How Long Does a Star Live When Converting Hydrogen to Helium?

In summary, the correct solution for the time it takes for a star to use up 10% of its mass through hydrogen fusion is dependent on the fraction of mass converted into energy and the equation T=E/L. In this problem, the 10% of the star's mass is converted into helium, not completely into energy, so the final answer must be multiplied by this fraction. The number 8x10^5 is not applicable in this problem and should not be used in the equation.
  • #1
Clara Chung
304
14

Homework Statement


46.png
[/B]

Homework Equations

The Attempt at a Solution


I tried T=E/L = 30 X (1.989X10^30) X 0.1 X (3 X 10^8)^2 /(8X10^5 * 3.828X10^26) =1.75 x 10^15 s = 1.33 x 10^9 years .
However the answer is 4x10^5 years
please help
 

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  • #2
Clara Chung said:

Homework Statement


View attachment 225212 [/B]

Homework Equations

The Attempt at a Solution


I tried T=E/L = 30 X (1.989X10^30) X 0.1 X (3 X 10^8)^2 /(8X10^5 * 3.828X10^26) =1.75 x 10^15 s = 1.33 x 10^9 years .
However the answer is 4x10^5 years
please help
It is hard to decode your attempt by reverse engineering your equation. Instead of numbers, please write your equation in terms of defined variables.
 
  • #3
Clara Chung said:

Homework Statement


View attachment 225212 [/B]

Homework Equations

The Attempt at a Solution


I tried T=E/L = 30 X (1.989X10^30) X 0.1 X (3 X 10^8)^2 /(8X10^5 * 3.828X10^26) =1.75 x 10^15 s = 1.33 x 10^9 years .
However the answer is 4x10^5 years
please help
You are doing the problem as if the 10% of the mass of the star was converted completely into energy (you are using E=mc^2). But this is NOT the case here. The 10% is a mass of hydrogen that will be converted to helium, so not all the mass is converted into energy. You need to multiply your answer by the fraction of th mass that is converted into energy in a hydrogen -> helium fusion process. Also, where does your number 8x10^5 come from?
 
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Likes Clara Chung

1. What is the average lifetime of a star?

The average lifetime of a star depends on its mass. The more massive a star is, the shorter its lifetime will be. For example, a star with the mass of our sun will have a lifetime of about 10 billion years.

2. How does a star's mass affect its lifetime?

A star's mass determines its core temperature and the rate at which it burns hydrogen fuel. The higher the mass, the hotter the core and the faster the star will use up its fuel, resulting in a shorter lifetime.

3. Can a star's lifetime be extended?

No, a star's lifetime is determined by its mass and there is no way to extend it. Even if a star were to consume more fuel, it would only speed up its process of burning through its fuel and shorten its lifetime.

4. What happens to a star at the end of its lifetime?

At the end of its lifetime, a star will either become a white dwarf, neutron star, or black hole, depending on its mass. These are the remnants of a star after it has used up all of its fuel.

5. Can we predict the lifetime of a star?

Yes, we can predict the lifetime of a star based on its mass and the rate at which it is burning through its fuel. However, there are many other factors that can affect a star's lifetime, so these predictions are not always accurate.

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