We confirm the concept of the geothermal effect in an alternative fashion to the discussion in the text. We know that the average rate at which heat is conducted through the surface of the ground in North America is 54.0 mJ/(s m2). Assuming a surface temperature of -2 oC, what is the temperature at a depth of 29.86 km? Hint: Ignore the heat generated by the presence of radioactive elements and use 2.5 J/(m s K) for the average thermal conductivity of the near-surface rocks. Start with Fourier's law.

Question

We confirm the concept of the geothermal effect in an alternative fashion to the discussion in the text. We know that the average rate at which heat is conducted through the surface of the ground in North America is 54.0 mJ/(s m2). Assuming a surface temperature of -2 oC, what is the temperature at a depth of 29.86 km? Hint: Ignore the heat generated by the presence of radioactive elements and use 2.5 J/(m s K) for the average thermal conductivity of the near-surface rocks. Start with Fourier's law. 
What process would I use to answer this?

drwls · Answer

Consider a 29.86 km thick layer as planar (since is a small fcraction of the earth's radius), with temperature T on one side and -2C on the other.

Then k*[T - (-2)]/29.86*10^3m
is the heat conducted per area to the surface. You have been given a value for that. You also have been given a value for k. Use those values to solve for T, the temperature at 29.86 km depth