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10-2.Transmission of Heat
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Six identical rods are arranged as shown in the figure. The temperature of the junction $B$ will be......... $^oC$
A
$\frac{240}{3}$
B
$240$
C
$140$
D
$\frac{140}{3}$
Solution
Let the thermal resistance of each rod be $\mathrm{R}$. The two resistance connected along two paths from $\mathrm{B}$ to $\mathrm{C}$ are equivalent to $2 \mathrm{R}$ each and their parallel combination is $\mathrm{R}$. Effective thermal resistance between $\mathrm{B}$ and $D=2 R$
temperature of inteface $\theta=\frac{R_{1} \theta_{2}+R_{2} \theta_{1}}{R_{1}+R_{2}}$
$\theta=\frac{R \times 20+2 R \times 200}{R+2 R}=\frac{420}{3}=140^{\circ} C$
Standard 11
Physics
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