Question

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

• A. $12$
• B. $24$
• C. $36$
• D. $48$

Answer 1

The correct option is D $48$

Let the heat transferred be $Q$ for rod $1$
$Q=\frac{kA}{l}\left(\Delta T\right)\times 12$ ... (i)
As, length of rod is doubled, the area of cross-section of rod will be halved. ($\because$ volume of rod is constant).
$Q=\frac{kA}{4l}\left(\Delta T\right)\times t$ ... (ii)
From (i) and (ii)
$t=4\times 12=48\text{seconds}$