The average temperature at Earth's core is 5500 °C and at the surface is 15 °C. If the thermal conductivity of the mantle is 3 W/(m·K) and its average thickness is 3000 km, estimate the heat flux per unit area (in W/m²) from the core to the surface.
Answer
0.0055 W/m²
The correct answer is 0.0055 W/m² — Round to (0.0055) W/m² for the final answer.
Step-by-step solution
- Calculate the temperature difference (Delta T = 5500 - 15 = 5485) °C.
- Convert mantle thickness to meters: (3000) km = (3,000,000) m.
- Apply Fourier's law of heat conduction: (q = k \frac{Delta T}{d}).
- Substitute (k = 3) W/(m·K), (Delta T = 5485) K, and (d = 3,000,000) m.
- Compute (q = 3 \times \frac{5485}{3,000,000} approx 0.005485) W/m².
- Round to (0.0055) W/m² for the final answer.
Common mistake: Using km instead of meters or forgetting to convert temperature units
Concept tested: Heat flux using Fourier's law
Published · How this solution was prepared and checked
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