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 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 is :

• 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 at the point of contact of three rod is $T$,as we know that total incoming of heat is equal to total outgoing heat.
We know that heat flow is given as $Q=\frac{KA\left(\Delta T\right)}{L}$
So, $\frac{KA(0-T)}{L}=\frac{KA(T-90)}{L}+\frac{KA(T-90)}{L}$
Therefore, $3T={180}^{0C}$
$T={60}^{0}C$