} + A_{2}}$

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