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 $B. A, B$ and $C$ are in arithmetic progressing, the ratio of thermal conductivity of thinner sheet and thicker sheet is
Diffcult
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Given $: L_{A}=d L_{B}=3 d$
As $T_{2}, T_{1}, T_{2} \& T_{3}$ are in arithmetic progression.
$\therefore 2 T_{1}=T_{2}+T_{2} \quad \Longrightarrow T_{1}=T_{2}$
Similarly, $2 T_{2}=T_{1}+T_{3}$
OR $\quad 2 T_{2}=T_{2}+T_{3} \quad T_{2}=T_{3}$
Using: $\frac{d Q_{A}}{d t}=\frac{d Q_{B}}{d t}$
$\therefore \frac{K_{A} A\left(T_{1}-T_{2}\right)}{L_{A}}=\frac{K_{B} A\left(T_{2}-T_{3}\right)}{L_{B}}$
OR $\quad \frac{K_{A}}{d}=\frac{K_{B}}{3 d}$
$\Longrightarrow K_{A}: K_{B}=1: 3$
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