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

Question

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

Aicharya · Accepted Answer

According to the figure $\begin{array}{rlrl} H & =H_1+H_2 \ \Rightarrow & \frac{3 K A(100-T)}{l} & =\frac{2 K A(T-50)}{l}+\frac{K A(T-0)}{l} \ \ 300-3 T =2 T-100+T \ 6 T =400 \ 	ext { or } T =\frac{200}{3}{ }^{\circ} \mathrm{C} \end{array}$

Three rods of same dimensional have thermal conductivity $3 K, 2 K$ and $K$. They are arranged as shown in…

Solution