Three rods of same material, same area of crosssection but different lengths 10 ,cm , 20 ,cm and 30

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10-2.Transmission of Heat

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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 ......... $^{\circ} C$

A

$19.2$

B

$16.4$

C

$11.5$

D

$22$

Solution

(b)

Let temperature of junction be $=\theta$

Heat flowing to junction = heat out flowing

$\frac{K A}{30}(30-\theta)=\frac{K A}{20}(\theta-20)+\frac{K A}{10}(\theta-10)$

$\frac{(30-\theta)}{3}=\frac{(\theta-20)}{2}+\frac{(\theta-10)}{1}$

$\frac{(30-\theta)}{3}=\frac{\theta-20+2 \theta-20}{2}$

$\frac{60-2 \theta}{3}=9 \theta-120$

$\frac{180}{11}=\theta$

$16.36^{\circ} C =\theta$

Standard 11

Physics

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