# Does 60kg of fusion fuel produce as much energy as 400 kilotonnes of coal?

Several people, including Fusion for Energy have posted this infographic:

To meet the energy needs of a city of 1 million people one would need:

Either
250,000 tonnes of oil
Or
400,000 tonnes of coal
Or
60 kg of fusion fuel

Ignoring the fact that the info-graphic doesn't include for how long, What I'm asking here is about the rough equality of two energies?

I assume by fusion fuel they mean deuterium/tritium.

Is 60kg of fusion fuel energy equivalent to 400,000,000kg of coal?

• Heck, one ounce of coal could power a city of a million people ... for a few nanoseconds. – Hot Licks Oct 15 '17 at 14:31
• What does this graphic even mean? For how long ? So silly..... – Fattie Oct 15 '17 at 17:16
• The initial part of the infographic is indeed vague, however the question as asked here is about the rough equality of two energies, which is a very valid question. – Fizz Oct 15 '17 at 18:10
• @Fattie The exact value of time span is irrelevant. It's enough to assume it's same for all 3 cases. – Agent_L Oct 15 '17 at 21:34
• @Fattie Energy generation by nuclear fusion is well within the domain of "things we haven't done, but we understand the physics well enough to know that they can be done". A matter-antimatter reactor, on the other hand, requires antimatter fuel. Coal is not antimatter, so throwing 30 kg of coal into a matter-antimatter reactor gives you zero energy. – Wouter Oct 16 '17 at 11:42

Yes. See for example this table of energy densities.

Let's take 30 MJ/kg for coal (the middle of the range in the table), then 400,000 tonnes of coal gives 1.2*1016 Joule.

Assuming they're talking about deuterium-tritium fusion (which is the easiest form of nuclear fusion), we have 340,000,000 MJ/kg, and the 60 kg gives us 2.04*1016 Joule.

Of course, both the coal and the (as-of-yet hypothetical) fusion plant will have inefficiencies that prevent us from extracting 100% of this energy.

The 340,000,000 MJ/kg number can be calculated from the energy released in a single deuterium-tritium reaction, see for example here.

• I think you should make it clear that we have no idea how to use this energy, except in order to destroy the city. – ugoren Oct 15 '17 at 16:15
• The basic problem is that we need another form of energy to spark the fusion reaction, but it takes more energy to start the reaction than we get back from it. This works in a fusion bomb because we wrap it inside a fission bomb. It's possible that a bigger fusion plant would work, but we won't actually know until we try it. – Brythan Oct 15 '17 at 16:51
• @ugoren Here in Europe, we’re working towards using the energy to power cities instead of destroying them. – Paul D. Waite Oct 15 '17 at 17:07
• @Brythan That article sums it up nicely: ""For $20 billion in cash," [Steve Cowley, director of the Culham Centre for Fusion Energy] says, "I could build you a working reactor. It would be big, and maybe not very reliable, but 25 years ago we didn't even know if we'd be able to make fusion work. Now, the only question is whether we'll be able to make it affordable."" – Nat Oct 15 '17 at 17:08 • @Nat Because his working reactor is still very theoretical and hasn't been proven even on a small scale, I think he is just making things up. Theoretical usages of things aren't up to Skeptics standards until they become real. – BobTheAverage Oct 15 '17 at 17:45 TL;DR: In theory, yes. In practice, with currently built technology, no. ### Theory As already posted the fusion reaction produces more energy from the 60 kg of deuterium/tritium mix than burning 400,000,000 kg of coal does. This comparison is probably the basis for the claim. ### Practice The problem comes in two parts. First, to utilize that power, we have to convert it from a fusion reaction to something else, e.g. electricity. We have a basic plan for that. As we do with coal, we'll create heat and then use the heat to power a steam turbine. Given heat, the problem is basically the same. The greater problem is that a fusion reaction requires a lot of energy to start and maintain. In the sun, part of that energy comes in the form of heat that is a side effect of the fusion reactions already occurring. Another part of that energy comes from gravity. Because the sun is so huge, it pulls things together so much that they fuse. On the Earth, we couldn't do that. So instead, we use magnets to push things together and simulate what gravity does in the sun. Unfortunately, the Tokamak version is not that efficient. In fact, the most efficient it has ever been is 65% of the energy needed to keep it going. So we might burn 60 kg of fusion fuel, but it would take something like 250 kilotons of coal to do it. And that just gets us to parity. I.e. zero output. And that takes the 65% number as gospel. But some dispute it, arguing that the real efficiency was more like 2% or even 1%. It's possible that a larger version would be able to produce a net output once started. Popular Science quotes Steve Cowley, director of the Culham Centre for Fusion Energy: "For$20 billion in cash," he says, "I could build you a working reactor. It would be big, and maybe not very reliable, but 25 years ago we didn't even know if we'd be able to make fusion work. Now, the only question is whether we'll be able to make it affordable."

And of course, even if we built a \$22 billion fusion reactor, we don't know what the efficiency would be. We can sort of guess, but we don't actually know. That's part of the point behind building the prototype: to find out how it performs in reality rather than in theoretical models. Perhaps it will produce more energy than is put into it. Or perhaps we will discover that practical fusion is still at least 30 years away.

This depends entirely on what you mean by "energy equivalent." If you're talking about the amount of the fuel that would be needed to provide a given amount of electrical power with current technology, then the answer is no, they are not equivalent. Given the infographic's discussion of "powering a city," it is suggesting this interpretation, as this is the only meaningful interpretation for how a city might be powered.

On the other hand, if you're merely asking about how much energy we can get out of the fuel if we don't care about things like, say, destroying the city in which the reaction takes place or getting any useful electrical power from the reaction, the amount of energy is actually underestimated a bit for the fusion, though the order of magnitude is accurate. So, if you're more concerned with destroying a city than with powering it, fusion is a great choice.

### Fusion for Electrical Power

Theoretically speaking, fusion power production would be great. There's lots of fuel available, the energy density is greater than even nuclear fission, and it doesn't produce as much radioactive waste. Unfortunately, however, as of 2017, despite about 6-7 decades of research, no one has yet been able to build a nuclear fusion reactor that produces positive net energy.

The reason for this is that fusion reactions generally require very large amounts of input energy both to create the plasma stream and to contain it. Lots of various designs have been proposed and/or tried in order to increase the ratio of produced power to input power, but, to date, none have reached a ratio of 1 or more, thus, all have produced negative net energy. Obviously, this is not very helpful when attempting to power a city. The infographic is being quite misleading by leaving out this little detail.

Of course, this is not to suggest that further research will not eventually create a fusion reactor that produces positive net energy. It's entirely possible (and, IMO, likely) that we'll eventually have a working design. But we've currently been unable to demonstrate a working prototype, so it's not a matter of just building a bunch of fusion plants today.

### Fuel Specific Energy

The Specific Energy of a fuel is its ratio of stored energy to mass, without any regard to how much external energy may be required to actually do something productive with the fuel.

Wikipedia lists the specific energies for many fuels in megajoules (MJ) of energy per kilogram (kg) of fuel mass:

• Deuterium-Tritium: 340,000,000 MJ/kg
• Coal: 24-35 MJ/kg
• Diesel fuel: 48 MJ/kg
• Gasoline: 46.4 MJ/kg

Using these numbers, we find that 60 kg of Deuterium-Tritium fuel stores the same amount of potential energy as (340,000,000 / 48) * 60 = 425,000,000 kg = 425,000 metric tonnes of Diesel.

For coal (being generous and assuming 35 MJ/kg for the coal,) the calculation is (340,000,000 / 35) * 60 = approximately 580,000,000 kg = approximately 580,000 metric tons of coal.

For gasoline, it's (340,000,000 / 46.4) * 60 = approximately 440,000,000 kg or 440,000 metric tons of gasoline.

The massive specific energy of fusion fuels is what allows us to construct fusion-based bombs. In the case of a bomb controlling and containing the reaction aren't primary concerns, since the whole point is to destroy everything nearby anyway in most cases. However, we unfortunately can't ignore those things when building a power plant.

tl;dr The infographic is more or less correct about the ratio of specific energies, but is incorrect in suggesting that we could use those amounts of fuel to actually provide electrical power to an equivalent market with present-day technology.

• The only worthwhile answer here. Note however that this sentence: "The infographic is more or less correct about the ratio of specific energies, but is incorrect in suggesting that we could use those amounts of fuel to actually provide electrical power to an equivalent market with present-day technology." wildly understates the total incoherence, the completely blatant scam aspect, of the infographic in question. I'd phrase it more like.... – Fattie Oct 16 '17 at 9:47
• "The infographic uses the technical concept 'specific energy' (which is all-but utterly irrelevant to the issues at hand) as clickbait to make a political point." Note too that like all good propaganda, the person who typed it out lacks even basic, arithmetic-level skills in the topic at hand. ("Energy needs" is utterly irrelevant unless you give a time/rate.) Note too that as a political matter, I am entirely, 10000% on the side of "Fusion for Energy" political action group - I would literally give them money to support them! But the infographic is ... hilarious. Totally risible. – Fattie Oct 16 '17 at 9:54
• @Fattie oh relax mate, you're acting like my objective here is some big conspiracy. I'm just asking an honest question to get a reasonable answer. Which I did – mateos Oct 16 '17 at 10:49
• @Fattie I'm not sure why you're going on crusades in these comments... You're saying it's nonsense because the "energy needs" don't give a timeframe for their power. The thing is, they don't need to really specify the timeframe that this energy is used. Over the period of time you would need to burn 400,000 tonnes of coal, there is theoretically the same power in 60 kg of fusion fuel. You don't need a time/rate at all. They would use equivalent energy per hour/day/month/year regardless. – JMac Oct 16 '17 at 11:39
• @Fattie You're implying that this infographic is saying "We should get all our energy from fusion now!" when what it suggests to me is "We need to research into fusion more as a fuel source". – JMac Oct 16 '17 at 11:42

Depends on the efficiency of the nuclear reactor in question, as well as the efficiency of the method used to extract said energy. Since the only nuclear fusion reactor that produces more energy that it takes in that we currently have access to is the Sun, and the Earth as a whole only receives 1 x 10^-9 of the Sun's radiated energy according to a page hosted by the University of Illinois (http://extension.illinois.edu/world/energy.cfm), and since according to Wikipedia, the Sun is currently fusing 620 million tons of hydrogen in its core each second, that means that about the energy of about 562 kilograms of fuel reaches the Earth each second (https://en.wikipedia.org/wiki/Nuclear_fusion).

Since the Earth receives about 174 petawatts of Solar energy each second according to wikipedia (https://en.wikipedia.org/wiki/Solar_energy), we can work out that the energy per kilogram of the Sun's fuel is 3.058 x 10^8 J/kg. So, multiply that by 60 to get the energy in 60 kg of nuclear fuel. However, since we only receive one billionth of that energy, we're only getting .3058 J/kg. Multiply that by 60 kg, and you get 18.35 J. That's not very much; approximately enough to life a bag of 18 apples one meter, and that's without taking the inefficiencies involved in converting solar energy into something useful.

• Umm, one observation. Most of that "174 petawatts" of Our Main Fusion Powerplant are already used to power all the cities today. If you only used coal, no way you could afford to heat the air in the whole city to nice ~290 kelvins or to fuel the ecosystem via photosynthesis (food&oxygen for inhabitants). – kubanczyk Oct 15 '17 at 18:59
• @kubanczyk - Oh, but the Sun is just a big lump of burning coal. Any other explanation is just science fiction voodoo. – Hot Licks Oct 15 '17 at 19:03