Fusion in a star

[Realitycheck]

What propels all of the heat and activity in a star if the rate of fusion is very slow? My guess is that the energy released by fusion is quite substantial in proportion to the quantity of components that go into it. So exactly what kind of energy is produced that keeps the rest of the star "alive"? Evidently, the matter within most of the star is in various plasma states, but I have a hard time seeing what exactly drives all of the heat and energy, or rather, what the energy consists of.

 

"The fusion of two nuclei lighter than iron or nickel generally releases energy while the fusion of nuclei heavier than iron or nickel absorbs energy; vice-versa for the reverse process, nuclear fission."

 

In the fusion process of the sun, it appears that we have both fission activity and fusion activity leading up to the end product of the Helium ion. This would lead me to believe that the two activities would somewhat cancel each other out in terms of energy released, according to the quote above, though I know better. The energy released by fusion is greater than the energy absorbed by fission?

 

Is all of the heat produced solely by the compression and fusion reactions, or are the fusion reactions enabled by the heat?

[insane_alien]

what makes you think the speed of fusion in stars is slow?

 

there is a volume about the size of mars where it happens in our sun and a couple of million tonnes of hydrogen fuses every second. that releases a LOT of energy. the tzar bomba came close to 1% of this output for a few nanoseconds.

 

it is by far enough to keep the sun shining.

[swansont]

In the fusion process of the sun, it appears that we have both fission activity and fusion activity leading up to the end product of the Helium ion. This would lead me to believe that the two activities would somewhat cancel each other out in terms of energy released, according to the quote above, though I know better. The energy released by fusion is greater than the energy absorbed by fission?

 

Is all of the heat produced solely by the compression and fusion reactions, or are the fusion reactions enabled by the heat?

 

While there is probably some reactions that split nuclei, they are probably classified as particle ejection reactions rather than fission, and AFAIK they would be relatively infrequent.

 

Fusion is enabled by the conditions (i.e. high temperature and pressure) you get from sufficient compression. Fusion will supply heat, and you'll get a steady-state where the gravitational attraction is countered by the pressure from the fusion.

[Realitycheck]

what makes you think the speed of fusion in stars is slow?

 

I had a hard time seeing how a solar mass full of hydrogen gas could keep on chugging for a gazillion years before the ratio of helium to hydrogen became too great. It just wasn't adding up. But my conclusion was confirmed here. Evidently, the sun is either full of lots of other activity than just the fusion, or the energy released by the limited amount of actual fusion is simply that great.

 

At the temperatures and densities in stellar cores the rates of fusion reactions are notoriously slow. For example, at solar core temperature (T ≈ 15 MK) and density (120 g/cm³), the energy release rate is only 276 mW/cm³—about a quarter of the volumetric rate at which a resting human body generates heat. [8] Thus, reproduction of stellar core conditions in a lab for nuclear fusion power production is completely impractical. Because nuclear reaction rates strongly depend on temperature (exp(−E/kT)), then in order to achieve reasonable rates of energy production in terrestrial fusion reactors 10–100 times higher temperatures (compared to stellar interiors) are required T ≈ 0.1–1.0 GK.

http://en.wikipedia.org/wiki/Nuclear_fusion

[insane_alien]

why couldn't it keep on chugging for a few thousand million years. a volume the size of mars with only a few million tonnes being used up every second is going to last a fair bit of time. especially since the density is somewhere around 150 times that of water.

 

i think it is that you just haven't comprehended the vast quantities of energy and matter present.

 

eventually, the sun will go to helium fusion but that will be when it explodes.

[Mr Skeptic]

Don't forget how enormous a star is! If you were as big as a star, you would die due to overheating because surface area increases as the square of the size, whereas volume increases as the cube of the size. Remember that the star's rate of fusion is also limited because the hotter it gets, the more it expands, so there is less density for reactions to occur. This is a good thing, or the sun would be more like a supernova.

[Reaper]

I guess if we do a bit of math it will help put things in perspective. For starters, the sun is about 1.99 × 10^30 kg. About 70% or so of this is hydrogen. And the sun converts about 6.224x10^11 kg into energy via nuclear fusion every second, at present anyway.

 

Now while that may seem like a lot, the mass of the sun is several orders of magnetude larger than what is being converted. If we do some math:

 

(.7(1.99x10^30) kg)/6.224x10^11(kg/s) = 2.23 x 10^18 seconds = 7.097 x 10^10 years

 

Now of course, just keep in mind that this calculation assumes all of the hydrogen is used up. The sun enters a red giant phase only when there is not enough left in the core. 5 more billion years or so is not an unreasonable estimate given the rate it burns up hydrogen compared with its mass.

 

If you want to do calculations for the core, the core is about 40% of the sun's total mass. So, that gives 1.99x10^30 * .40 = 7.96x10^29 kg. Of course, if we assume the same ratio of hydrogen to helium in the core, that figure goes down to 5.572x10^29 kg. And given the rate at which it burns up its fuel:

 

(5.572x10^29 kg) / (6.224x10^11 kg/s) = 8.95 x 10^17 seconds = 2.83 x 10^10 years. This is, of course, assuming the present rate and that all of it gets burned up. As it gets older, it will start to burn other things than hydrogen as its supply dwindles. So in light of this, 5 billion years is not an unreasonable estimate (rather, it is quite a low estimate as we have seen here).

[swansont]

Don't forget how enormous a star is!

 

That bears repeating.

 

A mole of monotomic hydrogen has a mass of a gram. The sun has a mass of about 2 x 10^30 kg, so if that were all hydrogen, we're talking ~10^57 atoms. Conversion to helium only reduces that by a factor of four.

[Realitycheck]

Thank you all for your help. It wasn't that I had a problem with the masses involved, just that 622,400,000,000 kg converted per second is so small compared to the 57,200,000,000,000,000,000,000,000,000 kg of hydrogen that the sun started out with.

 

0.00000000000000108811% used up per second

 

I can see how that would last.

 

So basically, the energy released by this little bit of fusion going on every second is what lights up the entire sun?

[insane_alien]

yep. power released at the core is equal to the power radiated at the surface as well as the power of the particle emissions.

[swansont]

And it also points to the fact that c² is pretty big.