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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
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"Sam Wormley" wrote in message
news:_jIGd.10927$OF5.9745@attbi_s52... ..... Thank you. http://www.madsci.org/posts/archives...2372.As.r.html "I bring this up because there can be ridiculously high temperatures in the Universe, but they don't mean much! And that is exactly my point. It would be absurd to plug that temperature (OR the 100 million C from the ITER fusion reactor) into the Boltzman equation, look at resultant watts, and make conclusions about lethal distance. Yet that is what the original illustration does. The Boltzman equation is an accurate translation of temperature to radiant power, assuming perfect emissivity, plus infinite power is available to maintain the temperature of the 1 mm^3 pinhead on earth. It is not in any way reflective of what a pinhead of solar core material would do on earth, any more than a pinhead of ITER plasma or a pinhead of Uranus magetosphere. |
#13
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Joe D. wrote:
"Sam Wormley" wrote in message news:_jIGd.10927$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
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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
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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
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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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