Two rods of same length & material transfer a given amount of heat in 12 s when they are joined end to end. But when they are joined length wise parallel to each other they will transfer same amount of heat in same condition in time

Question

Aicharya · Accepted Answer

Let the heat transferred be Q

When rods are joined end to end, heat transferred by each rod $=\mathrm{Q}=\frac{\mathrm{KA} \Delta \theta}{2 l} \times 12...(i)$
When rods are joined lengthwise, $\mathrm{Q}=\frac{\mathrm{K} 2 \mathrm{~A} \Delta \theta}{l} \mathrm{t}...(ii)$
From equation (i) and (ii), $\begin{aligned} & \frac{\mathrm{K} 2 \mathrm{~A} \Delta \theta}{l} \mathrm{t}=\frac{\mathrm{KA} \Delta \theta}{2 l} \times 12 \\ \therefore \quad & \mathrm{t}=\frac{12}{2 \times 2}=3 \mathrm{~s} \end{aligned}$

Two rods of same length & material transfer a given amount of heat in 12 s when they are joined end to end.…

Solution