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

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SUMMARY

The discussion centers on calculating the lifespan of a star during the hydrogen to helium fusion process. A user attempted to use the equation T=E/L with specific values but arrived at an incorrect lifespan of 1.33 billion years instead of the correct 400,000 years. The error stemmed from misunderstanding the mass-energy conversion, specifically that only a fraction of the mass (not the entire 10%) is converted into energy during fusion. The correct approach requires adjusting the calculation to account for the actual mass converted in the fusion process.

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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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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.
 
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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