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Why does the temperature of the core and sufrace of the sun differ so much?

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Wiki tells me that the surface of the sun is 5800K in temperature and the core is far more higher than that. Why isn't the heat in the core conducted to the surface ? What is the true reason for such a big difference in temperature?

 

Thanks in advance. I hope you guys can explain.

Big objects conduct heat badly. Imagine that their power, or the heat they content, increases as R3. Their heat conductance increases as the area but decreases as the length, that is R2/R1=R. That's slower than R3, so the temperature difference is bigger.

 

The same holds for Earth. Its whole internal heat source is as tiny as the whose energy used by Mankind, and though the core is hot. Earth would take a time in billion years to cool down if it had no internal heat source - so that whether the heat source exists was long unclear.

 

That was for conductance. Radiation can help big objects, but it doesn't so much at the Sun, because a star consists of plasma (ionized gas) which absorbs and emits light instead of letting it through.

Isn't the core of the Sun hotter, due to the immense gravitational forces at the core, as opposed to the surface ?

Gravitation first heats the core until, in a star of the main sequence, nuclear reactions start. The explanation by gravitation without nuclear fusion was the first that provided sensible figures for the power and life expentancy of stars in the XIX. century, and it holds for brown dwarves.

 

Equilibrium would imply that locations deeper in the gravitation well are hotter - but a star isn't at equilibrium. A surface hotter than the core would in fact be more stable (against convection) than the equilibrium.

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