Question

Two conductors $A$ and $B$ each of cross-section area $5c{m}^2$ are connected in series. Variation of temperature (in ${}^{\circ }C$) along the length (in $cm$) is as shown in the figure. If thermal conductivity of $A$ is $200J/m{s}^{\circ }C$ and thermal conductivity of $B$ is $K$ (in $J/m{S}^{\circ }C$), then find $\sqrt{\frac{K}{8\sqrt{3}}}$

Answer 1

As given, conductors $A$ and $B$ are connected in series,

So, heat flow from each conductor will be same.

$\frac{T_2-T_1}{\left(\frac{l_1}{K_{1}A}\right)}=\frac{T_3-T_2}{\left(\frac{l_2}{K_{2}A}\right)}$

As cross section of each conductor is same.

$K_A\left(\tan {60}^{\circ }\right)=K_B\left(tan{45}^{\circ }\right)$

$200\left(\sqrt{3}\right)=K\left(1\right)$

So, $\sqrt{\frac{K}{8\sqrt{3}}}=\sqrt{\frac{200\left(\sqrt{3}\right)}{8\sqrt{3}}}=5$