Question

Two rods made of same material, have same thermal conductivities and area of cross-section. It is observed that to conduct same amount of heat between temperatures $T_1$ and $T_2$, rod $1$ takes twice the time as the other. Find the ratio of their lengths.

• A. $2:1$
• B. $1:3$
• C. $1:1$
• D. $\sqrt{2}:1$

Answer 1

The correct option is A $2:1$

Given,
$k_1=k_2,A_1=A_2,Q_1=Q_2$ and $t_1=2t_2$
We know that,
$Q=\frac{kA(T_1-T_2)t}{l}$
$\therefore \frac{Q_1}{Q_2}=\frac{k_1}{k_2}\times \frac{A_1}{A_2}\times \frac{t_1}{t_2}\times \frac{l_2}{l_1}$
$\Rightarrow \frac{t_1}{t_2}=\frac{l_1}{l_2}$
$\Rightarrow \frac{l_1}{l_2}=\frac{2}{1}$
$\therefore$ option $\left(a\right)$ is correct.