A metallic prong consists of $4$ rods made of the same material, cross-sections and same lengths as shown below. The three forked ends are kept at $100^{\circ} C$ and the handle end is at $0^{\circ} C$. The temperature of the junction is ............. $^{\circ} C$
KVPY 2013, Medium
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(d)
Let junction temperature $=T^{\circ} C$.
As, heat inflow through three prongs = heat outflow through fourth prong.
So, $\quad 3 \frac{k A}{l}(100-T)=\frac{k A}{l}(T-0)$
$\Rightarrow 300-3 T =T$
$\text { or } T =75^{\circ} C$
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