What is the formula for calculating the lifetime of a star?

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To calculate the lifetime of a star, the formula used is lifetime = k * m/l, where k represents the sun's lifetime of approximately 10 billion years. For a star with 24 solar masses and 300,000 times the sun's luminosity, the calculation yields a lifetime of about 800,000 years. The reasoning behind the equation is that a star with greater mass has more fuel but burns it at a faster rate due to higher luminosity. The discussion seeks clarification on the formula's application and whether the calculated result is accurate. Understanding the relationship between mass, luminosity, and fuel consumption is crucial for accurate lifetime estimations of stars.
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Homework Statement



I have to calculate the lifetime of a star that is 300,000 times as luminous as the sun and 24 solar masses.

Homework Equations



lifetime = k * m/l

The Attempt at a Solution



lifetime = 10^10 * (24/300000)
lifetime = 800000 years


I feel as if this is almost too easy and am wondering if I have made an error along the way. In addition, I found this equation on the internet and don't really understand how it works despite knowing (or thinking I know) how to use it. I was hoping someone could explain it to me and if I am wrong, someone could point me in the right direction.

Many Thanks

John
 
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1)The lifetime of the sun is about 10 billion years - this is the 10^10 in your equation.
2) A star with 24 solar masses has 24 times as much fuel as the sun.
3) A star 300,000 times as luminous as the sun is burning its fuel 300,000 times faster than the sun.

This gives the equation in your post. Does this answer it?
 

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