Question

Consider that the upper continental crust is 10 km thick and made up of granitic rock having density of 2800 kg/m\(^3\). The surface heat flow due to radiogenic heat from the granitic rock having heat production value of \(10^{-9}\) W/kg is______________ mW/m\(^2\) (answer in integer).

Hint:

Multiply density by heat production per kg to get heat production per volume, then multiply by thickness.

Answer 1

Correct Answer: 28

Step 1: Recall how radiogenic heat production relates to heat flow.
Radiogenic heat production \(H\) is usually given per unit mass, in W/kg. To get the heat generated per unit volume, we multiply it by the density \(\rho\) of the rock:
\[ A = \rho \times H \]
where \(A\) is the volumetric heat production in W/m\(^3\).

Step 2: Compute the volumetric heat production.
Given \(\rho = 2800\) kg/m\(^3\) and \(H = 10^{-9}\) W/kg,
\[ A = 2800 \times 10^{-9} = 2.8\times10^{-6} \text{ W/m}^3 \]

Step 3: Relate heat flow to heat production and layer thickness.
For a layer of thickness \(z\) that produces heat uniformly through its own volume, the surface heat flow contributed by that layer, assuming the base of the layer contributes no heat flow of its own, is
\[ q = A \times z \]
This comes from integrating the volumetric heat production over the thickness of the layer.

Step 4: Convert the thickness to metres and substitute.
\[ z = 10 \text{ km} = 10000 \text{ m} \]
\[ q = 2.8\times10^{-6} \times 10000 = 2.8\times10^{-2} \text{ W/m}^2 \]

Step 5: Convert to mW/m\(^2\).
\[ q = 2.8\times10^{-2} \text{ W/m}^2 = 28\times10^{-3} \text{ W/m}^2 = 28 \text{ mW/m}^2 \]

Step 6: Final conclusion.
The surface heat flow contributed by radiogenic heat from the granitic upper crust is
\[ \boxed{28 \text{ mW/m}^2} \]