Question

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

• A. ${45}^{\circ }\text{C}$
• B. ${60}^{\circ }\text{C}$
• C. ${30}^{\circ }\text{C}$
• D. ${20}^{\circ }\text{C}$

Answer 1

The correct option is B ${60}^{\circ }\text{C}$

We know that,
Rate of heat flow
$\left(H\right)=\frac{\text{Temperature difference}\left(\Delta \theta \right)}{\text{Thermal resistance (R)}}$
where $R=\frac{l}{KA}$
$K=$ Thermal conductivity of the rod.
$l=$Length of rod.
$A=$Area of cross-section.

Let $\theta$ be the temperature of the junction (say $B$). Thermal resistance$\left(R\right)$ of all the three rods is equal. Rate of heat flow through $AB+$ Rate of heat flow through $CB=$ Rate of heat flow through $BD$.
$\therefore \frac{90-\theta }{R}+\frac{90-\theta }{R}=\frac{\theta -0}{R}$
$\therefore 3\theta ={180}^{\circ }\text{C}$
or $\theta ={60}^{\circ }\text{C}$