Question

Two ends of rods of length $L$ and radius $R$ of the same material are kept at the same temperature. Which of the following rods conducts the maximum heat ?

• A. $L=50cm,R=1cm$
• B. $L=100cm,R=2cm$
• C. $L=25cm,R=0.5cm$
• D. $L=75cm,R=1.5cm$

Answer 1

The correct option is B $L=100cm,R=2cm$

The rate of heat transfer is given by:
$\dot{Q}=KA\frac{\Delta T}{l}$
$A=\pi R^2$
$\dot{Q}=K\pi R^2\frac{\Delta T}{l}$
$\dot{Q}\propto \frac{R^2}{l}$
The option with the highest $\frac{R^2}{l}$ ratio would have the highest heat transfer rate.
This corresponds to option (B)