Q. Three rods of the same dimension have thermal conductivities $3K,\ 2K$ and $K$. They are arranged as shown in fig. Given below, with their ends at $100℃,\ 50℃$ and $20℃$. The temperature of their junction is
A) $60℃$
B) $70℃$
C) $50℃$
D) $35℃$
Explanation
(b) Let the temperature of junction be $\theta$ then according to the following figure
$H = H_{1} + H_{2}$
$\Rightarrow \frac{3K \times A \times (100 - \theta)}{l} = \frac{2KA(\theta - 50)}{l} + \frac{KA(\theta - 20)}{l}$
$\Rightarrow 300 - 3\theta = 3\theta - 120 \Rightarrow \theta = 70℃$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.