Question

Three rods of the same dimension have thermal conductivities $3K,2K$ and $K$. They are arranged as shown in figure given below, with their ends at ${100}^{\circ }C,{50}^{\circ }C$ and ${20}^{\circ }C$. The temperature of their junction is

• A. ${60}^{\circ }C$
• B. ${70}^{\circ }C$
• C. ${50}^{\circ }C$
• D. ${35}^{\circ }C$

Answer 1

The correct option is B ${70}^{\circ }C$

Let the temperature of junction be $\theta$. Then according to following figure,


Heat flow rate,
$H=H_1+H_2$
$\Rightarrow \frac{3K\times A\times (100-\theta )}{l}=\frac{2KA(\theta -50)}{l}+\frac{KA(\theta -20)}{l}$
$\Rightarrow 300-3\theta =3\theta -120\Rightarrow \theta ={70}^{\circ }C$