Question

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?

Answer 1

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.