Question

1) Assuming that 10 eV could be released by every atom in the Sun through chemical reactions,

(a) estimate how long the Sun could shine at its current rate (L=3.84 × 1026 Watts) through chemical processes alone. For simplicity, assume that the Sun is composed entirely of hydrogen (The mass of the Sun is ~1.989 x 1030 kg)

(b) How does this timescale compare to the lifetime of the Sun? What can you conclude from this comparison?

Answer 1

energy released by each atom E = 10eV = 10 x 1.6 x 10^-19 = 1.6 x 10^-18 J

mass of sun M = 1.989 x 10³⁰ Kg

mass of Hydrogen m = 1.67372 × 10^-27 kg

hence M/m = 1.989 x 10³⁰ / 1.67372 × 10^-27

⁼ 1.19 x 10⁵⁷ Kg

total energy released = M/m . E

= 1.19 x 10⁵⁷ x 1.6 x 10^-18

= 1.904 x 10³⁹ J

required time T = 1.904 x 10³⁹ / L

= 1.904 x 10³⁹ / 3.84 x 10²⁶

= 0.495 x 10¹³ s

= 1.57 x 10⁵ years

Clearly we see that it is not possible that the time scale for entirely chemical composition is too short for the age of the Sun