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Thermonuclear Fusion on the Sun

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If thermonuclear fusion in the Sun were suddenly to stop, what would eventually happen to the overall radius of the Sun? Justify your answer using the ideas of hydrostatic euqillibrium and thermal equillibrium.

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Once all the hydrogen in the core has been burned and converted to Helium, thermonuclear reaction stops. Therefore, gravity has no opposing force (namely, the gas pressure) and the core begins to contract. Due to energy conservation, this gravitational contraction, heats up the core (the core gains potential energy from the contraction and must release it in the form of heat). One a critical core temperature is reached, a second thermonuclear reaction takes place - the three Helium nuclei convert to one carbon nuclei.
Helium burns at a higher temperature than Hydrogen, hence the outer layers of the star actually expand. However, ...

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The expert examines thermonuclear fusion on the Sun.

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