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Question

Two metal rods 1 and 2 of same lengths have the 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 


Your Answer
A
K1A1=K2A2
Correct Answer
B
K1A1=4K2A2
Your Answer
C
K1A1=2K2A2
Your Answer
D
4K1A1=K2A2

Solution

The correct option is B K1A1=4K2A2
We know, rate of heat flow H=KAΔTΔx
ΔT is the same for both the rods and lengths (Δx) are also same, we can say that HKA= constant.
i.e H1K1A1=H2K2A2
H1H2=K1A1K2A2
From the data given in the question, H1H2=4
4K2A2=K1A1
Thus, option (b) is the correct answer.

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