Question

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 $B$. Under steady state, the temperature difference across the whole wall is ${36}^{\circ }C$. Then 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 ${12}^{\circ }C$

$\frac{d{\theta }_A}{dt}=\frac{d{\theta }_B}{dt}$
$2KA\left(\frac{x-0}{t}\right)=KA\left(\frac{36-x}{t}\right)$
$2x=36-x$
$x=\frac{36}{3}$
$x={12}^{\circ }C$