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 0^0C and $90^{o}$ 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

Answer: (B)

60^o C

Answer 2

Let the conductivity of each rod is K. By considering the rods B and C are in parallel, effective thermal conductivity of B and C will be 2K.

Now with the help of given formula

Temperature of interface $\theta = \frac{K_{1}\theta_{1} + K_{2}\theta_{2}}{K_{1} + K_{2}}$

$\theta = \frac{K \times 0 + 2K \times 90}{K + 2K} = \frac{180}{3} = 60^{o}C$.