Question

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 ${100}^{o}C,{50}^{o}Cand{20}^{o}C$. The temperature of their junction is

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Let the temperature of junction be q then according to following figure.

$H=H_1+H_2$
$\Rightarrow \frac{3K\times A\times (100-\theta )}{l}=\frac{2KA(\theta -50)}{l}+\frac{KA(\theta -20)}{l}$
$\Rightarrow 300-3\theta =3\theta -120\Rightarrow \theta ={70}^{o}C$