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I have heard that the Earth is made up of four layers, being the crust, the mantle, the outer core and the inner core. I have also heard that the Earth's temperature increases as you move from the crust to the inner core, with the inner core having a temperature of 4700 degrees.

Why is it that the inside of the Earth is so hot compared to the outside of the Earth?

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This is a very good question. There a few main heat sources: Heat(and work) left over from the formation of the earth, work (potential energy) generated by dense iron sinking into the center of the earth and forming a core, and radioactive energy. Since the Thermal diffusivity of the materials that make up the earth is low, heat transport is very slow and thus the planet retains a significant amount of its heat.

Another reason why the earth is so hot, is that mantle convection is a very inefficient way to transport said heat, and thus the earth loses energy very slowly.

We know how hot the interior of the earth might be because of laboratory experiments, and also volcanic eruptions. How much energy(temperature) does it take to melt gabbro (mantle rock)?

Interestingly enough, the earth is cooling. And the inner core / outer core boundary is a freezing front (meaning turning from a liquid outer core to a solid inner core). Though, it is a very hot freezing front.

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    $\begingroup$ Sort of; Heat is definitely transported from the inner core all the way to the crust. Thats what drives mantle convection and plate tectonics. But because it is transporting said heat (moving hot rock all the way up to the surface) it loses a lot of energy. Most of the surface heat comes from the sun, as the lithosphere ( more notable than and different than the crust) acts as an insulator for the planets interior, turning it into an oven. $\endgroup$ – Neo Apr 16 '14 at 6:03
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    $\begingroup$ @Mew Actually it does continuously, until a thermodynamical equilibrium is reached, but the continuous heat transport is the reason why geothermal heating systems work. $\endgroup$ – hugovdberg Apr 16 '14 at 6:09
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    $\begingroup$ Freezing at the inner/outer core boundary would also add heat. $\endgroup$ – Paul A. Clayton Apr 16 '14 at 17:59
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    $\begingroup$ This answer left me wanting, so I asked how is heat transferred from the core to the crust? $\endgroup$ – naught101 Apr 17 '14 at 6:51
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    $\begingroup$ "mantle convection is a very efficient way to transport said heat, and thus the earth loses energy very slowly" - shouldn't that sentence include a not? $\endgroup$ – Siv May 3 '14 at 20:02
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Mostly it's due to radioactive isotopes distributed throughout the earth decaying at rates corresponding to their half lives - some of which are very long. We lose heat from the surface so the centre is hot. NB Just found out there is some tidal squeezing by the moon on the earth, but it's minimal compared to Io for example.

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    $\begingroup$ groundwateruk.org/downloads/4%20Busby.pdf states "Much of the Earth's heat, between 45-85% is derived from the decay of the radioactive isotopes of Uranium Thorium and Potassium concentrated in the crust and mantle. The other main source is the primordial energy of planetary accretion. The Earth is cooling very slowly, the temperature of the mantle has decreased no more than 300-350 degrees C in 3 billion years, remaining at about 4000 degrees C at its base" $\endgroup$ – Siv Apr 23 '14 at 18:14

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