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. $r = 1 \, cm, l = 1 \, m$
• 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)

$r = 2 \, cm , l = \frac{1}{2} m$

Answer 2

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 $=d Q / d t$
$\frac{d Q}{d t}=\frac{K A\left(T_{1}-T_{2}\right)}{l}$
In given option, $r=2 \,cm$ and $l=\frac{1}{2} m$ will conduct most heat because rate of conduction.
$\frac{d Q}{d t} \propto \frac{A}{l} .$