# Comparing Nuclear vs Coal

1. May 5, 2011

### jschmidt

Hello,

I'm wondering if the brains here can help me point to some good sources for some particular information I'm looking for, and perhaps help me figure out the correct math for some problems I'm interested in solving.

I've seen a statement that, in general, ball-park figures, nuclear fission releases about a million times more energy than combustion. I believe that is at a discrete 'event' level, by which I mean, for nuclear fission, one event is the fissioning of a single nucleus (or a decay event, which is slightly different than fission, but also yields energy), while for combustion, I think a single event would be the binding of one atom of hydrogen or carbon, with one or two atoms of oxygen?

I know that the unit of energy usually used for discussing how much energy such atomic events release is the electronvolt, which according to Google, has the following equivalence relationship:

1 electron volt = 1.60217646 × 10^-19 joules

A Watt is one joule per second, so to produce 1 watt of power continuously, you need to release 1.60217646 × 10^19 electron volts in reactions, yes? I think I saw someone once say something along the lines of a combustion event releasing something like 3 electron volts, and nuclear fission releasing 1.something million eV? Can anyone provide me a good source, for citation, for the amounts of energy released by different combustion and nuclear reactions (e.g. a hydrogen combustion releases a slightly different amount of energy than a carbon combustion, which is slightly different than a nitrogen combustion, all of which will be happening in coal combustion, I believe, but all in the same order of magnitude, while a U-233 fission might release a bit more or less energy than a U-235 fission, which is different than a Pu-239 or Pu-240 fission, but they will all release about the same order of magnitude of energy, yes)?

Once I have the figures to work with, I want to do some math to figure out, in approximate values, how many combustion reactions happen per second to produce each watt of thermal power, vs how many fission and decay reactions happen per second in nuclear to produce each watt of power.

Can anyone provide any source for how much energy is released by various decay events which are common in nuclear fuel? I know that decay contributes a minority, but not negligible, amount of the power in a nuclear reactor. Obviously, there was enough decay heat to cause serious problems at the Fukushima-1 nuclear plant. . .

Bringing this back to Nuclear vs Coal, and the statement that nuclear fission releases about a million times more energy than combustion, in discussing nuclear power with people, and why it takes much less nuclear fuel than combustion fuel to produce a certain rate of energy, my understanding is that, ultimately, what it comes down to is this:

We want to get some amount of power out of an electric plant. Thermodynamic efficiencies of steam turbines give us basically, about 30-40% efficiency, resulting in needing to 'burn' (I use the term loosely here, to also include nuclear fuel in a critical reaction state) fuel at some rate, X. The rate of 'burn' for coal is about a million times faster than the burn rate for nuclear fuel, to produce the same rate of thermal heating, yes? This in turn means that, over time, you need about a million times more coal than nuclear fuel

Now, it's also my understanding that current reactor technology in use in the U.S. (I think the Canadian CANDU reactor is slightly more efficient, but not greatly so) is very inefficient with its fuel, extracting only about .5% of the energy from Natural Uranium (partly because we enrich the natural uranium up to Low Enriched Uranium (LEU), during which process, we create about 5 units of 'depleted uranium' for each unit of LEU which ends up in a reactor)? Is that figure correct? I've seen that figure (or something close to it) multiple places, but never with a citation. Can anyone provide me with a strong citation to use for reference for the correct figure?

Because of that inefficient use of nuclear fuel, the current nuclear to coal ratio (by mass) is more on the order of 1:5,000 than 1:1,000,000?

But, with next generation reactors, such as Thorium or Fast Breeder Reactors, we could get much, much closer to that 1:1,000,000 (due to technology limits, I wouldn't be surprised if we couldn't get exactly to 1:1,000,000, but I could live with 1:900,000 *grin*), correct?

2. May 5, 2011

### Staff: Mentor

From wikipedia: http://en.wikipedia.org/wiki/Nuclear_fission#Output

The remaining fuel can easily be reprocessed to remove the waste products, so that the remaining fuel can be used again. Can't provide any links at this time, I'm about to head home. I think you can find more info on wikipedia.

3. May 5, 2011

### jschmidt

Drakkith: Thanks, I do appreciate your effort in responding, but I was hoping for something a bit more. . . 'official' than Wikipedia. Can you provide any more academic or official sources for such figures?

4. May 5, 2011

### Staff: Mentor

http://www.new.ans.org/store/zoom/750027 [Broken] equates 1 UO2 fuel pellet (~5.3 gms) has about the same energy content as 1 tonne of coal. But then I've seen a bit more and a bit less.

For example - "A single uranium fuel pellet the size of a fingertip contains as much energy as 17,000 cubic feet of natural gas, 1,780 pounds of coal or 149 gallons of oil."
Ref: http://www.nei.org/howitworks/nuclearpowerplantfuel/

Each fission releases about 200 MeV, whereas a single chemical reaction releases a few eV. But then one has to convert that thermal energy into mechanical energy, and the mech eng into electrical energy. However, not all energy in the pellet is used. There is some left over when the fuel reaches its lifetime in the reactor, whereas much of the coal can be combusted.

On the other hand, a pellet (5.3 g) can provide an average power of 200 W for 25440 hrs to 38160 hrs or between 5 MWh to 7.6 MWh, or slightly more or less depending on how it is utilized. That's rougly 1 to 1.5 GWh/kg. One could find a heat value of coal in BTU/lbm or J/kg, and divide it into the specific energy of the nuclear fuel.

Nuclear plants have thermal efficiencies of about 32-37% (0.32-0.37) depending on the primary system and balance of plant. Some coal plants have similar efficiencies, but coal can go higher with superheat boiler to efficiencis in the low 40% range, or can be incorporated into coal gasification cycles using gas turbines with a steam cycle (so-called combined cycle plant) to get efficiencies in the 50 to 60% range.

Last edited by a moderator: May 5, 2017
5. May 5, 2011

### Andrew Mason

Let me put it this way. A 1000 MWe coal power plant (electrical output is 1000 MW) burns about 4 million tonnes of coal a year, or a little more than a 100 rail cars of coal per day. A 1000MWe Candu nuclear plant using natural U, uses about 175 tonnes of unenriched natural U per year. Natural U has about .7% U235 content.

AM

6. May 6, 2011

### seeyouaunty

Edit: Typo has been fixed

Last edited: May 6, 2011
7. May 6, 2011

### Staff: Mentor

Corrected the numbers.

8. May 6, 2011

### jschmidt

Thanks for the replies everyone.

I'd like to post a slightly off-topic, but ultimately getting at the same issue, followup question. So, I'm posting here instead of in a new thread.

I have read about fast breeder reactors, such as the Integral Fast Reactor, and I believe, theoretically, you can also create molten salt reactors which operate similarly, which among other things, have the ability to 'burn off' most nuclear waste (you will still end up with some waste at the end which can no longer be further fissioned).

I know that a significant proportion of that (perhaps all of it, not sure), comes from the fissioning of Pu-239/240 which was created from U-238 via neutron capture (I believe there is an intermediary stage of Neptunium or something, but for this question, the intermediate stage isn't too important).

My question is: are any of the fission fragments from U-235, Pu-239, or Pu-240, themselves fissile or fertile, which would then undergo a second stage of fissioning, releasing another large-ish amount of energy?

That is, in a fast breeder reactor, in addition to fissioning most of the U-238 which has transmuted to Pu-239/240, do you get some amount of additional 'free' fission of fragments which have undergone one fission already? If so, about how much additional energy could be expected to be contributed by such secondary fissions?

9. May 6, 2011

### Staff: Mentor

No.

U-233 is the lightest practical fissionable isotope.

Fission products do not fission, but could undergo spallation reactions, but that another requiring higher energy particle than fission neutrons.

One really needs to understand binding energy and nuclear theory to understand the answers to one's questions.

Start here -
http://hyperphysics.phy-astr.gsu.edu/Hbase/nucene/nucbin.html
http://hyperphysics.phy-astr.gsu.edu/Hbase/nucene/fission.html
http://hyperphysics.phy-astr.gsu.edu/Hbase/nucene/u235chn.html
http://hyperphysics.phy-astr.gsu.edu/Hbase/nucene/fisfrag.html

10. May 7, 2011

### jschmidt

@Astronuc,

First, I want to say thank you for attempting to answer my question and provide sources. However, the sources you provided do not answer my question.

You make the statement that "U-233 is the lightest practical fissionable isotope", which is probably true. However, the source you link to does not state that, nor provide any indication that that would, or should, be the case. Yes, it talks about binding energy, but the only thing it says is that isotopes heavier than iron can yield energy from fission, while isotopes lighter than iron can yield energy from fusion.

There are a LOT of isotopes that are heavier than iron, and further, according to that source, in the section on fission products, it indicates that lots of products are produced which are heavier than iron. In fact, it appears that ALL products of fission from Uranium or Plutonium are heavier than iron?

Also, while that source talks about thermal reactions, it does not really talk much about the physics of fast-spectrum reactions, which is not entirely responsive to my question about fast breeder reactors.

However, I do note that you used the adjective "practical" in your statement, and I suppose it's probably the case that while theoretically, you can fission other isotopes lighter than U-233, that it's difficult to do so, and will not happen in a reactor, even a fast reactor?

11. May 8, 2011

### Staff: Mentor

The hyperphysics site provides some basic and simple background with which one should be familiar. The site was not necessarily to provide the answers to one's questions.

What is most important is the difference between binding energy per nucleon of the reactants and products. Where there is little difference, it means that fusion or fission is unlikely, because the products and reactants are relatively stable.

Fast reactors are different animals from thermal reactors. Fast reactor fuel usually has greater enrichment to compensate for the lower fission cross-sections in the fast energy spectrum.

Even so, the fissile/fertile elements are the same, but in a fast spectrum, the fertile nuclides are nearly as likely to fission as fissile nuclides - in the fast energy range, although the fissile nuclides still have a higher cross-section (probablility) for fission in the resonance energy region.

See - http://www.nndc.bnl.gov/sigma/search.jsp

See attached - cross-sections (n,f) for Th232 (blue), U233(green), U235(red), U238 (black)
Pu239(blue), Pu240(green), Pu241(red)

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