Question

A metal rod of length $2m$ has cross sectional areas $2A$ and $A$ as shown in the figure. The ends are maintained at temperatures $100^\circ C$ and $70^\circ C$ . The temperature at middle point $C$ is___ $^\circ C$ .

Answer 1

Let $\theta $ be temperature middle point C and in series rate of heat flow is same.
$\Rightarrow \text{K} \left(2 \text{A}\right) \left(1 0 0^{^\circ } - \theta \right) = \text{KA} \left(\theta - 7 0^{^\circ }\right)$
$\Rightarrow 2 0 0 - 2 \theta = \theta - 7 0^{^\circ } \Rightarrow 3 \theta = 2 7 0 \Rightarrow \theta = 9 0 ℃$