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Three rods of same dimensional have thermal conductivity $3 K, 2 K$ and $K$. 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
Solution:
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Verified Answer
The correct answer is:
$\frac{100}{3}{ }^{\circ} \mathrm{C}$
According to the figure
$\begin{array}{rlrl}
H & =H_1+H_2 \\
\Rightarrow & \frac{3 K A(100-T)}{l} & =\frac{2 K A(T-50)}{l}+\frac{K A(T-0)}{l} \\
\\
300-3 T =2 T-100+T \\
6 T =400 \\
\text { or } T =\frac{200}{3}{ }^{\circ} \mathrm{C}
\end{array}$
$\begin{array}{rlrl}
H & =H_1+H_2 \\
\Rightarrow & \frac{3 K A(100-T)}{l} & =\frac{2 K A(T-50)}{l}+\frac{K A(T-0)}{l} \\
\\
300-3 T =2 T-100+T \\
6 T =400 \\
\text { or } T =\frac{200}{3}{ }^{\circ} \mathrm{C}
\end{array}$
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