Question

The heat flux at the Earth's surface is 60 mWm\(^2\). If the thermal conductivity at the surface is 2.5 Wm\(^{-1}\)°C\(^{-1}\), the geothermal gradient is \(\underline{\hspace{1cm}}\) °C/km. (round off to integer)

Hint:

To calculate the geothermal gradient, divide the heat flux by the thermal conductivity and convert units if necessary.

Answer 1

Correct Answer: 24

The geothermal gradient \( G \) is calculated using the formula: \[ G = \frac{q}{K}, \] where:
- \( q \) is the heat flux (60 mW/m² = 0.060 W/m²),
- \( K \) is the thermal conductivity (2.5 W/m°C).
Substituting the values: \[ G = \frac{0.060}{2.5} = 0.024 \, \text{°C/m}. \] To convert to °C/km, multiply by 1000: \[ G = 0.024 \times 1000 = 24 \, \text{°C/km}. \] Thus, the geothermal gradient is \( \boxed{24} \) °C/km.