Gujarati
Hindi
10-2.Transmission of Heat
hard

$ABCDE$ is a regular pentagon of uniform wire. The rate of heat entering at $A$ and leaving at $C$ is equal. $T_B$ and $T_D$ are temperature of $B$ and $D$ . Find the temperature $T_C$

A

$\frac{{3{T_B} + 2{T_D}}}{5}$

B

$3T_D -2T_B$

C

$3T_D + 2T_B$

D

Can have any value

Solution

$\mathrm{R}_{1}=\frac{2 \ell}{\mathrm{k} \mathrm{A}}$

$R_{2}=\frac{3 \ell}{k A}$

heat goes in inverse ratio of resistance

$\mathrm{i}_{1}=\frac{\mathrm{T}_{\mathrm{A}}-\mathrm{T}_{\mathrm{C}}}{\mathrm{R}_{1}}=\frac{\mathrm{T}_{\mathrm{B}}-\mathrm{T}_{\mathrm{C}}}{\mathrm{R}}$

$\mathrm{i}_{2}=\frac{\mathrm{T}_{\mathrm{A}}-\mathrm{T}_{\mathrm{C}}}{\mathrm{R}_{2}}=\frac{\mathrm{T}_{\mathrm{D}}-\mathrm{T}_{\mathrm{C}}}{\mathrm{R}}$

dividing, $\frac{\mathrm{R}_{2}}{\mathrm{R}_{1}}=\frac{\mathrm{T}_{\mathrm{B}}-\mathrm{T}_{\mathrm{C}}}{\mathrm{T}_{\mathrm{D}}-\mathrm{T}_{\mathrm{C}}}$

$3 \mathrm{T}_{\mathrm{D}}-3 \mathrm{T}_{\mathrm{C}}=2 \mathrm{T}_{\mathrm{B}}-2 \mathrm{T}_{\mathrm{C}}$

$\mathrm{T}_{\mathrm{C}}=3 \mathrm{T}_{\mathrm{D}}-2 \mathrm{T}_{\mathrm{B}}$

Standard 11
Physics

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