Question

Which of the following rods made of same material will conduct more heat in a given time when their ends are maintained at the same temperatures difference :

• A. $l=1m,r=1cm$
• B. $l=2m,r=2cm$
• C. $l=3m,r=1cm$
• D. $l=100cm,r=2cm$

Answer 1

The correct option is D $l=100cm,r=2cm$

Thermal conduction in a metal bar is given by
$Q=\frac{KA\left(\Delta \theta \right)t}{l}$
Since the material, temperature difference and the time are same.
$\Rightarrow Q\propto \frac{A}{l}=\frac{r^2}{l}$
A)$\frac{r^2}{l}=\frac{1^2}{100}=0.01$
B)$=\frac{2^2}{200}=0.02$
C)$=\frac{1^2}{300}=0.003$
D)$=\frac{2^2}{100}=0.04$