Question

Four rods with different radii $r$ and length $l$ are used to connect two heat reservoirs at different temperature. Which one will conduct most heat ?

• A. $r=1cm,l=1m$
• B. $r=1cm,l=\frac{1}{2}m$
• C. $r=2cm,l=2m$
• D. $r=2cm,l=\frac{1}{2}m$

Answer 1

Answer: (D)

Key Idea Rate of heat flow $\propto \frac{A\Delta T}{l}$
A rod maintained at temperature difference $\left(T_1-T_2\right)$
will have heat conduction rate $=dQ/dt$
$\frac{dQ}{dt}=\frac{KA\left(T_1-T_2\right)}{l}$
In given option, $r=2cm$ and $l=\frac{1}{2}m$
will conduct most heat because rate of conduction.
$\frac{dQ}{dt}\propto \frac{A}{l}.$