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Byju's Answer

Standard VII

Physics

Conduction

Two blocks of...

Question

Two blocks of the same thickness and thermal conductivities $k_{1} a n d k_{2}$ are placed in contact. Their outer surfaces are kept at constant temperatures $T_{1} a n d T_{2}$ . If $T_{2}$ > $T_{1}$ , and $k_{2}$ > $k_{1}$ the temperature of the interfaces in the steady state will be

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Solution

The correct option is A

Let T be the temperature of the interface in the steady state and let d be the thickness of each block. Now, insteady state, the rate of flow of heat through each block must be the same, i.e.

$\frac{k_{1} A (T_{1} - T)}{d} = \frac{k_{2} A (T - T_{2})}{d} o r k_{1} (T_{1} - T) = k_{2} (T - T_{2})$

Which give $T = \frac{k_{1} T_{1} + k_{2} T_{2}}{k_{1} + k_{2}}$ , which is choice (a)

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