Energy production that converts Hydrogen to Iron?

Suppose a craft derived its energy from fusion— converting Hydrogen into Iron…

If it started with a kilo of Hydrogen, how much mass of Iron would it have at the end and how much energy would be extracted?

The number of nucleons won't change in the process. You can look how many your target iron isotope has, that's how many hydrogen atoms you need per iron atom (if you start with normal hydrogen, it's less with deuterium or tritium). You can look up the masses of hydrogen and iron and compare.

Maybe I shouldn't mess with this but am going to do it anyway.

It has to do with the "relative isotopic mass." First simplify things by assuming that all your hydrogens and irons are purely of the most common isotopes. Take the relative isotopic mass of your hydrogen and multiply by the number of nucleons in your iron. This number will be higher than the relative isotopic mass of your iron. The difference is the amount of mass converted to energy during fusion. Use E=mc^2 to figure out how much energy.

Devin-M said:

Suppose a craft derived its energy from fusion— converting Hydrogen into Iron…

Not to rain on your parade, but while this fusion engine would not facially violate any laws of physics, as a practical matter, it is basically an engineering impossibility.

In the real world, iron is created through nuclear fusion processes that start with hydrogen in a multiple step process interrupted by supernovas at intermediate steps. Early stars converted hydrogen to intermediate sized elements, went supernova, and then had some of those intermediate sized elements that the supernova spits out end up in a new star where they are fused in the second star in the fusion sequence, and so on, until eventually Nth generation star in the sequence fuses medium sized elements into iron.

If the craft likewise used a multiple step process, the energy generated in the intermediate steps in a way that attempted to hold onto the fusion products produced would blow the craft apart before it could get to the next steps.

If the craft tried to do it in one step, the problem is that it is virtually impossible to get dozens of hydrogen atoms to all fuse and organize themselves into an iron nucleus in the same place at the same time. It is hard enough to get two component atoms in once place at the same time in the right conditions to fuse.

This said, most of the energy gains from nuclear fusion happen at the beginning of the nuclear fusion chain ending with iron, and not at the end of it, as illustrated by this chart:


The initial leap from deuterium to helium-4 produces about 80% of the energy per nucleon return of the entire chain from deuterium to iron, and is eminently possible from an engineering perspective.

ohwilleke said:

In the real world, iron is created through nuclear fusion processes that start with hydrogen in a multiple step process interrupted by supernovas at intermediate steps. Early stars converted hydrogen to intermediate sized elements, went supernova, and then had some of those intermediate sized elements that the supernova spits out end up in a new star where they are fused in the second star in the fusion sequence, and so on, until eventually Nth generation star in the sequence fuses medium sized elements into iron.

While I agree that what the OP proposed is an engineering impossibility, the above paragraph is not correct. A star more than about 20 solar masses can fuse hydrogen all the way to iron in a single star. It's believed that the fusion processes take place in shells, like this Wikipedia diagram:

ohwilleke said:

... basically an engineering impossibility.

If the craft likewise used a multiple step process, the energy generated in the intermediate steps in a way that attempted to hold onto the fusion products produced would blow the craft apart before it could get to the next steps.

I think this is overly-cynical and underly-supported.

1. If we grant the premise of being able to artificially create H>Fe Fusion in the first place, then it sort of goes without saying that part of that solution is to contain the products so it doesn't blow up.
2. That "energy generated" you are speaking of is not a liability; it is the desired goal. It is the purpose of the device in the first place, and we likewise assume that it is harvested and directed toward propulsion.

I mean, your statement, spoken in the 1920s could just as easily have been (and surely was) said about controllable nuclear fission - that is, until we found a way to not have it blow up, and a way to safely harvest the energy it produced.

And in 1959 they started putting them in ships.

{ Joke ...}
Handwavium:
"We use 'Red Mercury' as a catalyst-- More stable than Dilithium..."
/

DaveC426913 said:

I mean, your statement, spoken in the 1920s could just as easily have been (and surely was) said about controllable nuclear fission

What?

Nuclear fission was not discovered until 1938. Heck, the neutron wasn't discovered until 1932. Where are you getting this?

Vanadium 50 said:

What?

Nuclear fission was not discovered until 1938. Heck, the neutron wasn't discovered until 1932. Where are you getting this?

(Okay, so change '20s to '30s.**)

Like the OP's H>Iron fusion, it might have been effectively science fiction at the time (if not for the war).

My point being simply that "X can't work because we'll never be able control or contain it" is a very weak argument.

** Wow. I knew the atom bomb timeline was short but I did not know it went from unknown to employed in six years. I'd assumed it had been theorized well before being discovered in the lab.

ohwilleke said:

The initial leap from deuterium to helium-4 produces about 80% of the energy per nucleon return of the entire chain from deuterium to iron, and is eminently possible from an engineering perspective.

Proton-proton fusion has such a low cross section that we still haven't measured it (in the lab, we see it in the Sun). Fusion reactors on Earth use deuterium and tritium, reducing the difference to ~3.5 MeV per nucleon.

This thread went in a bad direction, and I got yelled at a little for responding to some of what is no longer here.

The word "spacecraft" in the title is unnecessary, and probably unhelpful. I will replace it with "extremely advanced technology".

I don't know how seriously to take this, now that we know it is about such an extremely advanced technology but: d-d fusion goes from a binding of 1.1 MeV perr nucleon to about 2 (3He + n or t + p) or 7 (the rarer 4He process). So there is some reason to go past 3He or tritium.

But since we are postulating a technology that can easily fuse all the way to iron, one needs to ask "Why?" By the time you get to, say, oxygen, you have already extracted 90% of the energy you are ever going to get. Further, you need 4 extra neutrons to get to Fe-56/ Where do they come from?

Such an advanced technology one needs to assume is starting to look like magic.

mfb said:

Proton-proton fusion has such a low cross section that we still haven't measured it (in the lab, we see it in the Sun). Fusion reactors on Earth use deuterium and tritium, reducing the difference to ~3.5 MeV per nucleon.

I don't disagree which is why I referenced starting with deuterium rather than hydrogen-1.

Getting a bit further into answering the original question.

Nuclear fusion generates 580,000,000 MJ of energy from a kilogram of heavy hydrogen (i.e. Hydrogen-2 and Hydrogen-3) by fusing it into Helium. In contrast, hydrogen fuel cell produces 142 MJ/kg. Natural gas (i.e. basically methane) produces 54 MJ/kg and gasoline produces 46 MJ/kg.

MJ = megajoule and kg = kilogram and 1 Joule [J] = 1 Watt-second [Ws] = 1 V A s (volt-ampere-second)= 1 N m (Newton meter) = 1 kg m²s⁻² (kilogram-meter squared per second squared).

In theory, if it went from heavy hydrogen straight to iron, it would generate 725,000,000 MJ of energy from a kilogram of heavy hydrogen (i.e. 7.25 * 10⁸ MJ).

The energy that would be created by converting 1 kg of matter directly to pure energy (via the E=mc² conversion) would be 89,875,517,878.0128 MJ (i.e. roughly 9 * 10¹⁰.

So, the energy produced in the fusion reaction would be equivalent to a mass almost exactly 8 grams converted to pure energy.

The mass of the end product of converting 1 kg of heavy hydrogen to iron in nuclear fusion would be 992 grams of iron.

These calculations have a roughly 1% uncertainty.

ohwilleke said:

Not to rain on your parade, but while this fusion engine would not facially violate any laws of physics, as a practical matter, it is basically an engineering impossibility.

In the real world, iron is created through nuclear fusion processes that start with hydrogen in a multiple step process interrupted by supernovas at intermediate steps. Early stars converted hydrogen to intermediate sized elements, went supernova, and then had some of those intermediate sized elements that the supernova spits out end up in a new star where they are fused in the second star in the fusion sequence, and so on, until eventually Nth generation star in the sequence fuses medium sized elements into iron.

If the craft likewise used a multiple step process, the energy generated in the intermediate steps in a way that attempted to hold onto the fusion products produced would blow the craft apart before it could get to the next steps.

If the craft tried to do it in one step, the problem is that it is virtually impossible to get dozens of hydrogen atoms to all fuse and organize themselves into an iron nucleus in the same place at the same time. It is hard enough to get two component atoms in once place at the same time in the right conditions to fuse.

Yet the reason any metals exist (other than some Li) is that three alpha particles get in the same place within 10^-16 s.
The moment you are as far as d, getting to Ni-56 is "trivial". Simply compress the matter to sufficient temperature and density, and the next reactions will go arbitrarily fast, at sufficient temperature.
It is fusing p that is problematic, even at arbitrarily high temperature!

Note that simple rearrangement of nucleons to Ni-56 gives you Ni-56, not Fe-56! There is some energy that won´t be released quickly, and that is slowly released in positron emission of Ni-56 (6 days) and then Co-56 (77 days).

What DO you get if you heat protium quickly?
Provided you have some C, N or O, you first get some cold CNO cycle. But it is the production of neutrons that is the rate controlling step of cold CNO cycle. The speed of cCNO-I is limited by the 10 minute halflife of N-13, that is not sped up by heating.

Heating can lead to hot CNO cycle by adding another proton to N-13 and producing O-14... halflife still 70 s. And hCNO-I is actually controlled by the halflife of O-15 at 122 s. Further heating is no help: F-16 and F-15 are unbound. Converting a proton to neutron will take minutes regardless of temperature.

So... If you rapidly heat some deuterium, so that all of it is converted into Ni-56 before it has time to expand, how much energy will be converted to mechanic velocity of the propagating Hugoniot shockwave? What are the detonation velocities of more common substances like He-4, C-12 or O-16?