A wall has two layers A and B, each made of different material. Both layers have same thickness. the

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10-2.Transmission of Heat

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A wall has two layers $A$ and $B,$ each made of different material. Both the layers have the same thickness. The thermal conductivity for $A$ is twice that of $B$ and under steady condition, the temperature difference across the wall is $36\,^oC.$ The temperature difference across the layer $A$ is....... $^oC$

A

$6$

B

$12$

C

$24$

D

$18$

Solution

$\mathrm{K}_{\mathrm{A}}=2 \mathrm{K}_{\mathrm{B}}$

$\therefore \quad \mathrm{R}_{\mathrm{A}}=\frac{\mathrm{R}_{\mathrm{B}}}{2}$

Suppose, $\mathrm{R}_{\mathrm{A}}=\mathrm{R}$ then $\mathrm{R}_{\mathrm{B}}=2 \mathrm{R}$

Heat current $\mathrm{H}=\frac{36}{\mathrm{R}+2 \mathrm{R}}=\frac{36}{3 \mathrm{R}}=\frac{12}{\mathrm{R}}$

Temperature difference across

$A=H \times R_{A}=\frac{12}{R} \times R=12^{\circ} C$

Standard 11

Physics

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