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

[Clara Chung]

Homework Statement

[/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

 

[haruspex]

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.

 

[nrqed]

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?