Nuclear Reactions

Nuclear Fusion within the Sun

Suppose the Sun is composed of hydrogen, and it is hot enough to run the P-P Chain. How long would its lifetime be (shining at its current intensity, at 1 L) as a nuclear-fusion powered object?

The Sun shines with an intensity of 4 × 10 ergs per second.
The Sun weights 2 × 10 grams.
The available energy from hydrogen fusion (the P-P Chain) is:

E = (6.4 × 10 ergs/grams) × (2 × 10 grams)

= 12.8 × 10 ergs
The lifetime of the Sun with fusion power would be:

L = 12.8 × 10 ergs × 1 sec

4 × 10 ergs

= 3.2 × 10 seconds

= 10 years

Looks pretty promising!
How much mass is the Sun losing through the fusion process?

M = 4 × 10 ergs/sec × 1

6.4 × 10 ergs/grams

= 6.25 × 10 grams/sec

685 milllion tons of hydrogen is converted into helium every second!

Bright red, orange, and yellow image of the Sun, showing huge plumes streamin goff of the surface

SOHO satellite images of the Sun, highlighting huge clouds of cool, dense plasma and
prominences suspended in the hot, thin corona (the outermost layer). Fusion takes
place deep within the inner core, hidden from our sight. [NASA]

Thanks to Mike Bolte (UC Santa Cruz) for the base contents of this slide.

L	=	12.8 × 10 ergs ×	1 sec
L	=	12.8 × 10 ergs ×	4 × 10 ergs
	=	3.2 × 10 seconds


	=	10 years

M	=	4 × 10 ergs/sec ×	1
			6.4 × 10 ergs/grams
	=	6.25 × 10 grams/sec


SOHO satellite images of the Sun, highlighting huge clouds of cool, dense plasma and prominences suspended in the hot, thin corona (the outermost layer). Fusion takes place deep within the inner core, hidden from our sight. [NASA]

E	=	(6.4 × 10 ergs/grams) × (2 × 10 grams)


	=	12.8 × 10 ergs