Question

A wall has two layers $A$ and $B$, each made of different materials. Both the layers have the same thickness. The thermal conductivity of the material of $A$ is twice that of $B$. Under thermal equilibrium, the temperature difference across the wall is ${36}^{\circ }C$. The temperature difference across the layer $A$ is

• A. $6^{\circ }C$
• B. ${12}^{\circ }C$
• C. ${18}^{\circ }C$
• D. ${24}^{\circ }C$

Answer 1

The correct option is B ${12}^{\circ }C$

$H=\frac{2kA(T_1-T)}{L}=\frac{kA(T-T_2)}{L}$
$\Rightarrow 2T_1-3T=-T_2$
adding $T_1$ on both sides:
$\Rightarrow T_1-T=\frac{T_1-T_2}{3}$
$=\frac{36}{3}={12}^{\circ }C$.