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Homework for Chapter 12-Star occupies its position on the main sequence as long at it fuses hydrogen into helium in its core.Eventually, the core stars to run out of hydrogen fuel, and the star begins to die.-main-sequence lifetime of a star equals the amount of time the stars fuses hydrogen in its core.-Which type of star has the shortest main-sequence lifetime?O stars- the most massive stars have the shortest lifetimes.-All stars are born with similar compositions: roughly ¾ hydrogen and ¼ helium, with no more than about2% heavier elements. A star’s main-sequence lifetime therefore depends on:Its mass, which determines how much hydrogen fuel it has in its core. A star twice as massive asthe Sun starts with twice as much fuel.Its luminosity tells us how rapidly it is producing energy by fusing hydrogen into helium. A startwice as luminous as the Sun fuses twice as many atoms each second.-Star with high luminosity and a small mass would have a very short lifetime, and a hypothetical star with alow luminosity and a high mass would have a very long lifetime.-Luminosity of a main-sequence star depends directly on the star’s mass.- luminosity of a main sequence star increases rapidly as the twice the Sun’s mass is much more than twiceas luminous as the Sun.If a star is twice as massive as the Sun, its main sequence lifetime will be:About 15% that of the SunWhy is the minimum temperature at which helium can fuse higher than that for hydrogen?Helium nuclei have higher charges, so they repel each other more strongly than hydrogen nuclei.Why does the core collapse once fusion stops:The pressure in the core can no longer support the weight of the overlying layers.Fusion begins here becausethis shell heats up as the core collapsesWhy does the shell heat up?As the core and surrounding gas collapse, potential energy is converted into heat.** Any time gas collapses, gravitational potential energy is converted into heat.Compare the luminosity of the hydrogen-shell-burning star to its luminosity as a main-sequence star:It is more luminousWhy does the Sun’s luminosity increase when shell burning beginsThe rate of hydrogen fusion is higher than during the main-sequence stage.