A metal rod of length $2\, m$ has cross-sectional areas $2A$ and $A$ as shown in the following figure. The two ends are maintained at temperatures $100\,^oC$ and $70\,^oC$. The temperature of middle point $C$ is ........ $^oC$
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Here; $\mathrm{K}_{1}=\mathrm{K}_{2}, l_{1}=l_{2}=1 \mathrm{m}$
$A_{1}=2 A, A_{2}=A$
$\mathrm{T}_{1}=100^{\circ} \mathrm{C}$ and $\mathrm{T}_{2}=70^{\circ} \mathrm{C}$
$\therefore$ Temperature at $\mathrm{C}$ be $\mathrm{T},$ then
$\frac{\Delta Q}{\Delta t}=\frac{K 2 A(100-T)}{1}=\frac{K A(T-70)}{1}$
or $T=90^{\circ} \mathrm{C}$
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