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Sun's core "pinhead" illustration in error



 
 
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  #11  
Old January 17th 05, 06:58 AM
John Popelish
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"Joe D." wrote:

"John Popelish" wrote in message
...
"Joe D." wrote:

"John Popelish" wrote in message
...

I don't think the exercise is about the Sun's power at all.

I assume you mean it's intended only as an illustration of
the sun's core temperature, not its power?


Exactly. It is an attempt to give a feel for the physical effects of
that kind of temperature.


I understand what you're saying and I accept what the
originator of that illustration was attempting.

My problem is he apparently just blindly plugged 15 million C into
the Stefan-Boltzman equation. That produces a POWER
output which in turn determines lethal range. The impact of
the illustration centers on power, regardless of whether
temperature was the goal. Without power you have no
lethal range. Yet that power doesn't exist in the stated
volume.

The Voyager space probe detected temperatures
of ONE BILLION degrees in the Uranus magnetosphere.
Plug that into the Boltzman equation and it spits out
3.4E23 watts!!!


Not a black body radiator, I'll wager.

By the exact same illustration, using the exact same
technique, a pinhead of material from the Uranus magnetosphere
would kill someone 100,000 km away (I just did the math).

Obviously you can't just convert temperature to radiant
power with that equation and have it mean something.
Yet that's what the original illustration does.

The only reason it slips by is the sun is viscerally hot, so
everybody figures that's accurate.

If I'm in error, let me know.

BTW there's a nice on-line calculator for the Stefan-Boltzman
equation at http://hyperphysics.phy-astr.gsu.edu...stefan.html#c2


Thanks.
--
John Popelish
  #12  
Old January 17th 05, 07:27 AM
Joe D.
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"Sam Wormley" wrote in message
news:_jIGd.10927$OF5.9745@attbi_s52...
.....
Thank you.
http://www.madsci.org/posts/archives...2372.As.r.html

"I bring this up because there can be ridiculously high temperatures in
the Universe, but they don't mean much!


And that is exactly my point. It would be absurd to plug that
temperature (OR the 100 million C from the ITER fusion reactor)
into the Boltzman equation, look at resultant watts, and
make conclusions about lethal distance.

Yet that is what the original illustration does.

The Boltzman equation is an accurate translation of temperature to radiant
power, assuming perfect emissivity, plus infinite power is available to
maintain the temperature of the 1 mm^3 pinhead on earth.

It is not in any way reflective of what a pinhead of solar core material
would do on earth, any more than a pinhead of ITER plasma or a
pinhead of Uranus magetosphere.





  #13  
Old January 17th 05, 07:30 AM
Sam Wormley
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Joe D. wrote:
"Sam Wormley" wrote in message
news:_jIGd.10927$OF5.9745@attbi_s52...
.....

Thank you.
http://www.madsci.org/posts/archives...2372.As.r.html

"I bring this up because there can be ridiculously high temperatures in
the Universe, but they don't mean much!



And that is exactly my point. It would be absurd to plug that
temperature (OR the 100 million C from the ITER fusion reactor)
into the Boltzman equation, look at resultant watts, and
make conclusions about lethal distance.

Yet that is what the original illustration does.

The Boltzman equation is an accurate translation of temperature to radiant
power, assuming perfect emissivity, plus infinite power is available to
maintain the temperature of the 1 mm^3 pinhead on earth.

It is not in any way reflective of what a pinhead of solar core material
would do on earth, any more than a pinhead of ITER plasma or a
pinhead of Uranus magetosphere.






And the density of the plasma at the center of the sun is?
And the temperature of the plasma at the center of the sun is?


  #14  
Old January 17th 05, 07:41 AM
Joe D.
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"Sam Wormley" wrote in message
news:xYIGd.11291$eT5.8148@attbi_s51...
Joe D. wrote:
"Sam Wormley" wrote in message
news:_jIGd.10927$OF5.9745@attbi_s52...
.....

Thank you.
http://www.madsci.org/posts/archives...2372.As.r.html

"I bring this up because there can be ridiculously high temperatures in
the Universe, but they don't mean much!



And that is exactly my point. It would be absurd to plug that
temperature (OR the 100 million C from the ITER fusion reactor)
into the Boltzman equation, look at resultant watts, and
make conclusions about lethal distance.

Yet that is what the original illustration does.

The Boltzman equation is an accurate translation of temperature to
radiant
power, assuming perfect emissivity, plus infinite power is available to
maintain the temperature of the 1 mm^3 pinhead on earth.

It is not in any way reflective of what a pinhead of solar core material
would do on earth, any more than a pinhead of ITER plasma or a
pinhead of Uranus magetosphere.


And the density of the plasma at the center of the sun is?
And the temperature of the plasma at the center of the sun is?

As stated previously in this thread, specific density of
the sun's core is 150 grams/cm^3. Temperature is 15 million C.


  #15  
Old January 17th 05, 07:50 AM
Sam Wormley
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Joe D. wrote:
"Sam Wormley" wrote in message
news:xYIGd.11291$eT5.8148@attbi_s51...

Joe D. wrote:

"Sam Wormley" wrote in message
news:_jIGd.10927$OF5.9745@attbi_s52...
.....


Thank you.
http://www.madsci.org/posts/archives...2372.As.r.html

"I bring this up because there can be ridiculously high temperatures in
the Universe, but they don't mean much!


And that is exactly my point. It would be absurd to plug that
temperature (OR the 100 million C from the ITER fusion reactor)
into the Boltzman equation, look at resultant watts, and
make conclusions about lethal distance.

Yet that is what the original illustration does.

The Boltzman equation is an accurate translation of temperature to
radiant
power, assuming perfect emissivity, plus infinite power is available to
maintain the temperature of the 1 mm^3 pinhead on earth.

It is not in any way reflective of what a pinhead of solar core material
would do on earth, any more than a pinhead of ITER plasma or a
pinhead of Uranus magetosphere.


And the density of the plasma at the center of the sun is?
And the temperature of the plasma at the center of the sun is?


As stated previously in this thread, specific density of
the sun's core is 150 grams/cm^3. Temperature is 15 million C.



Your figures are not much different than mine.
1.6 x 10^7 K
1.6 x 10^5 kg/m^3

  #16  
Old January 19th 05, 01:27 AM
Joe D.
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"Everett Hickey" wrote in message
...

Nuclear bombs don't convert anywhere remotely close to 100% of their
matter
to energy. Not even antimatter can accomplish that feat, and antimatter


The statement was in the Soviet 57 Mt bomb, 2.7 kg of matter was
100% converted to energy, NOT that the whole bomb was.

There is no fusion at the center of the sun. The core is primarily
helium,
with traces of other elements (including some unprocessed hydrogen that
escaped fusion, though a very very low figure). The actual fusion process
occurs in a slowly expanding shell around the core, at the boundry point
between helium and hydrogen.


Thanks for that point. However I used the core center because (a)
density is highest there, giving the illustration a better chance, and
(b) The below chart had specific numbers for various core radii

http://fusedweb.pppl.gov/CPEP/Chart_...ayers.html#Bib


If
de-confined there would be significant blast effects as the hydrogen is
under 250 billion atmospheres.


I'd think that alone would do the job. It would cool as it expanded, but
the intense heat combined with ravaging blast would kill for a great
radius.
How big a radius I have no clue or care.


The previously-listed calculations show how much specific heat is
contained in 1 mm^3 of hydrogen at core density. Helium has
only about 1/3 the specific heat capacity (5190 J/kg) of Hydrogen,
so would do much less heat damage.

Regarding energy released by de-confining 1 mm^3 of a gas at 250 billion
atmospheres, the illustration states pinhead so precludes this.

However just for kicks let's calculate that energy release. The formula
is that for adiabatic expansion. It's complex, but there's an on-line
calculator at:

http://hyperphysics.phy-astr.gsu.edu.../adiab.html#c3

1 mm^3 of hydrogen at specific density 150 contains .15 grams
by weight. Hydrogen is 0.084 kg/m^3 at normal atmospheric conditions,
so the tiny pinhead has 1.78 cubic meters crammed into it.

How much potential energy is stored in that? Plugging the numbers
into the above calculator, we see de-confining 1 mm^3 of hydrogen
at about 250 billion atmospheres and 15 million C releases 2.8E7 Joules,
or about the energy of 10 kg of TNT. That's a nice bang, but it
won't kill someone 160 km away, 1 km away, or probably
2 city blocks away.

I won't argue the figures as that's my weak suit, but what is hydrogen
doing
in any great quantity in the central core? Isn't the core defined more or
less as the fusion shell, inside of which there is negligible hydrogen
content?


That's a good point. I used the central core since pressure and
(by one reference) fusion energy density was highest. These
were the most liberal possible choices to try and make the illustration
work. It doesn't.

So 1 mm^3 hydrogen at that pressure is 0.15 grams, and specific heat is
14.304 Joules per g per degree K.

14.304 J/g/K * 15e6 K * 0.15 g = 32 megajoules.

By comparison gasoline contains 45 megajoules per kg.

So the pinhead of core material contains about the energy of 1 liter of
gasoline. That's not fatal at 160km, nor even 1 km.


Somehow that doesn't add up. I've played with Astrolite (chemical
explosive), which has a considerable expansion rate. That rate is still
nothing compared to the equivilant of 250 billion atm expanding almost
instantly. And one cubil milimeter of astrolite (at normal density) has
destructive power that I'd rate as higher than a liter of gasoline (which
would be difficult to ignite in one instant reaction anyway except as an
aerosol).

I won't support the destruction radius mentioned, but regardless of the
figures quotes, a cubic milimeter of solar core material would carry some
absolutely devastating effects.


The 32 megajoules in 1 mm^3 of Hydrogen is from specific heat
only. It didn't include pressure effects, since the illustration states
it remains in pinhead form.

However your point was interesting so I did the additional
calculation (in this post, above) to examine how much potential
energy was in the hyper-pressure gas.

1 mm^3 of Hydrogen at 250 billion atmospheres and 15 million C
when released produces energy equal to about 10 kg of TNT.

That's a nice big bang, but it's hardly devastating.


 




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