Two metal rods 1 and 2 of same lengths have same temperature difference between their ends. Their th

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10-2.Transmission of Heat

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Two metal rods $1$ and $2$ of same lengths have same temperature difference between their ends. Their thermal conductivities are $K_1$ and $K_2$ and cross sectional areas $A_1$ and $A_2$ , respectively. If the rate of heat conduction in $1$ is four times that in $2$, then

A

$k_1\,\,A_2=4k_2\,\,A_1$

B

$k_1\,\,A_1=4k_2\,\,A_2$

C

$k_1=4k_2$

D

$k_1\,\,A_1^2=4k_2\,\,A_2^2$

Solution

Let $L$ be length of each rod.

Rate of heat flow in rod $1$ for the temperature difference $\Delta T$ is

${H_1} = \frac{{{K_1}{A_1}\Delta T}}{L}$

Rate of heat flow in rod $2$ for the same difference $\Delta T$ is

${H_2} = \frac{{{K_2}{A_2}\Delta T}}{L}$

As per question, ${H_1} = 4{H_2}$

$\frac{{{K_1}{A_1}\Delta T}}{L} = 4\frac{{{K_2}{A_2}\Delta T}}{L}\,\,;\,\,{K_1}{A_1} = 4{K_2}{A_2}$

Standard 11

Physics

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