Question

Two rods of same length and material transfer a given amount of heat in 12 seconds, when they are joined end to end. But when they are joined lengthwise, then they will transfer same heat in same conditions in

• A. 24 s
• B. 3 s
• C. 1.5 s
• D. 48 s

Answer 1

Answer: (B)

3 s

Answer 2

$Q = KA\frac{\Delta\theta}{l}.t$ ∴$t \propto \frac{l}{A}$

[As Q, K and ∆θ are constant]

$\frac{t_{1}}{t_{2}} = \frac{l_{1}}{l_{2}} \times \frac{A_{2}}{A_{1}} = \left( \frac{l_{1}}{l_{1}/2} \right) \times \left( \frac{2A_{1}}{A_{1}} \right)$

$\frac{t_{1}}{t_{2}} = 4$ ⇒ $t_{2} = \frac{t_{1}}{4} = \frac{12}{4} = 3$