PX158 - I6a - stellar evolution

all thermally supported stars must have a finite lifetime since they lose heat. they must be using up 'fuel'
all stars must die

t = \frac{E}{L_{s}}

$E =$ total energy available

chemical energy

considering chemical energy, for $H$ , electrons have an energy $\sim 13.6 e V$
assuming that a star is entirely composed of $H : E_{c} = \frac{M_{⊙}}{M_{H}} \times 13.6 e V \approx 2.6 \times 10^{39} J$

t_{C} = \frac{E_{c}}{L_{s}} \approx 220 000 y e a r s

this is not realistic

nuclear energy

considering fusion energy, $\sim 7 M e V p e r H$
the source of stellar energy must be from nuclear energy, in particular, $H$ fusion
$H \to H e$ fusion $: 0.7 %$ mass $\to$ energy $: E = 0.007 M_{⊙} c^{2} \approx 1.3 \times 10^{45} J$

t_{f} \approx 100 G y r

this assumes that the entire mass fuses, but only the core $(\sim 12 %)$ is fused
actual lifetime of the sun is $\sim 12 G y r$