Energy density is essentially the amount of energy stored within a given fuel (doesn’t have to be fuel but for electricity production fuel is the energy storage method employed). The energy density of a fuel source also indicates the amount of waste produced per unit of energy output. Since these concepts are complimentary, it is worthwhile to compare several common sources of energy production on an energy density and waste volume basis.
*Consider This—By burning one kilogram of their respective fuels, coal can power a 100-watt light bulb for about four days, natural gas for about six days, and uranium in a light water reactor can power the light bulb for just over 140 years.
Fundamentals of Chemical and Fission Reactions
The first thing you need to know about these forms of energy production is that fuel sources are converted into heat energy, which is then translated into kinetic energy to spin a turbine that produces electricity. This is the same for nuclear, coal, natural gas, and oil. Where these energy production sources differ is in how they create the heat energy portion of the process.
Chemical Reactions
Coal, natural gas, and oil all utilize chemical reactions to produce heat. Chemical reactions are harnessing the power of the electrons orbiting the nucleus of an atom. Electrons only represent < 1% of the atomic mass of an atom, and therefore only represent less than 1% of the potential energy stored within the atom. It is based on this type of chemical reaction that coal, oil, and natural gas are converted from matter into heat energy – by only using less than 1% of the potential energy available.
Fission Reactions
Nuclear energy is a fission reaction that harnesses the potential energy stored within the nucleus of the atom, which represents over 99% of the potential energy stored . The difference between this and a chemical reaction is quite clear: chemical is using < 1% and fission is using > 99% of the mass of the atom to generate heat energy. Since Einstein proved to us via E = MC2 that matter and energy are interchangeable, it is easy to deduce that the reaction using more of an atom’s mass is going to generate more energy in the conversion process.
Energy Densities of Nuclear, Coal, Natural Gas, and Oil
Below is a table with a list of different fuel sources and their respective energy densities. Energy density can be calculated based on mass or on volume, depending on which measure makes the most sense for your situation. With energy production, density by mass is the appropriate measure since the mass of fuel, not the volume, is the base measure for a power plant’s fuel needs.
| Fuel Type | Energy Density (kWh/kg) | Number of Times Denser than Coal |
|---|---|---|
| Nuclear Fission (100% U-235) | 24,513,889 | 2,715,385 |
| Natural Uranium (99.3% U-238, 0.7% U-235) in a fast breeder reactor | 6,666,667 | 738,462 |
| Enriched Uranium (3.5% U-235) in a light water reactor | 960,000 | 106,338 |
| Natural Uranium (99.3% U-238, 0.7% U-235) in a light water reactor | 123,056 | 13,631 |
| LPG propane | 13.8 | 1.5 |
| LPG butane | 13.6 | 1.5 |
| Gasoline | 13.0 | 1.4 |
| Diesel fuel/Residential heating oil | 12.7 | 1.4 |
| Biodiesel oil | 11.7 | 1.3 |
| Anthracite Coal | 9.0 | 1.0 |
| Water at 100 m dam height | 0.0003 | N/A |
Energy Density of Chemical Reaction Fuels
The various chemical-reaction driven fuels are all similar in terms of energy density, ranging from coal at 9 kWh per kg to propane at 13.8 kWh per kg. That means we can power a 100-watt light bulb for about 90 hours (almost 4 days) with one kilogram (about 2.2 lbs) of coal, or up to almost 140 hours (almost 6 days) with one kilogram of natural gas.
Energy Density of Fission Reaction Fuels
On the other side of the spectrum are the fission reaction-based fuels that start with the least energy dense (natural Uranium [99.3% U-238, 0.7% U-235] in a light water reactor) at 123,056 kWh per kg and go up to fission of pure, 100% U-235, which yields 24,513,889 kWh per kg. This means that the typical nuclear fission reaction can power a 100-watt light bulb for 1,230,560 hours (just over 140 years) using one kilogram of natural uranium.
The least energy dense form of fission reaction is 13,631 times denser than coal. Contrast this with the fact that the densest form of fuel using a chemical reaction (propane) is only 1.5 times denser than coal. There are a variety of numbers floating around about how many times denser uranium is than coal, but all the estimates agree on one thing: it’s not even close. Suzy Hobbs at popatomic.org has made a great visual comparison of the energy density of coal and uranium. You will notice her research led to a uranium density figure of about 16,000 times denser than coal. This is close enough to the 13,361 calculated from my sources to still prove the point that fission reactions are enormously more powerful than chemical reactions.
How Energy Density Relates to Waste
Energy density also tells you how much fuel a plant requires to produce a given quantity of electricity. Since energy density is directly related to the amount of fuel required, it is also related to the amount of waste produced. The higher the energy density of a fuel, the less fuel a power plant will use. If less fuel is used, generally there is less waste.
Comparing Waste Outputs from Nuclear, Coal, Natural Gas, and Oil Power Plants
Chemical and fission reactions used to generate electricity produce two very different waste profiles. The chemical reaction-based sources all produce basically the same types of waste, just in different quantities. Coal, natural gas, and oil all produce emissions such as carbon dioxide, carbon monoxide, nitrogen oxides, particulates, and some others in relatively minute amounts such as mercury and even uranium (from burning coal). In addition to these emissions, burning coal also produces large volume of ash waste.
| Type of Plant | Amt of Electricity Produced (MWh) | Nuclear Used Fuel (tons) | Coal Ash (tons) | Sulfur Dioxide (tons) | Nitrogen Oxide (tons) | Carbon Dioxide (tons) | Small Particulates (tons) | Carbon Monoxide (tons) | Total Annual Waste (tons) | Waste per kWh (lbs) |
|---|---|---|---|---|---|---|---|---|---|---|
| Nuclear | 7,971,600 | 27 | 0 | 0 | 0 | 0 | 0 | 0 | 27 | 0.007 |
| Coal | 6,683,880 | 0 | 400,000 | 20,000 | 20,400 | 7,400,000 | 100 | 1,440 | 7,841,940 | 2,347 |
| Natural Gas | 998,640 | 0 | 0 | 2 | 157 | 199,472 | 12 | 68 | 199,711 | 400 |
| Petroleum (Oil) | 1,173,840 | 0 | 0 | 2,248 | 898 | 328,655 | 168 | 66 | 332,036 | 566 |
This table shows the amount of each type of waste produced by the four energy sources being compared based on the amount of energy produced by a 1,000 MW plant in one year. Understanding that not all power plants are 1,000 MW, nor are the various types of plants necessarily similar in size or duration of operation, these factors were built in to ensure an apples to apples comparison. The raw data for the coal waste was based on an annual operation of a 500 MW coal plant, so this analysis simply multiplied those waste figures by two. Natural gas and oil plants’ waste data was based on 1 billion BTU. This is equivalent to 292.875 MWh. I calculated the average output of a 1,000 MW rated natural gas and oil plant, with capacity factors of 11.4% and 13.4% respectively, to come up with the number of MWhs produced by each theoretical plant in one year (NG = 998,640, Oil = 1,173,840). These results were divided by 292.875 and then multiplied by the waste figures in the data. This calculation converts the raw data from the 1 billion BTU base to waste information for a 1,000 MW rated plant. Taking this further, I then broke down the waste amounts to pounds per kWh to give a true, levelized waste figure for each energy generation source using the same per unit base.
Renewables and Energy Density
A follow-up post discussing the concept of energy density and renewable energy sources is on the way – but probably not until after a post on energy conversion efficiency, since we will need a foundation in that topic before discussing renewables in this context.
Special Thanks to Suzanne Hobbs of PopAtomic Studios!
Suzy designed the Sometimes being dense is a virtue energy density poster. The original content can be found here.
19 Comments
Just a nitpick: natural uranium in a light water reactor won’t power anything, since H2O has too high an absorption cross section compared to D2O or graphite. I think what you meant to say was the amount of U-235 present in a kilogram of natural uranium would provide such and such amount of electricity. But to be fair, in your light water example, you should then subtract enrichment energy inputs, which are probably really small. Or you could say a heavy water or graphite moderated reactor and be done with it.
And, although not “used nuclear fuel”, depleted uranium tailings are a waste stream from nuclear fuel production, and there are sizeable amounts of it stored places.
In the end, nuclear will inevitably be the clear winner, and all of these wastes have the benefit of being stored rather than pumped into the atmosphere. But leaving out these factors give anti-nuclear folks an opportunity to criticize and probably exaggerate.
I’m not a nuclear engineer or scientist, so I can’t address your first issue regarding natural uranium in a LWR. All I can say is that I directly quoted the source I used, which is linked to in the paragraph above the table.
Regarding your point of other waste streams from nuclear – very valid, and I struggled with this when writing the post. I am aware of a number of other waste streams from nuclear but most of them are inert and more like standard waste that any type of manufacturing plant or power plant would have, therefore I chose not to include it because it is not the “waste” typically associated with nuclear energy, e.g. nuclear used fuel.
That said, if you click the “27″ tons of waste in the table it will take you to my source. I included the high level waste amounts. I suppose that the Medium level waste volumes could be included as well. That would take the figure from 27 tons to 90 tons, resulting in 0.023 lbs per kWh. I don’t think the low-level wastes have any place in this analysis because of the nature of the items that comprise it: paper, rags, tools, clothing, etc – this can be found at any of the plants mentioned in the post, and they also do not represent waste resulting from turning the fuel into electricity.
Good discussion, I appreciate your input.
Well to briefly explain about natural uranium: a reactor cannot be made critical with natural uranium and light water. Regular hydrogen-1 atoms have a tendency to soak up neutrons as well as slow them down, but hydrogen-2 or carbon-12 atoms are happier with their proton/neutron ratios. Across the globe you will find no LWR that doesn’t enrich its fuel. Instead you see two broad reactor types: those that run on natural uranium (and use heavy water or graphite as the moderator) and light water reactors, which use enriched fuel.
Anyway your WNA link is a very informative page and more people should read it, including me (I skimmed it). I’m not sure what classification depleted uranium gets, but WNA’s page on the topic mentions that about 50,000 tons are produced each year (http://www.world-nuclear.org/info/inf14.html). Dividing by the total worldwide nuclear capacity (372 GW according to IAEA) – and ignoring the fact that some reactors don’t contribute to this total (for simplicity’s sake) – would add about 135 tons of depleted uranium to the total tally.
So, 225 tons or 0.062 lbs per kWh. Still orders of magnitude lower than the others in the chart, of course.
“Einstein proved to us via E = MC2 that matter and energy are interchangeable, it is easy to deduce that the reaction using more of an atom’s mass is going to generate more energy in the conversion process.”
Thank you for this explanation! This was the missing link in my brain about comparing chemical and fission reactions- I love it when things make sense!
I came across a similar explanation in my research and thought that particular explanation of why fission is so much more powerful than chemical really brought it all together. You need a basic understanding of chemistry, but with that you are good to go! I’m glad the info was helpful.
@ Suzy,
If you have not seen this simple video I highly suggest it.
http://www.archive.org/details/isforAto1953
This was produced in 1953 and has a very detailed yet entertaining explanation for the power of Atomic Energy. Science in a fun way!!
@David,
Great find on the video—I thoroughly enjoyed it.
I don’t think E = mc^2 to explain why fission fuels are more energy-dense than chemical fuels.
The reason why is that both chemical and fission fuels are powered by the electromagnetic interaction (fusion fuels on the other hand are powered by the strong nuclear force). Electric fields have an inverse-squared dependence on distance, which is why fission fuels (whose relevant length scale is the size of a nucleus) are so much more powerful than chemical fuels (whose relevant length scale is the size of an atom).
@George.
Actuallty, that’s not quite true. The E=mc^2 relation is the fundamental difference between nuclear and coal power.
Coal power depends ona chemical reaction, and like all of chemistry is based on electromagnetic forces; only the atmoic composition of molecules changes, and energy is released in the change. Nuclear power is fundamentally nuclear, as the name suggests; it is dependent on the nuclear forces, and the energy that is released is from matter being converted to energy by E=mc^2.
@JD – great explanation, thank you for helping me to understand that. I did think it odd that they referenced natural uranium rather than enriched (3.5% U235), but I wasn’t confident enough in my knowledge to look at their information and say definitively that it didn’t seem correct. But, with this new understanding of the situation, I think that your hunch is probably right: “the amount of U235 present in a kg of natural uranium…” (not direct quote but used the punctuation anyway…creative license?)
I’m glad the WNA link was useful. I agree, I found it to be very informative and well explained so that a layman like myself can understand it.
“By burning one kilogram of their respective fuels, coal can power a 100-watt light bulb for about four days, natural gas for about six days, and uranium in a light water reactor can power the light bulb for just over 140 years.”
Excellent research. You may want to double-check a few things, though. Fossil and nuclear plants are on average about 30-35% thermally efficient. The conversion you made for the light bulb (MJ to kWh) assumes 100% efficiency for fossil and nuclear. You make the correct first step by converting MJ to kWh. One more step is needed, though, which is to convert from kWhs to Btus so we can account for heat rates.
We start with nuclear at 3,456,000 MJ/kg according to your source (3.5% enriched uranium), then divide by 3.6 MJ/kWh to convert to 960,000 kWh/kg which you already did. Then we multiply by 3,412 Btus/kWh to get 3,276 MMBtus/kg.
According to EIA, the thermal efficiencies of fossil and nuclear plants are about 10,000 Btus/kWh (aka heat rate). If they were 100% efficient, then their heat rates would be 3,412 Btus/kWh, but they’re hardly that efficient.
To calculate the kWh in a kg of uranium in order to account for thermal efficiencies, we divide 3,276 MMBtus/kg from above by 10,488 Btus/kWh (heat rate for nuclear in 2008) to get 327,600 kWh/kg and not 960,000 kWh/kg in your table.
Funny enough, the number you use for your quote above is for natural uranium but as JD pointed out above, the 3.5% enrichment figure is more appropriate. Nonetheless, instead of using 123,056 kWh/kg for natural uranium, the real number to use is 327,600 kWh/kg calculated in my previous paragraph.
So after going through all these calculations, the real number you should probably use for nuclear is 374 years to power a 100 watt bulb instead of 140 (funny how that worked out). If you understand these calculations and methodology and agree, then I recommend recalculating the numbers for fossil-fuels which will move lower.
One more thing, propane makes up a small fraction of natural gas. Natural gas is actually mostly made up of methane. Your calculations really don’t change though (other than recalculating for heat rates), because methane contains 55.6 MJ/kg compared to propane at 49.6 MJ/kg.
Those are just my thoughts, double-check me and let me know what you think.
MB – great comment. I completely agree with your assertion and re-calculations. I came across thermal efficiency (which I am hoping is the same as energy conversion efficiency because that’s the term for the concept I came across that describes the amount of heat energy converted to kinetic energy) near the end of my research. I didn’t think to go back and recalculate those numbers – mistake on my part.
I’m going to work through this stuff again taking into consideration the thermal efficiency.
I just found this doing research for a school project.
one question i have is what type of coal are you using for the waste chart? there are several grades of coal, the best of which is much cleaner(relativly)
anotherpoint is you are not counting the highly toxic parts of the coal emmisions, as well as the radioactives from coal.
I believe the waste amounts are for bituminous and subbituminous coal as they are the most commonly used in coal fired power plants.
I’m not sure what you mean that I’m “not counting the highly toxic parts of the coal emissions, as well as the radioactives from coal”. I agree that I did not include the radioactivity released because that is not a form of solid emission or waste. However, I disagree that I did not include the highly toxic parts of coal emissions because the things that meet that criteria are sulfur dioxide, coal ash, carbon monoxide, and carbon dioxide, all of which were included.
It seems like you have a small misprint. On the annual waste table, the final column should be waste per MWh, not kWh
IMHO, the energy density of a nuclear power plant is not limited by the energy content of the fuel, but by the energy density of the hot steam coming out of the reactor. This parameter defines, among other things, the efficiency and the size of the power plant.
I other words, a nuclear power plant is not 2.7 millions times smaller or cheaper than a coal power plant (even if the energy density of uranium is 2.7 M higher than coal). Fuel availability might not be the most important factor: we might just have enough uranium and domestic coal to cause ourselves more damages we really want to.
If we consider energy density alone, we have to accept solar power is 1.35 kW/m^2 and we only need a (relatively) small area in the desert for our energy needs.
No. Did you even bother to read the article?
The point is that nuclear technology requires five orders of magnitude less fuel and generates five orders of magnitude less “waste” (and used nuclear fuel can be recycled) than coal does.
Yeah, sure … if you happen to live in outer space. Besides, that’s still a very low energy density.
By the time the sunlight gets all the way down to the desert floor, it is greatly attenuated, and that is in the middle of the day. At night, there is no solar power.
The solar constant has almost nothing to do with the practical generation of electricity. If we take what is currently the largest solar energy generating facility in the world (SGES) as an example, the maximum energy density (based on nameplate capacity) that solar is able to produce is less than 55 watts per square meter — a factor of 25 less than the solar constant.
If we look at it’s actual performance, however, (based on data from 1998-2002), it produces less than 12 watts per square meter on average throughout the year.
To supply just the electricity that the United States consumes each year — which is a fraction of the amount of energy consumed by the US each year — the “small area in the desert” required for a solar plant would be about the size of the states of Maryland and Connecticut combined.
In other words, you would have to destroy about two-thirds of the entire Mojave Desert to build your solar collectors.
You have an awfully funny definition of “small.”
That, and you don’t necessarily have to have the massive cooling structures that are so commonly associated with nuclear power
Don’t knock all “massive cooling structures” at nuclear power plants. The one that is closest to my house has some very prime real estate next to it. It’s called a lake, which was built by the owner of the plant and which converted some relatively worthless land in the middle of nowhere into very expensive lake-front property for wealthy Washingtonians to use as a vacation home away from the city.
It also provides some very good fishing, I hear, since it is regularly stocked with stripped bass, which are not self sustaining in this region.
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