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If we would take the average number of supernovae per year and multiply that by the number of stars, could we figure out how many years it will be before all stars are gone?

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Not that easy way. Only stars heavy enough will undergo a supernova explosion. The majority of stars is too light. The lifetime of a star is mostly determined by its mass. In some cases (supernova type Ia) a companion star provides mass to white dwarf, which originally has been too light to explode as a supernova.

Hence your technique can only work, if it is applied to stars of a certain mass and composition separately, and then summed or integrated up over all these restricted classes of stars. All together you'll get results for stars which eventually will end up as supernova, i.e. the heavy ones with more than about 8 solar masses.

... And in the meanwhile new stars will form.

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and binary stars count as well. Where 1 is a red giant and 1 is a white dwarf. Would ternary stars which are 3 stars orbiting around themselves have a supernova type 1a? Yes new stars will form but you know there might be a point in time very far in which there are no more stars and stars have to form from the atoms once again, like a second big bang. –  caters Mar 2 at 18:54
@caters In the long run fuel for star formation will run short, and the longest-living stars will cool down, yes. If a ternary contains a white dwarf and a giant, close enough to each other, a type 1a supernova can be the result. –  Gerald Mar 2 at 19:52
but why? I mean in all these supernovas you have not only heavier metals forming like gold but also the smaller atoms like hydrogen released so isn't there like an equilibrium between hydrogen used and hydrogen released? –  caters Mar 2 at 20:28
@caters No, part of the hydrogen is fused to heavier elements, releasing energy. Fusing or splitting iron nuclei needs energy. Most of the hydrogen released by supernovae has never been fused, but has been in the outer shell of the collapsing star. There is no equilibrium, because there is no source of energy needed to split heavier nuclei to hydrogen. –  Gerald Mar 2 at 21:34
yes but there are regions in the star where a certain element never fuses. That is what is released to make new stars. Why wouldn't the energy released from the supernova form heavier elements and split atoms into alpha particles and smaller atoms and sort of forcing alpha decay? –  caters Mar 2 at 21:44
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