Question 373: Properties of Matter

Question

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

Accepted Answer

Let L be length of each rod. Rate of heat flow in rod 1 for the temperature difference $$\Delta T$$ is
$${H_1} = {{{K_1}{A_1}\Delta T} \over L}$$
Rate of heat flow in rod 2 for the same difference $$\Delta T$$ is
$${H_2} = {{{K_2}{A_2}\Delta T} \over L}$$
As per question, H
1
= 4H
2
$${{{K_1}{A_1}\Delta T} \over L} = 4{{{K_2}{A_2}\Delta T} \over L}$$
$$ \Rightarrow {K_1}{A_1} = 4{K_2}{A_2}$$

Answer

K
1
A
1
= 4K
2
A
2

Answer

K
1
A
1
= 2K
2
A
2

Answer

4K
1
A
1
= K
2
A
2

Answer

K
1
A
1
= K
2
A
2

Properties of Matter

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

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