A metal rod of length 2, m has cross-sectional areas 2A and A as shown in following figure. two ends

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10-2.Transmission of Heat

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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 ........ $^oC$

A

$80$

B

$85$

C

$90$

D

$95$

Solution

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 $T=90^{\circ} \mathrm{C}$

Standard 11

Physics

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