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Thermal Resistance

A composite s...

Question

A composite slab has two layers of different materials, having thermal conductivities $k_{1}$ and $k_{2}$ . If each layer has same thickness, then what is the equivalent thermal conductivity of the slab?

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

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

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\frac{2 k_{1} k_{2}}{3 (k_{1} + k_{2})}

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

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Solution

The correct option is A $\frac{2 k_{1} k_{2}}{(k_{1} + k_{2})}$
Let $t$ be the thickness of each slab and
$A$ be the cross sectional area.

From thermal resistance analogy,
$\Rightarrow \frac{t}{k_{1} A} + \frac{t}{k_{2} A} = \frac{2 t}{k_{e q} A}$
$\Rightarrow \frac{t A (k_{1} + k_{2})}{k_{1} k_{2} A^{2}} = \frac{2 t}{k_{e q} A}$
$\Rightarrow k_{e q} = \frac{2 k_{1} k_{2}}{k_{1} + k_{2}}$

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Thermal Resistance

Standard XII Physics

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A composite slab has two layers of different materials, having thermal conductivities k1 and k2. If each layer has same thickness, then what is the equivalent thermal conductivity of the slab?

The correct option is A 2k1k2(k1+k2)Let t be the thickness of each slab and A be the cross sectional area. From thermal resistance analogy, ⇒tk1A+tk2A=2tkeqA ⇒tA(k1+k2)k1k2A2=2tkeqA ⇒keq=2k1k2k1+k2

A composite slab has two layers of different materials, having thermal conductivities $k_{1}$ and $k_{2}$ . If each layer has same thickness, then what is the equivalent thermal conductivity of the slab?