Assume that the Sun has been producing energy at a constant rate over its lifetime of 4.6 billion years (1.4 × 1017 seconds). (A) How much mass has it lost creating energy over its lifetime? (B) The current mass of the Sun is 2.0 × 1030 kg. What fraction of its current mass has been converted into energy over the lifetime of the Sun?
6.1 x 1011kg of Hydrogen has to be converted to Helium every second to produce a luminosity of 3.85 x1026J/s.
In 4.6 billion years it has converted 6.1 x 1011 kg/s x 1.4 x 1017s = 8.6 x 1028 kg of H into He.Of this mass, only 0.007 of it has actually been converted into energy (the other 0.993 was converted to Helium).So 0.007 of 8.6 x 1028kg is 6.0 x 1026kg.This is [6.0 x 1026kg / 2 x 1030kg] = 0.0003 or 0.03% of the Sun’s mass hasactually been converted to energy.
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