Yes it is trapped for a long time but that doesn't change the fact that the amount of it is determined by the volume of the core, not the surface area of the star.
If you multiply the amount of energy generated at the core which subequently escapes through the surface of the star by 16, the surface temperature will double. If the star stays the same size.
Alternatively, multiply core energy by 16 and maintaining surface temperature requires 16 times the surface area to radiate said energy
And the star will expand to 4 times its diameter.
If more energy is escaping from the star either it gets bigger or its surface heats up.
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Forget it - you're clearly stuck with simple black body physics - stars are more complex.
Suit yourself.
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*Sigh* I hate having to resort to this, seemingly unfair tactic.
Unsheaths wikipedia article:
Stellar luminosity:
A star's luminosity can be determined from two stellar characteristics: size and effective temperature.[3] The former is typically represented in terms of solar radii, R⊙, while the latter is represented in kelvins, but in most cases neither can be measured directly. To determine a star's radius, two other metrics are needed: the star's angular diameter and its distance from Earth, often calculated using parallax. Both can be measured with great accuracy in certain cases, with cool supergiants often having large angular diameters, and some cool evolved stars having masers in their atmospheres that can be used to measure the parallax using VLBI. However for most stars the angular diameter or parallax, or both, are far below our ability to measure with any certainty. Since the effective temperature is merely a number that represents the temperature of a black body that would reproduce the luminosity, it obviously cannot be measured directly, but it can be estimated from the spectrum.
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There's only one way to sort this, slide rules at 10 paces ladies and gentlemen, nominate a second.
Have already repped you this thread...