Question 350: Properties of Matter

Question

Two metal rods 1 and 2 of same lengths have same temperature difference between their ends. Their thermal conductivities are K1 and K2 and cross sectional areas A1 and A2, 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

K1A1 = 4K2A2

Answer

K1A1 = 2K2A2

Answer

4K1A1 = K2A2

Answer

K1A1 = K2A2

Properties of Matter

Two metal rods 1 and 2 of same lengths have same temperature difference between their ends. Their thermal conductivities are K1 and K2 and cross sectional areas A1 and A2, respectively. If the rate of heat conduction in 1 is four times that in 2, then

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