Question

Two sheets of thickness $d$ and $3d$, are touching each other. The temperature just outside the thinner sheet side is $A$, and on the side of the thicker sheet is $C$. The interface temperature is $B$. $A,BandC$ are in arithmetic progression, the ratio of thermal conductivity of thinner sheet and thicker sheet is :

• A. $1:3$
• B. $3:1$
• C. $2:8$
• D. $1:9$

Answer 1

The correct option is A $1:3$

Since $\frac{Q}{t}=KA\frac{dT}{dx}$

$\frac{k_1\times a\times (A-B)}{d}=\frac{k_2\times a\times (B-C)}{3d}$
As $A-B=B-C$
$\frac{k_1}{k_2}=\frac{1}{3}$