Question

The heat is flowing through two cylindrical rods of same material. The diameters of the rods are in the ratio 1 : 2 and their lengths are in the ratio 2 : 1. If the temperature difference between their ends is the same, the ratio of rate of flow of heat through them will be

• A. 1 : 1
• B. 2 : 1
• C. 1 : 4
• D. 1 : 8

Answer 1

Answer: (D)

1 : 8

Answer 2

$\frac{Q}{t} = \frac{KA\Delta\theta}{l}$ ⇒ $\frac{Q}{t} \propto \frac{A}{l} \propto \frac{d^{2}}{l}$ (d = Diameter of rod)

⇒ $\frac{(Q/t)_{1}}{(Q/t)_{2}} = \left( \frac{d_{1}}{d_{2}} \right)^{2} \times \frac{l_{2}}{l_{1}} = \left( \frac{1}{2} \right)^{2} \times \left( \frac{1}{2} \right) = \frac{1}{8}$