Question

A slab consists of two layers of different materials of the same thickness and having thermal conductivities $K_1$ and $K_2$ are connected in series. The equivalent thermal conductivity of the slab is

• A. $\frac{2K_{1}K_{2}}{K_{1}+K_{2}}$
• B. $\sqrt{K_{1}K_{2}}$
• C. $\frac{K_{1}K_{2}}{K_{1}+K_{2}}$
• D. $K_{1}+K_{2}$

Answer 1

Answer: (A)

In series combination, $\frac{t}{K_{1}}+\frac{t}{K_{2}}=\frac{2t}{K}$
$\Rightarrow \frac{1}{K_{1}}+\frac{1}{K_{2}}=\frac{2}{K}$
$\Rightarrow K=\frac{2K_{1}K_{2}}{K_{1}+K_{2}}$.