What is the energy content of nuclear weapons?

[NNadir]

Recently I learned that much of the world's enriched uranium for power plants is provided by Russia, the fuel being mixed down material from dismantled nuclear weapons. This arrangement arose because of a Clinton era treaty in which the United States agreed to buy its fuel from Russia in order to destroy the fissionable material contained in Soviet nuclear weapons. For the Russians, the Americans, humanity as a whole and the environment this was a win-win-win-win. Without the destruction of isolated highly enriched uranium (and for that matter, plutonium), meaningful nuclear disarmament is not really possible. Russia now provides nuclear fuel to every major nuclear nation on earth, except Taiwan, Taiwan being excluded for political reasons.

For nearly a decade much of the uranium fuel worldwide provided to nuclear power plants has come from inventory and not from mines, as there has been a huge surplus of fissionable material.

Recently I read the Nobel Peace Prize lecture of Dr. Mohamed Elbaradei http://nobelprize.org/peace/laureates/2005/elbaradei-lecture-en.html who has been a tireless worker for the advancement of nuclear power and for the prevention of nuclear war. I was struck by this remark he made:

We still have eight or nine countries who possess nuclear weapons. We still have
27,000 warheads in existence. I believe this is 27,000 too many.

A good start would be if the nuclear-weapon states reduced the strategic role given to these weapons. More than 15 years after the end of the Cold War, it is incomprehensible to many that the major nuclear-weapon states operate with their arsenals on hair-trigger alert – such that, in the case of a possible launch of a nuclear attack, their leaders could have only 30 minutes to decide whether to retaliate, risking the devastation of entire nations in a matter of minutes.

These considerations led me to consider the energy content of nuclear weapons. If we assume that the average nuclear weapon contains 20 kg of fissionable material, we see that 27,000 nuclear weapons would contain about 540,000 kg of fissionable material. Since a nuclear weapon typically has an isotopic concentration wherein the fissionable isotopes represent about 95%, one can show that the total energy content is about 41 exajoules. For comparison, the entire energy demand of the United States is about 100 exajoules. Thus the amount of energy in the world's nuclear weapons is enough to fuel all of the energy demand (from all sources) in the entire United States for about 5 months.

[wtmusic]

1. Just think how many bombs we could make if we turned out the lights

:crazy:

[Massacure]

2. Seems low

E=MC^2. So that means 20 * (299,792,458 ^ 2) should be about 1.8 exajoules per nuclear weapon.

Exajoule = 10^18 joules, right?

Of course, a nuclear weapon doesn't destroy all of its matter though.

[Vinnie From Indy]

3. Correct!

Man has yet to devise a bomb (thank God) that is able to convert anywhere close to 100% conversion efficiency. If we were able to attain that level of proficiency, a sugar cube could take out several square miles.

[NNadir]

4. A nuclear weapon converts just a tiny fraction of its mass to energy.

Most of the mass is retained as fission products, which in nuclear weapons parlance is called "fallout."

Here is how you do this calculation: You convert the mass into moles (I used, IIRC, the mass no 239 in my crude calculation, which is the mass of the prominent plutonium isotope, although many nuclear weapons use U-235.). You multiply the number of moles by Avogadro's number to give the number of atoms. Each atom fissioned produces about 190 million electronvolts (MeV) of energy per fission (plus 10 Mev of neutrinos, which can be ignored). Note that this 190 MeV is only a tiny fraction of the binding energy in a uranium atom - the fission products will also have binding energy. Next you multiply the resultant number by 1.602 X 10^(-19) coulombs, the charge on an electron, and you convert it to joules. You end up with 41 exajoules.

The result is crude but illustrative. There is an enormous amount of energy contained in nuclear weapons that could be recovered for use as energy as part of a disarmament program. In fact, the Clinton administration was well along on this process when our government was usurped by insane people.

As a practical matter, since the world doesn't have the infrastructure (enough nuclear reactors) to provide all of its energy via nuclear means, the weapons material could effectively fuel our existing reactors for many years.

[Dogmudgeon]

8. What does the "tonnage" refer to?

Some time ago, I myself thought of calculating the energy in a thermonuclear blast, but figured I'd have to find the formula to convert kilo- or megatons to joules (or in this case, exajoules). And I was thinking of the twin 20-MT blasts that knocked the Earth off its orbit in The Day The Earth Caught Fire, a movie I strongly recommend, in spite of the scientific errors.

However, my understanding of how -- and how efficiently -- nuclear blasts convert matter to explosive energy is poor. There the some simplified math to deal with, which I could have handled, but there are at least three methods of exploding radioactive material, as far as I know, and they're all different.

I'm also happy that the weaponized stuff is being beaten into plowshares, but I never cease to be amazed by just how much energy we really use, and how much more we will need in just a decade. Heating my house is one thing, but powering an entire civilization like ours seems to even challenge the potential output of the current stocks of nuclear material.

And if we have 20 years to figure out how to do it -- will we be able to?

--p!

[phantom power]

9. "tonnage" usually refers to "tons of TNT equivalent"

So a "10 megaton" warhead releases the same energy as detonating 10 million tons of TNT. It is not a measure of the amount of mass converted to energy, which is miniscule.

[phantom power]

5. We could get 100% conversion with matter/antimatter reactions.

But it's hot stuff. You could blow Mount Everest a mile high by reacting a gram of antimatter. And nobody has ever produced more than a picogram of it. Or maybe a nanogram. At any rate a really small amount. Which is fine with me. It's hard enough storing hydrogen, never mind anti-hydrogen.

[NNadir]

6. Ah, but annihilation energy is all gamma radiation.

It is difficult to convert gamma radiation into a form suitable for operating blow dryers. One can, in theory, use gamma radiation for removing one's hair, thereby eliminating the need for hair dryers, but even if this approach gained public acceptance, I don't think that the antimatter technology will be available in any case.

;-)

[phantom power]

7. Oh right, that.

That bit is usually side-stepped in hard SF novels by using it for weapons (where it's all about destroying stuff with uncontained gamma rays) or space drives (where they just blow all the gamma rays out the back, for thrust).

This brings up something about photons that confuses me. Photons have no mass, and yet they can confer momentum. When they bounce off of something like a solar sail, they propel the sail. And (if you believe Larry Niven) they can be ejected out the back of a space ship to propel it, which also usually works because of conservation of momentum.

How do photons get to have momentum without mass? Clearly I am missing something important.

[NNadir]

11. This problem troubles most people.

I was just discussing it with my son who is just entering into the conception of what energy, in particular, light energy, is. (I am introducing him to the first law of thermodynamics in his discussion of his fifth grade geology homework, which involves seismic waves.)

I always try to explain it this way: The particle/wave duality is without physical meaning in the sense that we are trying to impart macroscopic phenomena (massive objects and waves) on atomic scale events. For some type of problems it is convenient to describe light and/or mass as particles. For other types of problems, it is convenient to rely on its wave properties. The problem arises at the intersection of the two and the fact that people have no direct visible experience in the macroscopic world of what this might mean.

Once the photoelectric effect was explained, it was necessary to assume that a photon, the photon being a concept invented by Einstein's explanation, had momentum from conservation of momentum arguments. This momentum has in fact now been measured to some precision. When a photon transfers its energy to an electron, it disappears and no longer exists. I saw an interview with Richard Feynman in which he said he explained this (to his father) as if the photon was a word (ie a sound), it has an effect so long as it exists, but when it no longer exists, it disappears and no one is troubled by it. One can, at a loud concert for instance, actually feel sound pressure, but the sound is, as we all know, actually a wave. Of course one knows that sound pressure is transported in a medium, air, so one is somewhat more comfortable than one is with light, but on some level the analogy holds.

The energy of a photon is given by the relation E = hf = pc, where f is the frequency (usually designated by the greek letter nu). The momentum of light, p, is given by the relationship p = E/c. Since c = lf where l is the wavelength (usually designated by lamda) p = c/l.

Since force is simply the change in momentum dF = dp, the change in momentum induced by the absorption of light or its generation results in a net force on the emitting or absorbing object. One can in fact use solar sails in space, although for my money, ion engines (where the transfer of momentum is much larger) are a better deal.

It may not be satifying to say it this way, but it is "just so."

[phantom power]

13. Physics demands that I live with a lot of peculiar things.

I can't even get past Newton without feeling like everything is a bit dogdy. Force = mass X acceleration? What is "mass?" Well... it's, um, force divided by acceleration. I feel queasy.

[Dead_Parrot]

14. I'd say you're in good company...

If anybody says he can think about quantum physics without getting giddy, that only shows he has not understood the first thing about them.

Niels Bohr

[NNadir]

15. Hey, don't get all metaphysical on me!

:shrug: ;)

It's hard enough to do physics, never mind metaphysics.

Mass is, well, um, stutter, mass.

[Dead_Parrot]

12. e=mc^2 (or, m=e/c^2)

Photons have a sort of mass-by-proxy, since they're packets of mass-energy the same as boring baryonic matter. If you know the energy of a photon, drag it through e=mc^2 backwards to get the "mass" (disclaimer - this is a bit of a fudge, but you get within an order of magnitude)

One of my old lecturers had us weighing moonbeams, just because. Happy days...

(Edit - I missed NN's other post which has a more practical way of working out the thrust. I still recomend weighing moonbeams, though, just so you can say you've done it.)

[Dead_Parrot]

10. Reminds me of a "Bad Science" article...

Colour Nation, hairdressers to the stars in Soho, London, offers Bioionic’s IHR. Its public relations material explains how it works: "Positive ions have lost an electron, and are considered unhealthy," whereas negative ions "have gained an electron, and greatly assist in a body’s mood, energy level, and overall health". When these benevolent negative ions encounter water, "the water molecules are broken down to a fraction of their previous size... diminutive enough to penetrate through the cuticle, and eventually into the core of each hair".

I might be wrong, but surely shrinking water molecules must cost more than the £230 Colour Nation charges for IHR? The only other groups who have managed to create that kind of superdense quark-gluon plasma used a relativistic heavy ion collider, and if Colour Nation has got one of those at the back of the salon then I’m glad I don’t live in the flat upstairs.

http://www.badscience.net

But I digress...

[NNadir]

16. Here is another way of looking at this question.

Here is a table listing all of the world's nuclear reactors: http://www.world-nuclear.org/info/reactors.htm

According to the table, the 2005 demand for uranium was 68,357 metric tons. Most reactors (excluding special types like CANDU reactors which use natural uranium or breeders that used highly enriched fuel) use 3% enriched uranium. Natural uranium contains 0.7% fissionable U-235. Therefore - viewed in a simplified manner - most reactors require a 2.3% "boost." This means that nuclear reactors world wide require about 1570 MT of fissionable isotopes, usually U-235, but Pu-239 is also suitable.

The world inventory of highly enriched uranium and all of its plutonium, including civilian plutonium, is 3750 MT. The portion of this material designated for military use is about 3 times as large as I estimated; it is 1880 MT.

http://www.isis-online.org/global_stocks/end2003/summary_global_stocks.pdf

Thus the world's inventory of isolated fissionable material (the military stocks) is sufficient to run the world's nuclear reactors for more than two years. Were plutonium recovered from spent fuel, this quantity could easily be extended to fuel the world's reactors for 4 to 5 years. Note that, in the putative case where this were to happen, the fissioning of the stocks would lead to the creation of additional plutonium representing about 90% of the inventory charged into the reactors. Thus one would in theory need to add only 157 metric tons of new plutonium to the reactors for each charge.

If one contemplates this matter, it becomes immediately clear that the world's existing nuclear reactors could be made to operate for a number of years without any additional uranium mining whatsoever.

Once a reactor is charged with fuel, they typically run for 1 to 2 years without refueling.

This analysis is somewhat simplistic, still were humanity to operate the same number reactors as it does now (actually the number will increase substantially over the next decade or so), there is sufficient fissionable material already in existence - with no additional enrichment - to operate the world's reactors for 1 to 2 decades. In the case where thorium were to replace the depleted uranium removed from the reactors to a substantial extent, this period could be extended for many decades more.