Question

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

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

Answer 1

Answer: (D)

Rate of heat flow $ \propto \frac{A \Delta T}{l}$
A rod maintained at temperature difference $\left(T_{l} - T_{2}\right)$ will have heat conduction rate $=\frac{d Q}{d t}$
$\frac{d Q}{d t}=\frac{K A \left(T_{1} - T_{2}\right)}{l}$
In given option, $r=2cm$ and $l=\frac{1}{2}m$ will conduct most heat.