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Question

A rod of length l made of a material of thermal conductivity k can transfer a given amount of heat in 12 seconds. If the length of the rod is doubled keeping the volume constant, it is noted that the rod can transfer the same heat in t seconds. Find the value of t


Solution

Let the heat transferred be Q for rod 1
Q=kAl(ΔT)×12   ... (i)
As, length of rod is doubled, the area of cross-section of rod will be halved. [ volume of rod is constant]
Q=kA4l(ΔT)×t   ... (ii)
From (i) and (ii)
t=4×12=48 seconds

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