Two sheets of thickness d and 3d , are touching each other. temperature just outside thinner sheet s

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10-2.Transmission of Heat

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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

A

$1 : 3$

B

$3 : 1$

C

$2 : 3$

D

$1 : 9$

Solution

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 $\quad \frac{K_{A}}{d}=\frac{K_{B}}{3 d}$

$\Longrightarrow K_{A}: K_{B}=1: 3$

Standard 11

Physics

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