Two metal rods 1 and 2 of same lengths have same temperature diff… - Vidyadip

MCQ

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
$k_1\,\,A_2=4k_2\,\,A_1$
✓
$k_1\,\,A_1=4k_2\,\,A_2$
C
$k_1=4k_2$
D
$k_1\,\,A_1^2=4k_2\,\,A_2^2$

✓

Answer

Correct option: B.

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

b
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, ${H_1} = 4{H_2}$

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

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