Question

Three rods made of the same material and having the same cross-section have been joined as shown in the fig. Each rod is of the same length. The left and right ends are kept at $0^{o}C$ and ${90}^{o}C$ respectively. The temperature of the junction of the three rods will be:

• A. ${45}^{o}C$
• B. ${60}^{o}C$
• C. ${30}^{o}C$
• D. ${20}^{o}C$

Answer 1

The correct option is B ${60}^{o}C$

Let the temperature of the junction be $\theta$.

The rate of heat transfer between two points is proportional to the temperature difference across the points.

Thus (rate of heat transferred from ${90}^{\circ }C$ to $\theta$ in each rod) $\propto ({90}^{\circ }C-\theta )$.

And, (rate of heat transferred from $\theta$ to $0^{\circ }C$)$\propto \theta$

From conservation of heat,

$2({90}^{\circ }-\theta )=\theta$

$⟹\theta ={60}^{\circ }C$