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Properties of Matter question

2013 · Q155
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Properties of Matter question

2013 · Q155

NEETPhysicsProperties of MatterMCQ+4 / −1
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
  1. A
    K1A1 = 4K2A2
  2. B
    K1A1 = 2K2A2
  3. C
    4K1A1 = K2A2
  4. D
    K1A1 = K2A2
View written solutionFree

Correct answer: A

Let L be length of each rod. Rate of heat flow in rod 1 for the temperature difference ΔT\Delta TΔT is

H1=K1A1ΔTL{H_1} = {{{K_1}{A_1}\Delta T} \over L}H1​=LK1​A1​ΔT​

Rate of heat flow in rod 2 for the same difference ΔT\Delta TΔT is

H2=K2A2ΔTL{H_2} = {{{K_2}{A_2}\Delta T} \over L}H2​=LK2​A2​ΔT​

As per question, H1 = 4H2

K1A1ΔTL=4K2A2ΔTL{{{K_1}{A_1}\Delta T} \over L} = 4{{{K_2}{A_2}\Delta T} \over L}LK1​A1​ΔT​=4LK2​A2​ΔT​

⇒K1A1=4K2A2 \Rightarrow {K_1}{A_1} = 4{K_2}{A_2}⇒K1​A1​=4K2​A2​

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