Assuming steady state one-dimensional heat conduction in a composite slab- if Tinter - T1-T22- then which of the following statements is true about the respective thermal conductivities-

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Standard XIII

Physics

Conduction Law

Assuming stea...

Question

Assuming steady state one-dimensional heat conduction in a composite slab, if $T_{i n t e r} = \frac{T_{1} + T_{2}}{2},$ then which of the following statements is true about the respective thermal conductivities?

2 K_{1} = K_{2}

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K_{1} = K_{2}

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2 K_{1} = 3 K_{2}

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K_{1} = 2 K_{2}

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Solution

The correct option is D $K_{1} = 2 K_{2}$
Given, $T_{i n t e r} = \frac{T_{1} + T_{2}}{2}$
As heat flow throughout the slabs is same [steady state],
$Q_{1} = Q_{2} . . . . . . . (1)$
Rate of heat flow in slab -1 : $Q_{1} = K_{1} A \frac{(T_{1} - \frac{T_{1} + T_{2}}{2})}{2 b} = K_{1} A \frac{T_{1} - T_{2}}{4 b}$
Similarly:
$Q_{2} = K_{2} A \frac{(\frac{T_{1} + T_{2}}{2} - T_{2})}{b} = K_{2} A \frac{T_{1} - T_{2}}{2 b}$
[Area $A$ is the same]
From $(1)$ , we get
$\frac{K_{1}}{2} (\frac{T_{1} - T_{2}}{2}) = K_{2} (\frac{T_{1} - T_{2}}{2})$
$\Rightarrow \frac{K_{1}}{2} = K_{2}$ or $K_{1} = 2 K_{2}$
Thus, option (d) is the correct answer.

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Conduction Law

Standard XIII Physics

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Assuming steady state one-dimensional heat conduction in a composite slab, if Tinter=T1+T22, then which of the following statements is true about the respective thermal conductivities?

Assuming steady state one-dimensional heat conduction in a composite slab, if $T_{i n t e r} = \frac{T_{1} + T_{2}}{2},$ then which of the following statements is true about the respective thermal conductivities?