Three rods of same material, same area of crosssection but different lengths $10 \,cm , 20 \,cm$ and $30 \,cm$ are connected at a point as shown. What is temperature of junction $O$ is ......... $^{\circ} C$
Medium
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(b)
Let temperature of junction be $=\theta$
Heat flowing to junction = heat out flowing
$\frac{K A}{30}(30-\theta)=\frac{K A}{20}(\theta-20)+\frac{K A}{10}(\theta-10)$
$\frac{(30-\theta)}{3}=\frac{(\theta-20)}{2}+\frac{(\theta-10)}{1}$
$\frac{(30-\theta)}{3}=\frac{\theta-20+2 \theta-20}{2}$
$\frac{60-2 \theta}{3}=9 \theta-120$
$\frac{180}{11}=\theta$
$16.36^{\circ} C =\theta$
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