Q. Four rods of different radii $r$ and length $l$ are used to connect two reservoirs of heat at different temperatures. Which one will conduct heat fastest?
A) $r$= 2 cm, $l\ $ 0.5 m
B) $r$ = 1 cm, $l$= 0.5 m
C) $r$ = 2 cm, $l = \ $2 m
D) $r$ = 1 cm, $l$= 1 m
Explanation
(a) $\frac{\mathrm{\Delta}T}{\mathrm{\Delta}t} = KA\left( \frac{\mathrm{\Delta}T}{\mathrm{\Delta}x} \right) = \ K\left( \pi r^{2} \right)\frac{\mathrm{\Delta}T}{(l)}$
$\therefore\ \left( \frac{\mathrm{\Delta}Q}{\mathrm{\Delta}t} \right)\ \propto \frac{r^{2}}{l}\ $, which is maximum in case (a).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.