Question:medium

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).

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Multiply density by heat production per kg to get heat production per volume, then multiply by thickness.
Updated On: Jul 20, 2026
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Correct Answer: 28

Solution and Explanation

Step 1: List the given data with correct units.
The crust layer is $z=10$ km thick. Its density is $\rho=2800$ kg/m$^3$. Its heat production per unit mass is $H=10^{-9}$ W/kg. We want the heat flow at the surface in mW/m$^2$.

Step 2: Turn mass based heat production into volume based heat production.
Multiplying heat production per kilogram by the mass in one cubic metre of rock, which is just the density, gives the heat produced per cubic metre:
\[ A=\rho H = 2800\text{ kg/m}^3 \times 10^{-9}\text{ W/kg} = 2.8\times10^{-6}\text{ W/m}^3 \]

Step 3: Turn volume based heat production into flow through a surface.
Picture a column of rock one square metre in cross section and $z$ metres tall. The whole column generates heat at a rate $A$ per cubic metre, so the total power leaving the top of the column per square metre is $A$ times the height of the column:
\[ q=Az \]

Step 4: Put the thickness in metres.
\[ z=10\text{ km}=10^4\text{ m} \]

Step 5: Multiply through.
\[ q=2.8\times10^{-6}\times10^4=2.8\times10^{-2}\text{ W/m}^2 \]

Step 6: Change watts to milliwatts.
Since $1$ W $=1000$ mW,
\[ q=2.8\times10^{-2}\times1000=28\text{ mW/m}^2 \]
$\boxed{28 \text{ mW/m}^2}$
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