Q. Which of the following cylindrical rods will conduct maximum heat, when their ends are maintained at a constant temperature difference?
A) $l = 1m,\ r = 0.2m$
B) $l = 1m,\ r = 0.1m$
C) $l = 10m,\ r = 0.1m$
D) $l = 0.1m,\ r = 0.3m$
Explanation
(d) $\frac{\Delta Q}{\Delta t} = KA\left( \frac{\Delta T}{\Delta x} \right) = \ K\pi r^{2}\left( \frac{\mathrm{\Delta}T}{l} \right) \propto \frac{r^{2}}{l}$
As $\frac{r^{2}}{l}$ is maximum for (d), it is the correct choice.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.