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Fundamentals Of Physics
Found in: Page 1332

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Short Answer

A star converts all its hydrogen to helium, achieving a 100% helium composition. Next, it converts the helium to carbon via the triple-alpha process,

H4e+H4e+H4e12C+7.27 MeV

The mass of the star is role="math" localid="1661754478822" 4.6×1032kg, and it generates energy at the rate of 5.3x103 W. How long will it take to convert all the helium to carbon at this rate?

The required time is 1.6×108 yr.

See the step by step solution

Step by Step Solution

Step 1: Describe the expression for the time

Let m be the mass of helium, the number of three-helium atoms in this mass equals the number of moles multiplied by the number of atoms in one mole, where the number of moles equals the mass divided by three the molar mass of the helium.


Let be the energy release per fusion, then the total energy released by fusion equals the number of fusions multiplied by N3He.

Efusion=N3HeQ =mHeNAQ3MHe

The energy also can be written as follows:


Step 2: Find the time required to convert all the helium to carbon

Substitute all the known values in equation (1).

t=4.6×1035 g6.022×1023 mol-17.27 MeV1.602×10-13 J/MeV34.0 g/mol5.3×1030 W =5.07×1015 s =5.07×1015 s3.154×107 s/yr =1.6×108 yr

Therefore, the required time is 1.6×108 yr.

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