Q. A wall has two layers $A$ and $B$ made of different materials. The thickness of both the layers is the same. The thermal conductivity of $A$ and $B$ are $K_{A}$ and $K_{B}$ such that $K_{A} = 3K_{B}$. The temperature across the wall is $20℃$. In thermal equilibrium
A) The temperature difference across $A = 15℃$
B) The temperature difference across $A = 5℃$
C) The temperature difference across $A\ $is $10℃$
D) The rate of transfer of heat through $A$ is more than that through $B$
Explanation
(b) In series rate of flow of heat is same
$\Rightarrow \frac{K_{A}A(\theta_{1} - \theta)}{l} = \frac{K_{B}A(\theta - \theta_{2})}{l}$
$\Rightarrow 3K_{B}\left( \theta_{1} - \theta \right) = K_{B}(\theta - \theta_{2})$
$\Rightarrow 3\left( \theta_{1} - \theta \right) = (\theta - \theta_{2})$
$\Rightarrow 3\theta_{1} - 3\theta = \theta - \theta_{2} \Rightarrow 4\theta_{1} - 4\theta = \theta_{1} - \theta_{2}$
$\Rightarrow 4(\theta_{1} - \theta) = {(\theta}_{1} - \theta_{2})$
$\Rightarrow 4(\theta_{1} - \theta) = 20 \Rightarrow {(\theta}_{1} - \theta) = 5℃$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.