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

Answer: 90

Let $\theta$ be temperature middle point C and in series rate of heat flow is same.
$\Rightarrow \text{K}\left(2\text{A}\right)\left(100^{{}^{\circ }}-\theta \right)=\text{KA}\left(\theta -70^{{}^{\circ }}\right)$
$\Rightarrow 200-2\theta =\theta -70^{{}^{\circ }}\Rightarrow 3\theta =270\Rightarrow \theta =90℃$