What is the efficiency of the Sun, really?

[cragwolf]

Does all (i.e. 100%) of the energy generated in the Sun's core via nuclear fusion eventually escape out into space (as photons, neutrinos, ... and umm solar wind?), or is some energy lost to internal processes? Surely the photons must lose energy as they take their long, indirect path from the core to the surface (e.g. frequent absorption and re-emission). But then maybe this energy lost is converted back to photons at some stage. And what about the energy involved in counteracting the gravitational force of all that matter (radiation/gas pressure stops the Sun from collapsing further).

So what is the ratio of energy produced by fusion reactions in the Sun to the energy released at the Sun's surface as photons, neutrinos and other stuff?

 

[Drakkith]

See here: http://en.wikipedia.org/wiki/Sun
That can answer most of that.

All I can say is that ALL of the energy produced from fusion and gravitational compression is eventually released. For example, a White Dwarf is a star that is no longer producing energy via fusion. It is still extremely hot, but eventually this residual heat will radiate away and it will be the same temperature as the background radiation of space.

 

[qraal]

Does all (i.e. 100%) of the energy generated in the Sun's core via nuclear fusion eventually escape out into space (as photons, neutrinos, ... and umm solar wind?), or is some energy lost to internal processes? Surely the photons must lose energy as they take their long, indirect path from the core to the surface (e.g. frequent absorption and re-emission). But then maybe this energy lost is converted back to photons at some stage. And what about the energy involved in counteracting the gravitational force of all that matter (radiation/gas pressure stops the Sun from collapsing further).

So what is the ratio of energy produced by fusion reactions in the Sun to the energy released at the Sun's surface as photons, neutrinos and other stuff?

There's an old 19th Century finding that an object will heat up internally to the point at which its heat loss from it's surface is matched by the rate of heat production inside. The Sun's core is thus 15,700,000 K at its hottest, but the heat production rate is sufficiently low that it is only 5,800 K at the surface. The temperature difference is due to the overall resistance of the Sun's insides to heat flow. But eventually ALL the heat gets out - some is just delayed.

 

[Nabeshin]

There's an old 19th Century finding that an object will heat up internally to the point at which its heat loss from it's surface is matched by the rate of heat production inside. The Sun's core is thus 15,700,000 K at its hottest, but the heat production rate is sufficiently low that it is only 5,800 K at the surface. The temperature difference is due to the overall resistance of the Sun's insides to heat flow. But eventually ALL the heat gets out - some is just delayed.

Don't forget that the 5,800K is spread out over a much larger surface area than the 15e6 K in the sun's interior! If the temperature were the same throughout, there would be some mysterious mechanism which generated more and more energy the further out from the center you went!

 

[cragwolf]

The implication of the Wikipedia article is 100%, real-time and not just eventually, i.e. it's on a Joules/sec (Watts) basis. For if you accept their number of 9.2 x 10³⁷ proton-proton chain reactions per second, and ignore the CNO cycle, you come up with an energy-generated number that exactly matches their stated number for the luminosity, L_sol = 3.846 x 10²⁶ Watts. Presumably they just assumed 100% (energy generated = energy released at surface per unit time), and then derive the 9.2 x 10³⁷ number from the luminosity.

By the way, I don't understand heat very much. I understand energy much better. What follows is my crappy understanding of what happens in the Sun. Please criticize it:

1. In the core, nuclear fusion reactions release energy in the form of photons (mostly gamma rays), neutrinos and kinetic energy of particles (like positrons). Actually, I think this can all be considered as kinetic energy of particles.
2. This kinetic energy is transferred to the medium of mostly ionised gas through particle interactions. I have no idea of the nature of these interactions.
3. At the same time the gas is losing energy again through particle interactions. I assume photons are released in this process. Again, no idea of the nature of the interactions.
4. The resulting pressure (and temperature) of the gas stays constant because of hydrostatic equilibrium. Obviously these properties vary with distance from the centre of the Sun, but not with time if we ignore the slowly-changing composition of the gas.
5. If these properties stay constant then the energy lost by the gas must be the same as the energy gained. If there was a net gain of energy, the gas temperature/pressure would go up; if there was a net loss the gas temperature/pressure would go down.
6. I won't mention the different methods of the radiation transport to the surface (diffusion, convection, conduction). Or that neutrinos rarely interact. Or other complications. That will just confuse me.

Am I on the right track? Or am I completely wrong? My physics knowledge sucks. Thanks very much for the replies so far.

 

[qraal]

The implication of the Wikipedia article is 100%, real-time and not just eventually, i.e. it's on a Joules/sec (Watts) basis. For if you accept their number of 9.2 x 10³⁷ proton-proton chain reactions per second, and ignore the CNO cycle, you come up with an energy-generated number that exactly matches their stated number for the luminosity, L_sol = 3.846 x 10²⁶ Watts. Presumably they just assumed 100% (energy generated = energy released at surface per unit time), and then derive the 9.2 x 10³⁷ number from the luminosity.

The energy escaping the Sun's surface doesn't immediately originate from the Core. The photons produced by fusion processes have to be degraded down from their initially high energy state to the much lower temperature we see. Higher frequency photons we see at the surface are made afresh by magnetic processes releasing field potential energy as accelerated particles, which then throw off high-energy photons.

By the way, I don't understand heat very much. I understand energy much better.

"Heat" is best understood as energy in flow in a given direction. In an equilibrium system there's lots of energy moving around, but no *net* flow.

What follows is my crappy understanding of what happens in the Sun. Please criticize it:

1. In the core, nuclear fusion reactions release energy in the form of photons (mostly gamma rays), neutrinos and kinetic energy of particles (like positrons). Actually, I think this can all be considered as kinetic energy of particles.

1. 
   
   The particles involved gain energy from the fields inside them being reconfigured. The fields also mediate the exchange of energy between the particles.
   
   

   [*]This kinetic energy is transferred to the medium of mostly ionised gas through particle interactions. I have no idea of the nature of these interactions.

   
   Electromagnetism, pure and simple.
   
   

   [*]At the same time the gas is losing energy again through particle interactions. I assume photons are released in this process. Again, no idea of the nature of the interactions.

   
   A particle approaches another particle and experiences a decceleration or acceleration, thanks to their fields, thus resulting in the production of electromagnetic waves. This is called bremsstrahlung.
   
   

   [*]The resulting pressure (and temperature) of the gas stays constant because of hydrostatic equilibrium. Obviously these properties vary with distance from the centre of the Sun, but not with time if we ignore the slowly-changing composition of the gas.

   
   True. The change rate is very slow.
   
   

   [*]If these properties stay constant then the energy lost by the gas must be the same as the energy gained. If there was a net gain of energy, the gas temperature/pressure would go up; if there was a net loss the gas temperature/pressure would go down.

   
   There is a net gain from fusion reactions, but equilibrium is maintained much as you describe, just with the complication of fusion energy being added to the gas.
   
   

   [*]I won't mention the different methods of the radiation transport to the surface (diffusion, convection, conduction). Or that neutrinos rarely interact. Or other complications. That will just confuse me.

It's not that confusing.

Am I on the right track? Or am I completely wrong? My physics knowledge sucks. Thanks very much for the replies so far.

Good so far. There's lots of stellar physics material online, so just look around.

 

[Astronuc]

In the core, nuclear fusion reactions release energy in the form of photons (mostly gamma rays), neutrinos and kinetic energy of particles (like positrons). Actually, I think this can all be considered as kinetic energy of particles.

Here is the main fusion process in the sun.

http://csep10.phys.utk.edu/astr162/lect/energy/ppchain.html
http://hyperphysics.phy-astr.gsu.edu/hbase/astro/procyc.html

http://hyperphysics.phy-astr.gsu.edu/hbase/astro/solarpp.html

 

[Borek]

or is some energy lost to internal processes?

Loss of energy usually means that energy is converted to heat or radiation. In this case it would be heat lost to heat.