Topic: Heat Transfer
If two ends of rods of length L and radius r, made of same material are kept at the same temperature difference, which of the following rods conduct most heat per unit time?
- A. L = 50 cm, r = 1 cm
- B. L = 2 cm, r = 0.5 cm
- C. L = 100 cm, r = 2 cm
- D. L = 3 cm, r = 1 cm
Answer: D. L = 3 cm, r = 1 cm
Explanation: According to Fourier's Law of Heat Conduction, the rate of heat transfer $Q$ is given by $Q = -kA\frac{dT}{dx}$, which means $Q \propto \frac{A}{L}$. Since the area $A = \pi r²$, the heat transfer is proportional to $\frac{r²}{L}$. Evaluating this ratio for each option: (a) $1^2 / 50 = 0.02$, (b) $0.5^2 / 2 = 0.125$, (c) $2^2 / 100 = 0.04$, and (d) $1^2 / 3 \approx 0.33$. Option (d) has the highest ratio, hence it conducts the most heat per unit time.