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Three rods of same dimensional have thermal conductivity $3 \mathrm{~K}, 2 \mathrm{~K}$ and $\mathrm{K}$. They are arranged as shown in the figure below
Then, the temperature of the junction in steady state is
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Then, the temperature of the junction in steady state is
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Verified Answer
The correct answer is:
$\frac{200}{3}^{\circ} \mathrm{C}$
From figure, $H=H_{1}+H_{2}$
$$
\begin{array}{l}
\Rightarrow \frac{3 K A(100-T)}{l}=\frac{2 K A(T-50)}{l}+\frac{K A(T-0)}{l} \\
\Rightarrow 300-3 T=2 T-100+T \Rightarrow 6 T=400 \\
\Rightarrow T=\frac{200}{3}{ }^{\circ} \mathrm{C}
\end{array}
$$
$$
\begin{array}{l}
\Rightarrow \frac{3 K A(100-T)}{l}=\frac{2 K A(T-50)}{l}+\frac{K A(T-0)}{l} \\
\Rightarrow 300-3 T=2 T-100+T \Rightarrow 6 T=400 \\
\Rightarrow T=\frac{200}{3}{ }^{\circ} \mathrm{C}
\end{array}
$$
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