High-mass stars start off with much more fuel than low-mass stars. Why don't high-mass stars live longer?

The Orion Nebula is about 20 light-years (20 × 1018 cm) across, enclosing a roughly spherical area with a volume of 4.19 × 1057 cm3. Calculate the number of 0.1 solar mass stars that might be formed in such a nebula. Assume that the nebula has a density of 1000 atoms/cm3.

A main sequence star of mass 25 M⊙has a luminosity of approximately 80,000 L⊙. a. At what rate DOES MASS VANISH as H is fused to He in the star’s core? Note: When we say “mass vanish '' what we really mean is “gets converted into energy and leaves the star as light”. Note: approximate answer: 3.55 E14 kg/s b. At what rate is H converted into He? To do this you need to take into account that for every kg of hydrogen burned, only 0.7% gets converted into energy while the rest turns into helium. Approximate answer = 5E16 kg/s c. Assuming that only the 10% of the star’s mass in the central regions will get hot enough for fusion, calculate the main sequence lifetime of the star. Put your answer in years, and compare it to the lifetime of the Sun. It should be much, much shorter. Approximate answer: 30 million years.

How much energy would be released if a star with a mass of 25 Msun and a radius of 10 Rsun detonates as a supernova explosion in 1 second? (Hint: think about the definition of binding energy). Express your answer in terms of solar luminosities.