### Re: How much heat from the earth's core contributes to our conditions?

Date: Mon Sep 14 13:56:45 1998
Posted By: Dan Berger, Faculty Chemistry/Science, Bluffton College
Area of science: Earth Sciences
ID: 903557017.Es
Message:

We are told that the sun is the source of life on earth, and it clearly makes a large contribution. However, the earth's core also appears to contribute. How much of a contribution does it make? Relative to the sun?

Also, does the heat from the earth's core "drive" ocean currents to any significant degree? If not, what is the source of this energy?

The Sun's contribution to the Earth's total energy budget can be easily calculated. The Sun is a blackbody with a surface temperature of 5800 Kelvins; such an object radiates at a rate of 6.4´107 watts per square meter. Since the radius of the Sun is 695,000 km, the surface area may be found by

S.A. = 4pr2 = 6.1´1018 m2

and therefore the Sun's total output is 3.9´1026 watts. The Earth intercepts only a fraction of that: 1.8´1017 watts, or an average of 353 watts on every square meter of the Earth's surface. This number is a rock-bottom minimum!
Obviously the number is higher at the equator and lower at the poles; the number is also averaged over the whole surface, while only half of the Earth receives sunlight at any given time. The energy intercepted by the Earth may be calculated by determining the surface area of the sphere of 1 AU radius, dividing into the cross-sectional area of the Earth, and multiplying by the Sun's total output. The Earth's radius is 6378 km.
The average surface temperature of the Earth (which is another blackbody) is 287 Kelvins (14°C). This works out to an energy output of 385 watts per square meter, while we have calculated solar energy input as 353 watts per square meter (which corresponds to a surface temperature of about 281 Kelvins, or 8°C).

Given the closeness of the numbers (±32 watts < 10%), the Earth radiates little or no more energy than it receives from the Sun. In other words, there is no significant energy received at the Earth's surface from any interior source. (Contrast this with Jupiter, which radiates about 10 times the energy it receives from the Sun.)

This answers your second question: the energy which drives ocean currents comes from the Sun, not from the Earth's interior. One has to go more than 100 miles down (the boundary between the Earth's crust and upper mantle) before reaching a point where interior heat is the primary driving force for physical processes.

Resources used in preparing this answer:

The questioner asked for further explanation; I though it important enough to append my answer to his questions here. Format conventions are:
```> quotes of my initial answer
```
Further questions

I think you need to take the total amount of energy into account here. See below for a detailed exposition.

Firstly, what is a blackbody? I gather this relates to heat generation, or lack thereof?

A blackbody is an object which perfectly absorbs all radiation which falls on it. When heated to incandescence, it radiates all frequencies, with lambda-max dependent on temperature. (Read any history of quantum mechanics for "the ultraviolet catastrophe" which involved blackbody radiation and was solved by Planck's introduction of the quantization of energy.)

```> Given the closeness of the numbers (±32 watts < 10%), the
> Earth radiates little or no more energy than it receives from the
> Sun. In other words, there is no significant energy received at the
> Earth's surface from any interior source. (Contrast this with
> the Sun.)
```
A point of clarification: the earth's surface temperature would be lower (about -14 C) if it were not for greenhouse gases in the atmosphere, which retain some of the energy radiated as heat, but eventually a new equilibrium is reached and the planet once more radiates most of what it receives from the sun. In point of fact, the temperature discrepancy makes up most of the difference between the (theoretical) blackbody radiation expected from the earth and the energy it receives from the sun.
```> This answers your second question: the energy which drives ocean
> currents comes from the Sun, not from the Earth's interior. One
> has to go more than 100 miles down (the boundary between the
> Earth's crust and upper mantle) before reaching a point where
> interior heat is the primary driving force for physical processes.
```
So what happens to this heat from 100 miles down? I find it difficult to accept that it just dissipates, particularly because there's even more energy just a bit deeper. And none of this energy is being radiated. Where does this energy go - it must DO something (work) to not be evident closer to the surface, surely? It can't just dissipate into nothingness!

Is it then true to say that ocean currents are driven by the sun's energy input only? Is there any other contributor, such as the kinetic energy of the earth's rotation, or the presence of the moon?

For exact contributions you need an oceanographer, not a chemist or a physicist. But I can say the following:

1. Most (if not all) the heat from the Earth's interior is converted into the mechanical energy of plate motion. Convection cells within the mantle are thought to drive crustal plates across the earth's surface. Some heat is dissipated by volcanic activity; the waste heat from friction associated with plate motion goes partly into earthquakes; my guess is that very, very little is actually radiated to the oceans as "general heat" over a wide area (as opposed to local heat contributions from an underwater volcano).

2. Remember that factor of 10%. Even if all the excess heat at the Earth's surface (and its 10% overage of expected blackbody radiation from what it receives from the sun) is due to internal heat, it still means that 90% of the earth's surface heat is received from solar radiation. Thus, it is quite doubtful that internal heat has any major effect on the overall system of ocean currents. Coriolis forces probably contribute somewhat; currents tend to move, like the trade winds, in one direction in the Northern Hemisphere and the other in the Southern Hemisphere; but again I'd bet most of the actual driving energy comes from the sun.
Tidal forces are 2/3 from the moon and 1/3 from the sun, but if you add the sun's 90% heat contribution... I'd say the sun still dominates.

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2/21/2000
Thank you to Mike Fox, who pointed out that radioactivity is the primary source of the roughly 10% excess heat that the Earth radiates, and further that radioactivity provides the heat which drives geophysical processes such as plate tectonics, the Earth's internal dynamo, and other effects of convection within the Earth.
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