Question

Dying stars produce red giants at the end of its lifespan because of the expanding gases...But why does the elimination of a stars nuclear fuel cause it to expand when the gravity is pulling it in?

Answer 1

I think it's related to the lack of hydrogen in the core. The reactions slow down / stop, so the core contracts, which releases energy to the region outside the core (which still has hydrogen). This pushes the outer layers further out. The effect of the core's gravitational pull is less in these regions, so the layers can move out quite far.

Answer 2

When a star exhausts its hydrogen, its outward radiation pressure cannot counteract the its weight, and so teh star collapses. As it does so the internal temperature and pressure increases to a point when it becomes hot enough to burn helium. This then reasserts a radiation pressure which halts the stars collapse. Whats more, because helium "burns hotter" than hydrogen, the radiation pressure exceeds that of hydrogen, and so it "puffs" the outer layer of the star up to a larger diameter than it previously was.

Depending upon the stars mass, similar reactions can occur with heavier elements when the helium is used up (such as Carbon and Oxygen), until iron is formed. When this happens the fusion process turns from exothermic to endothermic (that is it takes energy to fuse elements heavier than iron), so the radiation pressure drops, and the core collapses. This then causes the outer layers to fall upon the collapsing iron core, and the rebound causes a shockwave within the star that causes it to explode in a supernova. Well thats the simple version anyway

Answer 3

simply: the fuel slows down gravity wins over pressure, shrinking the star until the new density heats up elements to burn new fuels, and pressure increases dramatically back into a state of equilibrium that is larger.