Question

A furnace is made of a red brick wall of thickness $0.5\text{m}$ and conductivity $0.7\text{W/mK}$. For the same rate of heat conduction and the same temperature drop, this can be replaced by a diatomite wall of conductivity $0.14\text{W/mK}$ and the same cross-sectional area. Find the thickness of the diatomite wall.

• A. $0.05\text{m}$
• B. $0.1\text{m}$
• C. $0.2\text{m}$
• D. $0.5\text{m}$

Answer 1

The correct option is B $0.1\text{m}$

We know that, rate of heat flow
$Q=KA\frac{T_1-T_2}{l}$
From the data given in the question,
Rate of heat conduction in brick wall = Rate of heat conduction in diatomite wall
$\Rightarrow {(0.7\times A\times \frac{T_1-T_2}{0.5})}_{\text{brick wall}}={(0.14\times A\times \frac{T_1-T_2}{l^{\prime }})}_{\text{diatomite wall}}$
[Given, $A$ and $T_1-T_2$ are same]
$\Rightarrow l^{\prime }=\frac{5}{7}\times 0.14=0.1\text{m}$
Thus, option (b) is the correct answer.