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Posted by Masao (Member # 232) on :

Minutiaeman and I have been trying to figure out the density of antimatter as stored on starships and used in torpedo warheads. According to TNGTM, antideuterium is transported as a type of slush. If we assume, for the sake of simplicity, that antideuterium is stored under pressure, what is it's density? At what temperature does deuterium become a solid or slushy liquid?

(Show your work, please).

In a related question (asked previously I think), what's the explosive yield of 1.5 kg of antimatter (in joules or megatons of TNT or both)?

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Posted by MinutiaeMan (Member # 444) on :

Let me tell you about some of the assumptions I was working with. I figure since antihydrogen would have the same physical properties as normal hydrogen, we can use the same storage specs.

According to the TNG:TM, they store deuterium at 13.8� Kelvin. So my guess would be that they store antimatter at the same temperature.

I was trying to use the Ideal Gas Law to determine either the volume or the amount (measured in moles) of antimatter that could be stored in a photon torpedo. The problem is that we have two variables: volume and pressure.

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Posted by Masao (Member # 232) on :

So far, we have PV = nRT, where r = 0.082056 L*atm/(mol*K). Minutiae tells me that this gives a volume of 1.6851 cubic meters or 1685 liters at 1 atm. This seems a bit high to fit into a warhead and is still probably a gas (since it's less than 1% of the weight of water at room temperature). So, this means that the deuterium has to be under pressure. A pressure of 1000 atm would get that down to 1.6 liters, which seems like a nice little package, but is the pressure to high for safety?

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Posted by Malnurtured Snay (Member # 411) on :

I have a headache...

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Posted by Masao (Member # 232) on :

By the way, we've also assumed that 1.5 kg of hydrogen is 1488.1 mol. That gives V (liters) = 1488.1 mol x 0.082056 L*atm/(mol*K) x 13.8 K = 1685 liters or 1.685 cubic meters. But I was wondering if antimatter is stored as antideuterium (that has an atomic weight of 2). Would that double the weight? I'm not up on the molecular forms of hydrogen isotopes.

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[This message has been edited by Masao (edited May 08, 2001).]

Posted by Daniel (Member # 453) on :

Wait, under what impression is it that you think slush deuterium is a gas? I mean, if you have an explanation by all means, but "slush" in my mind means liquid. And at 13 K or whatever? That's really cold. Probably liquid. In which case you can't use PV=NRT, I'm afraid.

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Posted by Masao (Member # 232) on :

Yes, I didn't know how to handle this phase change. Antideuterium is supposedly stored as a semiliquid/semisolid slush. So how do we calculate this properly? Any rocket scientists here with experience with liquid gases? Anyone with a LPG tank beside their house?

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Posted by MinutiaeMan (Member # 444) on :

quote:
Wait, under what impression is it that you think slush deuterium is a gas? I mean, if you have an explanation by all means, but "slush" in my mind means liquid. And at 13 K or whatever? That's really cold. Probably liquid. In which case you can't use PV=NRT, I'm afraid.

Crap crap crap crap crap! That is so obvious, it's stupid!

*smacks head in frustration*

Back to square one...

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You know, you really should keep a personal log. Why bore others needlessly?
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Posted by Fructose (Member # 309) on :

What you need to do is find the density of liquid hydrogen. Fluids are very difficult to compress, so the density of liquid hydrogen would be about the same at any pressure, assuming 1 atm. And (anti)deuteriun has an atomic mass of 2 since it's got a (anti-)proton and a (anti-)neutron. Just double the density since you now have twice the mass.

Take that info, and the fact that the density of solid deuterium would be slightly higher than the liquid since most liquids are slightly less dense than their solids. (Water being a notable exception.)

Also, when a solid melts, it will stay at it's melting point until it is completely liquid. So, increase the density of deuterium ever so slightly and you'll probably have a pretty close number to what it's density would be.

Some sice notes: According to my research, hydrogen melts at 14 K, and since deuteruim is heavier, I would assume it's melting point is a little different. So 13.8 K sounds right.

Also, the ideal gas law is pretty much worthless in this temp range. You would need the van der Waals equation:

(p + (n^2a/V^2))(V - nb) = nRT

If you want to get more info on this, go to http://www.chem.ualberta.ca/~plambeck/che/struct/s0307.htm , and http://www.chemicalelements.com/elements/h.html .

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Posted by BlueElectron (Member # 281) on :

Ideal Gas Law are only meant for gas in an "ideal" situation.

"IF" antihydrogen have similar properties as hydrogen the we assume it exist in a gaseous form in its' nature state. However, in StarTrek, antihydrogen is stored in a liquid form (hence, slush). Ideal Gas Law can be be apply because the "gas compressibility" does not remain as a constant 1 or close to constant of 1 in extreme environment(curve line, instead of a straight line graph) but decrease or increase with different condition.

Different gas laws have to be applied.

Damn, I feel like a geek!!!

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Posted by Starbuck (Member # 153) on :

I was under the impression deuterium was a liquid at room temperature... "heavy water"?

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Posted by Lee (Member # 393) on :

Then you have to take into account certain constants, like the amount of time on your hands, which has a value of way too much. . .

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Posted by Harry (Member # 265) on :

http://www.britannica.com/eb/article?eu=30608&tocid=0

Deuterium is very much the same as ordinary hydrogen. It reacts slighly slower than it's lighter counterpart.
http://www.britannica.com/eb/article?eu=126113

This is probably all the relevant data about deuterium.

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Posted by Ritten (Member # 417) on :

Okay, with all the math: 1=1 What is the density of slush hydrogen?? There is your answer...

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Posted by Fructose (Member # 309) on :

Deuterium is just like hydrogen. So it's a gas at room temp. Heavy water is just regular water, but with two deuteriums instead of hydrogens. It's about 10% heavier than regular water.

P.S. FYI: I have a bachlor's degree in chemistry.

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Posted by Treknophyle (Member # 509) on :

I have been told that although starships do indeed keep their matter reserve as deuterium (thus it can double-up as fuel for the impulse fusion generators), the antimatter is plain old anti-hydrogen. I believe the source is Sternbach (about as canon as you can get).

Logically, it makes sense, as antihydrogen has to be easier to acquire/make than anti-deuterium. There is no parity/symmetry issue, its not as if the reactor needs anti-deuterium. The matter/antimatter reactor would gladly accept coffee and anti-earl gray tea as reactants, as long as they were first converted into gasses, and the masses were in correct proportion.

So, what is the mass of 1 cubic meter of liquid slushy hydrogen? (This will allow me to estimate the amount of antimatter in a storage pod for my evil plans).

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Posted by Ritten (Member # 417) on :

you forgot to add this.....

BWHAHAHAHAHAHAHAHAHA

i am done

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"One's ethics are determined by what we do when no one is looking" Nugget
Star Trek: Gamma Quadrant
Star Trek: Legacy
Read them, rate them, got money, film them

"...and I remain on the far side of crazy, I remain the mortal enemy of man, no hundred dollar cure will save me..." WoV

Posted by MinutiaeMan (Member # 444) on :

Yes, it's definitely anti-hydrogen, not anti-deuterium. Although anti-deuterium wouldn't be too hard either, all you need to add is a neutron. (There is no such thing as an "anti-neutron" since neutrons have no charge.)

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Posted by James Fox on :

Well, a Quick Web Search revealed the following link: http://www.magicdragon.com/ComputerFutures/SpacePublications/STAR.html
which gives the density of LH2 at 0.078 g/cc, and the density of solid hydrogen at 0.076 g/cc (which rather surprises me). I suppose 0.077 g/cc could do for slush hydrogen.

Personally, however, I always thought that the matter and antimatter would be in solid metallic form, since to get a good clean reaction the two components should be mixed well before the reaction occurs, and the best way to do this could be to have granules that are suspended in space by some kind of field, one could then try to mix them beforehand without having the granules actually touch, until one is ready to detonate the torpedo.

Also, from the TNG TM, since the antimatter tanks on the ship are much smaller than the matter tanks, antimatter would have to be stored at a very high density in order to match the amount of matter, thus requiring it to be stored in metallic form, which is much denser than solid.

Next, anti-neutrons exist, since animatter is not just charge-reversed matter. See: http://www.sciencenet.org.uk/database/Physics/9812/p01230d.html for a quick definiton.

Finally, since Starfleet ships are apparently able to refuel thier stocks of deuterium from interstellar gas clouds, I would think they have a proton-proton fusion process better than any conjectured by current science, so they could perhaps have an antimatter one to create anti-deuterium. Personally, I think that having symmetric M/AM reactions is much cleaner.

James Fox

Posted by TSN (Member # 31) on :

Of course there's an anti-neutron! It still has a neutral charge, but don't think it's the same thing. Put one together w/ a normal neutron, and you're still going to have a quantity of gamma radiation on your hands (or pass through your hands, as is more likely...).

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Posted by TSN (Member # 31) on :

Hey! No posting what I'm saying while I'm still typing it!

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Posted by Fructose (Member # 309) on :

Yeah, an anti-neutron has an opposite spin. But there is a particle that is it's own opposite. I can't remember it's name, but I know there is one.

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Posted by TSN (Member # 31) on :

I don't think the spin is different...

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Cat: "I'm courting."
Lister: "Courting who?"
Cat: "Whoever shows up!"
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Posted by Omega (Member # 91) on :

Well, SOMETHING is different. If not spin and charge, what could it be?

As for a particle that's its own anti-particle, photons and pions, to name two.

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Posted by Shik (Member # 343) on :

Y'know...as we find ever smaller & smaller particles, I'm waiting for more of the comedy names to show up..y'know, like gluons. (which as a modeler I find hilarious) My proposed choices are peon, hardons, morons, & condons (say it quick).

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Posted by Masao (Member # 232) on :

Thanks, everyone. You've been very helpful.

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Posted by Gammera on :

Quote....
"Also, from the TNG TM, since the antimatter tanks on the ship are much smaller than the matter tanks, antimatter would have to be stored at a very high density in order to match the amount of matter, thus requiring it to be stored in metallic form, which is much denser than solid."

Remeber that the M/ARC only runs at a 1:1 ratio @ warp 8+ so of course you do need alot more matter then anti-matter.

Posted by Masao (Member # 232) on :

Okay, I did my own number crunching and came up with some figures.
How many joules are released by 1 kg of antimatter? This page (http://astp.msfc.nasa.gov/antimatter.html) says that you get 9 x 10^16 J/kg antimatter from mass-energy equation, which agrees with several other pages. (http://www.cm.nu/~shane/lists/rec.arts.startrek.tech/2000-09/0245.html http://www.cm.nu/~shane/lists/rec.arts.startrek.tech/2000-09/0245.html and http://www.fivedoves.com/letters/feb99/goneby214.htm http://www.fivedoves.com/letters/feb99/goneby214.htm . Some pages include the matter in the calc, others only the antimatter. So, if 1 ton of TNT gives you 4.18 x 10^9 J (http://www.aeic.alaska.edu/Input/lahr/magnitude/energy_calc.html and http://www.ieer.org/clssroom/unitconv.html http://www.ieer.org/clssroom/unitconv.html and others), then 1 megaton produces 4.18 x 10^15 J. Therefore, 1 kg of reactant will give you a bang equivalent to 21.53 megatons of TNT and 1.5 kg, supposedly carried by a TNG torpedo, will give you 32.3 megatons. This amount of antimatter will fit into a sphere 34 cm in diameter. In comparison, the Hiroshima bomb was only 15 kilotons.

The page referenced by James Fox (http://www.magicdragon.com/ComputerFutures/SpacePublications/STAR.html) says the density of hydrogen slush is about 70.7 g/l. Since a cubic meter is 1000 l, it would weigh 70.7 kg. If that blows, it would yield a blast equivalent to 1522 megatons of TNT, which is a bad day for anyone. How much antimatter is carried on a Galaxy class starship?

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[This message has been edited by Masao (edited May 09, 2001).]

Posted by Ritten (Member # 417) on :

30 pods holding 100 m³ each...
3,000 m³ total....
3,000,000 l
4,566,000 megatons....
A planetary system killer, since a 5 megaton warhead is considered a city killer

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Posted by Sol System (Member # 30) on :

The difference between a neutron and an antineutron is rather subtle. Neutrons, like almost everything else, are made up of quarks. Specifically, I believe the neutron is composed of one up quark and two down quarks. This is significant because quarks have charge, but only a fractional one. An up quark has a charge of +2/3, while a down quark has a charge of -1/3. So two down quarks plus one up quark gives us a total charge of zero. Which is why neutrons are neutral.

However, there are antiquarks too. An antineutron is made up of one anti-up quark and two anti-down quarks, with charges of -2/3 and +1/3, respectively. So the antineutron still has a total charge of zero, even though it is the exact opposite of a neutron.

Beyond that, the antineutron carries the opposite magnetic moment, but frankly, my dime store physics gives out at this point.

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[This message has been edited by Sol System (edited May 10, 2001).]

Posted by Treknophyle (Member # 509) on :

Coould someone check these figures - I get a different result:

[Density of LH (Slush):]
1cc = .0707 grams
1 cubic meter (1x10exp3 meter) = 7.07 x 10exp1 kg
1 pod anti-hydrogen shush (1x10exp3 meter) = 7.07x10exp4 kg

[Energy Released by Matter/Antimatter Reaction]
1 kg AM + a kg M = 1.8x10exp17 Joules
(using matter-energy conversion formula where 1 kg = 9.0x10exp16J - then double figure to allow for 1 kg of matter as well)
Reactant mass for 1 pod: 7.07x10exp4 kg x 2 = 1.1414x1-exp5kg
1.414x10exp5kg x 9.0x10exp16 = 2.5452x10exp23J

[Megatonnage/Potential Explosive Power per Pod]
1 pod + reactant = 2.5452x10exp23J
1 megaton of TNT = 4.18x10exp515
1 pod + reactant = 6.088x10exp7 megatons

I need the correct data to work out the power/fuel-consumption curve for various starships - given the TNG Tech Manual curve.

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Posted by Masao (Member # 232) on :

1. One discrepancy I see right away is the size of the antimatter pod. Ritten says it is 100 cubic meters while you (Treknophyte) says it is 1000 cubic meters.
2. Another problem is that you're including the mass of the matter reactant twice: once in the energy mass equation where you double the figure for 1 kg to get the figure for 2 kg of reactant and in the line "reactant mass for 1 pod" you double it again ot account for 2 pods.
3. A math mistakes creeps in when you multiply 1.414 x 10^5 x (9.0 x 10^16 x 2 = 1.8 x 10^17): you get 2.5 x 10^23 but the correct answer is 2.5 x 10^22. You added a ^1. (You didn't write the additional 2 in that equation to get 1.8 x 10^17 J/kg, but you multiplied by 2).
4. Everything after that is correct, so I get 3 x 10^6 MT, which, when multiplied by 20, is what you get.

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Posted by Treknophyle (Member # 509) on :

"I'm a designer, not a mathematician..."

Actually, I think we both may have let an error creep in. Looking at your corrections, I sought to simplify the calculations. Check this out please:

[Density of LH (Slush):]
1cc = .0707 grams
1 cubic meter (1x10^3 meter) = 7.07 x 10^1 kg
1 pod anti-hydrogen shush (1x10^2 cubic meters) = 7.07x10^3 kg

[Energy Released by Matter/Antimatter Reaction]
1 kg = 9.0x10^16J - remember double figure to allow for 1 kg of matter as well
Reactant mass for 1 pod: 7.07x10^3 kg AM + 7.07x10^3 kg M = 1.1414x10^4kg
1.414x10^4kg x 9.0x10^16 = 1.2726x10^21J

[Megatonnage/Potential Explosive Power per Pod]
1 pod + reactant = 1.2726x10^21J
(1 megaton of TNT = 4.18x10^15)
Therefore
1 pod + reactant = 3.0444976x10^5 megatons
= 3.0444976x10^2 gigatons

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Posted by Ritten (Member # 417) on :

I got the 100m³ from the most canon,

, of all sources...... the TNG TM....

So it may be in error....

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"One's ethics are determined by what we do when no one is looking" Nugget
Star Trek: Gamma Quadrant
Star Trek: Legacy
Read them, rate them, got money, film them

"...and I remain on the far side of crazy, I remain the mortal enemy of man, no hundred dollar cure will save me..." WoV

Posted by Treknophyle (Member # 509) on :

No, 100 cubic meters sounds about right. Since the pods seem to be two-lobed, it roughs out to each pod being 2 approx 3.5 meter cubes.

Masao - how are my calcs?

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Posted by Masao (Member # 232) on :

Ok, here's what I figured.

70.7 g/L AM x 1000 l/cubic meter x 100 cubic meters/pod = 7.07 x 10^3 kg AM/pod.

1 kg AM yields 9 x 10^16 J/kg
1 MT TNT yields 4.18 x 10^15 J
Therefore,
1 kg AM yields 2.153 x 10^1 MT. (21.53 MT/kg AM)

7.07 x 10^3 kg AM/pod x 2.153 x 10^1 MT/kg AM =
1.522 x 10^5 MT/pod
x 2 pods (one M, one AM) =
3.044 x 10^5 MT

So, we seem to get the same answer.

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Posted by AndrewR (Member # 44) on :

Antimatter... where does it actually comefrom? Is it the same 'partical' as real matter when it's just made except ??opposite?? If so, where is the matter partical... does antimatter comefrom another universe? If so, does the matter partical go to the antimatter universe?? or do we now get MORE particals than the antimatter universe... or is it balanced because even though this antimatter is in our universe - its opposite - so it doesn't 'register' in our universe!?!

Bizzaromatter ;o)

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Posted by Sol System (Member # 30) on :

You cannot have matter without antimatter. You know that matter and energy are interchangeable under the right conditions, yes? Well, whenever you convert energy to matter, say, in a particle accelerator, you get new particles plus their corresponding antiparticles. Conservation of energy, etc, etc, blah blah blah.

The really interesting question is, since matter and antimatter are created together, where is all the antimatter? As far as we can tell, the universe is almost entirely matter, with antimatter found only in a few exotic locations where it is currently being created...the jets of certain black holes, for instance. (Like the one presumably at the center of our galaxy.)