# Heat of Fusion for Hydrogen: Calculating Distance from 0.10 g Reaction

• ckirmser
In summary, if one is within a tenth of a gram of a hydrogen fusion reaction, the temperature will reach a level of a house on fire.f

#### ckirmser

Hello, all!

I am involved in a discussion where the topic is the heat of fusion for hydrogen. From what I've found, the heat of fusion for H2 is around 22.5 million °F and the average house fire is no more than 1,800 °F or so.

So, what I'm trying to find is, how far from 0.10 grams of a hydrogen fusion reaction must one be for the temperature to be about that of a burning house?

If there is a formula, that'd be great so that I could have a general answer.

You got something confused. 22 million degrees is a temperature, not a heat of fusion. Or of anything.
You mean that as the temperature to ignite the proton-proton reaction?

You got something confused. 22 million degrees is a temperature, not a heat of fusion. Or of anything.
You mean that as the temperature to ignite the proton-proton reaction?

Well, I will not deny the option of being confused. I'm guessing what I found was the temperature should one be in contact with the fusing hydrogen. I mean, the Sun is hydrogen undergoing fusion and it's get a temperature. Speaking of the Sun, I seem to recall reading somewhere what the effects would be if a teaspoon of the Sun were moved to the Earth's surface, but I can't find it now.

Here's the deal;

We're talking in a SciFi forum and weaponry in a SciFi game is being discussed. Someone mentioned a fusion gun using H2 as the medium and I commented that the temperatures produced by fusing hydrogen would cook everything around, just because of the heat produced, so the rules were way off on its use as a personal weapon. The other guy said that it was only a tenth of a gram and I countered that the weight may limit the duration of the event, but not the heat. To support his claim, he used an analogy of choosing to stand near a lit match or a burning house.

So, I thought I'd see just how far from a hydrogen fusion reaction one would have to be to have it cooled down to a mere 2,000°F.

The problem with fusing hydrogen is that you need to heat is up to millions of degrees before the reaction starts.
The temperature inside the sun gives you an indication about how high it should be in order to have this reaction going.
Pressure is also an important factor.

The result of using the energy resulted from fusion for heating up the environment it depends on how much hydrogen is fused.
But this is not relevant for your scenario. Unless you assume that you can fuse the hydrogen at room temperature as a SF scenario. Then, by the same device, why not assume that the energy released is all directed forward and none of it reaches the gun handle?
If it's a fantasy , you can even have a sword with fusion. :)

The result of using the energy resulted from fusion for heating up the environment it depends on how much hydrogen is fused.

The particular rules don't specify. They are more concerned with the effects of recoil and weight of the weapon. But, the guy I'm aiming this towards has specified a 0.10 gram hydrogen source.

But this is not relevant for your scenario. Unless you assume that you can fuse the hydrogen at room temperature as a SF scenario.

Presumably, the weapon contains the reaction and ejects the energy as a stream from the muzzle. I'd guess this stream has a temperature along the lines of the internal reaction.

Then, by the same device, why not assume that the energy released is all directed forward and none of it reaches the gun handle?
If it's a fantasy , you can even have a sword with fusion. :)

Well, sure, but this is supposed to be hard SciFi.

Actually, I'm not really concerned about the stream itself. Basically, it is presumed some sort of containment field guides the stream towards the target.

But, at the target, in order for the weapon to be more than just a really powerful flashlight - I'm not even considering the brightness of the stream and that the radiated energy would probably fry everything all on its own - at the target, the energy must be released to be effective. So, at that point of release, I'm figuring that it's the same as placing a small amount of solar material there. Material that, I figure, has MASSIVE heat, heat that should melt everything in miles, if not vaporize.

I could swear that I'd found a formula for this back in the 80's and had come up with the radius of effect. But, I've slept since then.

Basically, I'm trying to show that the Fusion gun sounds cool, but is a total fail as an infantry weapon. Like a 1kT hand-grenade.

You mean that the reaction will take place at the target? I am not sure I understand you.

But your analogy with having a small piece of the Sun is not very useful.
At ITER they will fuse something like 0.5g of hydrogen in 1000 s. And nobody around the reactor will be vaporized. And they won't be miles away.
The power predicted is some hundreds of MW.

So even if you don't want to consider it, the main problem is how do you make that hydrogen fuse and not the fact that it will vaporize things for miles around.
If you could fuse very small amounts of hydrogen, the heat and radiation can be as small as you want it. IF.

In its simplest form, fusion amounts to putting enough energy into atoms to overcome Coulombic repulsion and getting them close enough together to let the short-range nuclear forces take over so they can fuse. For a proton-proton reaction, this is something like 3.6 x 109 K. This translates to a black body emissive power of something like 9.5 x 1030 W/m2 based solely on the temperature required to start the reaction. The amount you fuse therefore absolutely matters, as it determines the time frame over which the reaction occurs and how much energy is added from the reaction itself.

For a spherical emitter, this intensity would decrease according to an inverse square law and the distance over which it would be dangerous would be fairly limited given the time scales involved in fusion reactions. For example, the attempts at inertial confinement fusion at the National Ignition Facility (NIF) fuse about 150 μg of deuterium and tritium and the reaction lasts on the order of 10 ns. If you only had 10 ns of the above reaction, that is 9.5 x 1022 J/m2 plus whatever was produced by the reaction (roughly 1 to 2 orders of magnitude higher than the input energy).

Sso the question isn't just the temperature of the reaction and distance from the reaction, but also the initial temperature of the objects in question nearby, how much of them is exposed to the emitted energy, what mass and composition they have (i.e. how much energy it takes to raise their temperature), how much reactant was used (i.e. the time over which this power was released) and what temperature is dangerous for those people or objects. That is for a very idealized case, as well.

Of course, if you were to somehow focus all of the energy into a coherent beam like a laser, then the rules are essentially the same as for a laser where it all depends on how long you point the beam at an object and how intense the beam is.

You mean that the reaction will take place at the target? I am not sure I understand you.

Well, no, the reaction takes place in the weapon. I think it's like a very small fusion drive which is why the rules cover recoil - trying to stand while a fusion rocket in your hands is blasting away - more than the effects of the stream.

But your analogy with having a small piece of the Sun is not very useful.

Hmm. Well, then, I'm not visualizing this thing well at all.

At ITER they will fuse something like 0.5g of hydrogen in 1000 s. And nobody around the reactor will be vaporized. And they won't be miles away.
The power predicted is some hundreds of MW.

So, the entry I found - wiki, I believe, though my browsing history isn't storing wiki hits, so I've been unable to find the reference again - listing the temperature of fusion at 22.5 million °F was in error? I mean, not outside the realm of possibility, but it just seems strange that so much energy is so, well, cool - not in the Fonzie sense.

So even if you don't want to consider it, the main problem is how do you make that hydrogen fuse and not the fact that it will vaporize things for miles around.
If you could fuse very small amounts of hydrogen, the heat and radiation can be as small as you want it. IF.

Well, it's not a matter of wanting to consider it or not. More trying, at this point, to understand what I thought I already understood.

Boiled down, it's this;

Is a weapon that uses the energy of a hydrogen fusion reaction - as I said earlier, like a small fusion rocket drive - is this weapon something that is reasonable as an infantry weapon, even if the user is encased in an armored suit?

I'm thinking, "no," but it seems that I'm wrong on that count. See, I figure the fusion stream blasting from the muzzle would simply annihilate everything around because it's so hot, but I guess not, from what I read here.

In its simplest form, fusion amounts to putting enough energy into atoms to overcome Coulombic repulsion and getting them close enough together to let the short-range nuclear forces take over so they can fuse. For a proton-proton reaction, this is something like 3.6 x 109 K. This translates to a black body emissive power of something like 9.5 x 1030 W/m2 based solely on the temperature required to start the reaction. The amount you fuse therefore absolutely matters, as it determines the time frame over which the reaction occurs and how much energy is added from the reaction itself.

The game rules don't specify the amount or the time frame.

Following is how the game describes the weapon;

"The power pack powers a laser ignition system in the weapon itself which heats hydrogen fuel to a plasma state. The plasma is contained in the ignition chamber until a fusion reaction takes place and then released through a magnetically focused field along the weapon's barrel. The high initial velocity plasma jet is 2 cm in diameter but begins to dissipate immediately."

Maybe I am placing too much on the word, "fusion," and am in error to think that it is hot. But, the Sun is a fusion reaction and it heats the entire planet with only a fraction of its output.

Something just isn't coalescing in my head properly.

For a spherical emitter, this intensity would decrease according to an inverse square law and the distance over which it would be dangerous would be fairly limited given the time scales involved in fusion reactions. For example, the attempts at inertial confinement fusion at the National Ignition Facility (NIF) fuse about 150 μg of deuterium and tritium and the reaction lasts on the order of 10 ns. If you only had 10 ns of the above reaction, that is 9.5 x 1022 J/m2 plus whatever was produced by the reaction (roughly 1 to 2 orders of magnitude higher than the input energy).

Well, my initial thought was to use the inverse square law, but was wanting to back it up, in case the guy asked for substantiation. That's what led me to do a search on the corollary effects of a fusion reaction.

Sso the question isn't just the temperature of the reaction and distance from the reaction, but also the initial temperature of the objects in question nearby, how much of them is exposed to the emitted energy, what mass and composition they have (i.e. how much energy it takes to raise their temperature), how much reactant was used (i.e. the time over which this power was released) and what temperature is dangerous for those people or objects. That is for a very idealized case, as well.

The objects in question are just what might be around in a random combat situation; buildings, trees, hills, vehicles, etc.

I thought I could just take the temperature I found - the 22.5 million °F - slap it into an equation with a factor for distance from the reaction, and show that the distance it takes for the heat to attenuate to that of a burning house - ~1,800°F - is 'X.' With 'X' being some large number that shows the game designers didn't take into account the power that they were talking about.

Of course, if you were to somehow focus all of the energy into a coherent beam like a laser, then the rules are essentially the same as for a laser where it all depends on how long you point the beam at an object and how intense the beam is.

Since the energy was contained by some sort of magnetic field, or, maybe just a handwavium field, I figure the total energy of the reaction was being channeled into the 2cm beam.

How about a general question, then...

If it were possible to transport a 0.10 gram piece of the Sun to the Earth, what would be the effects?

How about a general question, then...

If it were possible to transport a 0.10 gram piece of the Sun to the Earth, what would be the effects?

It would likely immediately cease all fusion reactions and dissipate as a gas. The only reason such a reaction is sustained in the sun is that the extremely high pressures due to gravity can confine the plasma for a long enough time (essentially indefinitely) for sustained fusion to occur. On Earth, we have no means of confining a plasma for that length of time (gravity is obviously much less here) so we have to find a means to confine the plasma for "long enough" for sufficient fusion to take place. Typically this is either done using magnetic confinement (e.g. a pinch or a tokamak) or through inertial confinement (e.g. laser-driven ICF). Even then, our plasmas tend to blow right back apart before a meaningful amount of fusion has occurred.

Of course, the hypothetical situation of bringing 0.1 g of solar plasma to the Earth implies that we would have determined how to confine such a plasma indefinitely without solar gravity, so in that case, I'd just have to say it would almost immediately finish its fusion reaction and you would instead end up with a little bit of helium instead. It would not be able to sustain helium fusion, though, without some means of further increasing the pressure/temperature.

Of course, the hypothetical situation of bringing 0.1 g of solar plasma to the Earth implies that we would have determined how to confine such a plasma indefinitely without solar gravity, so in that case, I'd just have to say it would almost immediately finish its fusion reaction and you would instead end up with a little bit of helium instead. It would not be able to sustain helium fusion, though, without some means of further increasing the pressure/temperature.

There would be no energy release? Just the helium? I understood fusion to be the creation of helium along with a release of energy.

Well sure there would be energy released. How much would result from 0.1 g would depend on how much of that mass actually fused into helium. You could calculate the ideal case where it all fused but in practice that is highly unlikely.

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News Flash! The Sun is not a little homogenous ball of hydrogen. Perhaps you knew this and were just being sloppy. Fusion (mostly) takes place in the CORE of the Sun (where temperatures are guestimated to range up to 28 million degrees F (°F ? really?? LMFAO!)) Quick quiz: order the following from most to least energy producing per kilogram of material: A. Candle, B. (Live) Human body C. Core material of Sun. The correct order is BAC, the energy of the Sun per kg of material is about the same as a compost heap. The hydrogen in the Sun's core is compressed to about (another guestimate) 110 g/cc (Iron has a density in the lab of 8 g/cc and the densest metal (at Room Temperature and pressure) is about 22.6 g/cc), so a kilogram of that is much smaller in volume than us with densities near 1 g/cc, but still your conception of how the Sun works is basically wrong. Its possible for two hydrogen atoms in a balloon to fuse. The question is at what T and P will the reaction be "likely"? (or "very likely"). Anyway. Once you know the energy content of 0.1 g (about 50 MJ) all you need do to get "an idea" is to figure out how much,say, iron that would melt (at Room Temperature). It is quite a bit.Very roughly 60 kg.

Let's try it this way...

Given a fictional weapon that operates as;

"The power pack powers a laser ignition system in the weapon itself which heats hydrogen fuel to a plasma state. The plasma is contained in the ignition chamber until a fusion reaction takes place and then released through a magnetically focused field along the weapon's barrel. The high initial velocity plasma jet is 2 cm in diameter but begins to dissipate immediately."

And, given that the recoil from this weapon is strong enough to require either a powered battlesuit or fictional artificial gravitics to keep the firer in place when firing, would not the general effects of the beam merely existing be enough to cause widespread damage around it, let alone to whatever happens to the target?

My thought is that a weapon that is based on projecting the destructive energy of hydrogen fusion would not create a sterile beam, like a laser, that only damages the target. That the energy will not be contained to a nice small spot on the target, but that just the presence of the beam would be devastating to some distance around it.

Also, wouldn't just the brightness of the beam be highly destructive in its own right? I'm thinking here of the "shadows" made by vaporized people on concrete at Hiroshima. Wasn't that an effect of merely the light from the explosion?

Perhaps I'm letting the emotional impact of "fusion" color my imagination, but it just seems that such a weapon would be destructive to everything around it, not just the target.

Fusion is not necessarily destructive in its own right. Sure, if you start the fusion reaction with a fission bomb and let it continue uncontrolled, then it is massively destructive, but that doesn't mean that the presence of a fusion reaction in a more controlled form means certain doom for the surroundings.

Also, if said beam was composed of plasma, then yes it would be more dangerous to the surroundings because a plasma key is going to widen and disperse as it leaves the barrel. If it is just the released energy focused into a beam, though, then it ought to behave just like a laser.

Fusion is not necessarily destructive in its own right. Sure, if you start the fusion reaction with a fission bomb and let it continue uncontrolled, then it is massively destructive, but that doesn't mean that the presence of a fusion reaction in a more controlled form means certain doom for the surroundings.

Also, if said beam was composed of plasma, then yes it would be more dangerous to the surroundings because a plasma key is going to widen and disperse as it leaves the barrel. If it is just the released energy focused into a beam, though, then it ought to behave just like a laser.

But, a laser is coherent, this energy is not.

It's not so much the actual reaction I'm thinking of, but the heat given off by the reaction. 'Course, maybe I'm separating the two when they are actually the same.

Referring to the hypothetical weapon, though, the documentation says that it is a plasma jet that leaves a 2cm aperture, but then dissipates immediately. I presume that would mean dispersion.

Bit of clarity; the lower tech version of this fusion gun is a plasma gun. The only change is the part where it says, "the plasma is contained in the ignition chamber until a fusion reaction takes place." Otherwise, it performs the same as the lower tech plasma gun - well, except for the increase in effectiveness due to higher tech level and being "fusion."

I'm picturing this, as I said earlier, as a small, hand-held fusion rocket held horizontally. As I understand it, if a craft landed on the Earth using a fusion drive, it would devastate everything around the landing zone. Well, at least, so goes my readings of SciFi - not the best source, I know, but the authors seem to know what they're talking about (Niven and Pournelle).

To be honest, it sounds to me more like the concept for this fictional weapon is perhaps slightly too fictional to try to apply actual physical principles. If you had the technology to project the plasma like that without it immediately turning back to a gas, then I suspect you could just as easily have the technology to shield all but the target from its effect.

Fusion of two protons is very slow. It's why the Sun burns over billions of years instead of exploding. Our current fusion experiments are based on the deuteron + triton reaction. This produces high energy neutrons and alpha particles. But there's no way to control the direction these neutrons come out. No way to focus it into a beam. It takes about a meter of shielding to block the neutrons, so a gun is out of the question. Unless, there is some fictional way to control the direction in which the reaction takes place.

To be honest, it sounds to me more like the concept for this fictional weapon is perhaps slightly too fictional to try to apply actual physical principles. If you had the technology to project the plasma like that without it immediately turning back to a gas, then I suspect you could just as easily have the technology to shield all but the target from its effect.

Hmm.

Well, what of a fusion drive for a space ship? Wouldn't that have the same problem?

Isn't a fusion drive throwing a reaction mass out of a nozzle providing a thrust? Wouldn't a weapon of this sort be simply a scaled-down version of this?

Fusion of two protons is very slow. It's why the Sun burns over billions of years instead of exploding. Our current fusion experiments are based on the deuteron + triton reaction. This produces high energy neutrons and alpha particles. But there's no way to control the direction these neutrons come out. No way to focus it into a beam. It takes about a meter of shielding to block the neutrons, so a gun is out of the question. Unless, there is some fictional way to control the direction in which the reaction takes place.

But, like I asked boneh3ad, isn't this sort of weapon simply a scaled down version of a fusion rocket motor? From what I can tell, NASA is working on this technology, so there must be a way to direct a reaction mass from a fusion reaction. Otherwise, there'd be no thrust.

We are a long way off having a fusion rocket working but Wikipedia has some info..

https://en.wikipedia.org/wiki/Fusion_rocket

An attractive possibility is to simply direct the exhaust of fusion product out the back of the rocket to provide thrust without the intermediate production of electricity. This would be easier with some confinement schemes (e.g. magnetic mirrors) than with others (e.g. tokamaks). It is also more attractive for "advanced fuels" (see aneutronic fusion). Helium-3 propulsion is a proposed method of spacecraft propulsion that uses the fusion of helium-3 atoms as a power source. Helium-3, an isotope of helium with two protons and one neutron, could be fused with deuterium in a reactor. The resulting energy release could be used to expel propellant out the back of the spacecraft . Helium-3 is proposed as a power source for spacecraft mainly because of its abundance on the moon. Currently, scientists estimate that there are 1 million tons of helium-3 present on the moon, mainly due to solar wind colliding with the moon's surface and depositing it, among other elements, into the soil.[1] Only 20% of the power produced by the D-T reaction could be used this way; the other 80% is released in the form of neutrons which, because they cannot be directed by magnetic fields or solid walls, would be very difficult to use for thrust.

Yes, I've seen the wiki articles. But, they would seem to support the idea that fusion can be used as a thrusting agent. Presumably, it's only a matter of technical progress before much - if not all - of that remaining 80% can be used for thrust.

But, the basic question is, wouldn't such a reaction, if contained to a beam, cause significant collateral damage due simply to the massive temperatures involved? Or, is the reaction just not that hot? And, if not that hot, would it even make a viable weapon, given successfully scaling the hurdles to weaponize the reaction?

Temperature doesn't cause damage. It just tells you which way energy spontaneously flows. It is energy that can cause damage.

You could say it's only a matter of technical progress before we solve every problem. That doesn't mean we have any idea how to do it. It's a vacuous statement.

nasu
Temperature doesn't cause damage. It just tells you which way energy spontaneously flows. It is energy that can cause damage.

You could say it's only a matter of technical progress before we solve every problem. That doesn't mean we have any idea how to do it. It's a vacuous statement.

Oh, I don't think that any amount of technical progress will give us Star Trek-like transporters. But, NASA is working on fusion drives. It's not a farfetched, pie in the sky concept with no hope of resolution.