Passage VI

Three students were asked to estimate the Sun's life span (the time that will have elapsed from the time the Sun began emitting energy until the time it exhausts its energy supply). The students were told that the Sun's mass is about 10³⁰ kg and that the Sun's rate of energy emission is about 10³⁴ joules per year (J/yr).

Student 1

Energy is produced in the Sun by the combustion of molecular hydrogen gas (H₂). In this chemical reaction, 2 molecules of H₂ react with 1 molecule of oxygen gas (O₂). For every 1 kg of H₂ molecules consumed, about 10⁸ J of energy is produced. Therefore, if the Sun was composed entirely of H₂ at the start of its life span, then the Sun will have exhausted its fuel in approximately:

Thus, the Sun's life span is 10 thousand years.

Student 2

Energy is not produced in the Sun. The Sun formed when an interstellar cloud collapsed under the force of its own gravity. The collapse converted the cloud's mechanical energy, E, into thermal energy (heat) that was stored in the forming solar core. The mechanical energy in the cloud is estimated to have been approximately 10⁴¹ J. If 100% of this mechanical energy was converted to thermal energy as the Sun formed, then the Sun will have emitted all of it in approximately:

Thus, the Sun's life span is 10 million years.

Student 3

Energy is produced in the Sun by the fusion of hydrogen (H) nuclei. In this nuclear reaction, 4 H nuclei fuse together to form 1 helium (He) nucleus. For every 1 kg of H nuclei consumed, about 10¹⁵ J of energy is produced. However, only within the solar core (the innermost 10% of the Sun's mass) are the temperature and pressure great enough for fusion to occur. Therefore, if the Sun was composed entirely of H at the start of its life span, then the Sun will have exhausted its fuel after approximately:

Thus, the Sun's life span is 10 billion years.