How does a star's temperature change as the star ages from a main sequence star to a red giant and from a red giant to a white dwarf?
The temperature and pressure in the core of a main sequence star are high enough to allow for hydrogen fusion, but not high enough to fuse the helium that is building up in the core. When the Sun runs out of hydrogen, its core will rearrange itself and the outer layers will expand due to the energy coming out of helium fusion. This will lower the Sun's temperature and cause it to emit light in the redder part of the visible spectrum, giving rise to the name "Red Giant," though it will first burn a layer of extra hydrogen surrounding the core to start the Red Giant Stage. The Sun is about 0.2 AU in the main sequence stage, and about 2 AU as a Red Giant. You can imagine what energy Helium fusion can produce to maintain that size.
This time, however, the inward acting gravity will prevail because there will be more pressure to balance that gravity because the temperature inside the core of a red giant star is still building up until it is ready to fuse Helium into carbon and other heavier elements. The Sun will never be hot enough to burn carbon.
The sun's outer layers will eventually blow off, leaving only the core, also referred to as a White Dwarf. Because of the intense gravity inside the core, pressure and temperature have greatly increased.
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The temperature of a main sequence star decreases as it ages and runs out of hydrogen fuel. Its core contracts and its outer layers expand, resulting in a transformation into a red giant. The temperature of the star falls during this phase. The red giant eventually transforms into a white dwarf. The temperature of a white dwarf stays high at first because of residual heat, but eventually cools down.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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