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Is it possible to fabricate a uranium or plutonium "hot cube" that could be used to keep a cup of coffee hot? Basically a piece of fissile material, shielded, and covered with a non-toxic material that could be dropped into a cup of coffee. Could it be made small enough to drop in a cup, and large enough not to be a choking hazard?

I see a lot of information about the total amount of energy stored in uranium, but I'm not sophisticated enough to understand how small a piece could be and still generate heat, and how much shielding, etc would be necessary. Pointers as to how to do those calculations appreciated.

For particulars, imagine a 12 ounce (355 ml) cup, maintaining a temperature equilibrium of 170 degrees F (77 degrees C).

disclaimers:

  • It should go without saying this is only a thought experiment, and that nobody should be dropping chunks of any hazardous materials in their beverages.
  • 77 degrees C was the first match for "how hot should coffee be?"; I have no opinion on this topic.
  • The various GPTs decline to answer, noting only that this is both dangerous and likely illegal, and suggest thermos flasks as a good way to maintain the temperature of a beverage.
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    $\begingroup$ There's some interesting info about RTG & plutonium-238 in space.stackexchange.com/q/50282/38535 "Some pacemakers used to have plutonium batteries". $\endgroup$
    – PM 2Ring
    Commented Oct 29 at 18:57
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    $\begingroup$ The YouTube genre seems to be "red hot metal ball versus"; see e g. m.youtube.com/watch?v=u94akpfMSkg $\endgroup$
    – rob
    Commented Oct 30 at 11:33
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    $\begingroup$ There are, in effect, real hot cubes just not using radiation. Heating liquids with hot stones works fine, and is surely closer to how an ice cube works? $\endgroup$ Commented Oct 30 at 17:33
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    $\begingroup$ check out PuCube smbc-comics.com/comic/pu $\endgroup$ Commented Oct 30 at 18:34
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    $\begingroup$ 77 degrees is a bit too hot for any liquid to be drinkable - anything over 40 degrees is going to be 'warm' or worse. Not that that makes much difference to the core question. $\endgroup$
    – MikeB
    Commented Oct 31 at 12:31

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Yes, it's possible, but as others have mentioned, such "hot cubes" would be rather dangerous. Perhaps a self-warming coffee cup is possible, but it's still not a great idea.

To be specific, let's assume we're using plutonium-238, which has a half-life of ~87.7 years. Plutonium-238 oxide pellet

Plutonium-238 oxide pellet glowing from its decay heat

It primarily decays by alpha emission, but there's a probability of ~$1.9×10^{-7}$% that a decay instead results in spontaneous fission, releasing neutrons and hazardous daughter isotopes. Pu-238 also emits some X-rays under 20 keV, and some gamma rays at 0.0436, 0.0996, and 0.152 MeV.

The density of plutonium-238 at room temperature is about 19.8 g/cm³. It generates about 0.57 watts per gram, or 11.3 watts per cm³, so you need a few cubic centimetres to keep your coffee hot, and that's not counting the shielding.

It's easy enough to shield against the alpha particles. A sheet of paper stops alphas. A smoke particle stops alphas - that's how smoke detectors work (although they use americium-241 as the alpha source).

The X-rays and gammas are a different story. You can shield against the energies mentioned using metal, but you need a couple of centimetres, and some gammas will always make it through the shielding material. The shielding attenuates the radiation exponentially: it works like half-life. So if a certain thickness of shielding allows half the gammas through, doubling the thickness allows 1/4 of the gammas through, and triple the thickness allows 1/8 of the gammas through.

Another problem is that a RTG pellet cannot be totally sealed, it needs to "breathe". Alpha particles are just high speed helium nuclei, and that helium needs to escape. So the shielding needs to be a little porous. Fortunately, helium atoms are very good at leaking through stuff, and helium can leak through pores that are too small for water or air molecules to pass through. Still, over its half-life, 238 g of Pu-238 emits 2 g of helium, which is ~11 litres at STP.

Finally, Pu-238 isn't exactly cheap. :) I suppose the price could drop if production increases, though. It's made from neptunium extracted from reactor waste, and that waste contains some really nasty fission daughter isotopes, which can only be handled remotely. And waste can also contain some fissile material which emits neutrons, which tends to make other stuff radioactive.

The world reserves of Pu-238 are currently rather low. Both NASA and the ESA would like more to be produced for use on deep space missions, and a few years ago it was announced that Pu-238 was to be ramped up, but we're still waiting. There's some discussion (with relevant linked articles) on this topic on the Space Exploration stack.


Despite all of these issues, Pu-238 was used in heart pacemakers half a century ago. From The Oak Ridge Associated Universities (ORAU) Museum of Radiation and Radioactivity:

Plutonium Powered Pacemaker (1974) Plutonium pacemaker

Pacemakers are used to stimulate a regular heartbeat when the body's natural electrical pacing system is irregular or not transmitting properly

At present (2003), there are between 50 and 100 people in the U.S. who have nuclear powered pacemakers [...] containing 2 to 4 curies of plutonium-238.
The unit's electronics are embedded in epoxy. The hard titanium case is designed to withstand any credible event including gunshots and cremation.

Dose rates at the surface of the pacemaker are approximately 5 to 15 mrem per hour from the emitted gamma rays and neutrons. The whole-body exposure is estimated to be approximately 0.1 rem per year to the patient and approximately 7.5 mrem per year to the patient's spouse.

Size: ca. 2.75" in diameter.

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    $\begingroup$ "The shielding attenuates the radiation according to a power law. So if a certain thickness of shielding allows half the gammas through, doubling the thickness allows 1/4 of the gammas through." Power law means constant power. Here, power increases with number of layers. $\endgroup$
    – Paul Kolk
    Commented Oct 30 at 11:06
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    $\begingroup$ @PaulKolk I'll rephrase that. $\endgroup$
    – PM 2Ring
    Commented Oct 30 at 11:08
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    $\begingroup$ “Perhaps a self-warming coffee cup is possible” - I also have one of those. They’re not cheap but they come with a charge pad that you set it on, and an internal battery powers a resistive coil in the bottom of the mug. $\endgroup$ Commented Oct 30 at 17:16
  • $\begingroup$ @controlgroup and you buy electricity from a nuclear plant or whats your point? $\endgroup$
    – DonQuiKong
    Commented Oct 30 at 18:49
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    $\begingroup$ No, just saying that it’s a thing that exists and that you can buy, which I thought would add context. $\endgroup$ Commented Oct 30 at 18:50
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These exist. They are not uranium; they are just small (~1 cm) metal blocks. They store a lot of heat, and so when heated in warm water for a while and then placed in coffee, they keep the coffee warm for a very long time. They also can be placed in the freezer and made to be reusable ice cubes. I own several. They're much more fun and much more compact than a bulky thermos flask.

Do not put uranium anywhere close to anything you plan to eat/eat off of, even if it's shielded. Uranium is not only radioactive but extremely toxic and any impurities on the outside or flaws in the shielding will mean you are ingesting raw uranium, which would probably be fatal given how toxic polonium can be.

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    $\begingroup$ Acute radiation poisoning from the 138-day half life is quite different from the more nuanced uranium exposure effects. $\endgroup$
    – Jon Custer
    Commented Oct 29 at 18:28
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    $\begingroup$ Sure, uranium & plutonium are heavy metals, so they have some chemical toxicity. But most of their toxicity is due to their radioactivity, not chemical toxicity, per se. Please see How toxic chemically is plutonium (Pu), neglecting the radioactive damage? $\endgroup$
    – PM 2Ring
    Commented Oct 29 at 20:28
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    $\begingroup$ Water has a higher specific heat capacity than most metals, so I'd expect even a 100 °C, 1 cm³ metal cube to heat 1 ml of water less than 100 °C or 100 ml less than 1 °C. Are you sure your cubes don't have uranium in them? $\endgroup$
    – Vaelus
    Commented Oct 30 at 2:30
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    $\begingroup$ Adding to what @Vaelus said, although many metals are 10x as dense as water, their heat capacity per gram is usually a tenth or less. Interestingly this seems to scale so that the lighter ones have higher heat capacity per gram than heaver ones. Wikipedia has a table where water has the highest listed volumetric heat capacity. $\endgroup$
    – user126527
    Commented Oct 30 at 10:57
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    $\begingroup$ If the cubes contained molten wax inside, they could store quite a lot of heat. This also works for other materials that may change phase at temperatures of interest. $\endgroup$
    – user4574
    Commented Oct 30 at 18:11
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A more practical variant, and (supposedly) more effective than controlgroup's suggestion, is an capsule of a substance who's melting temperature has been calibrated to be the same temperature as you like your coffee.

Examples: the original, a refinement.

Imagine some aliens who think 0C is a pleasant temperature for drinking mercury. They can easily heat it to 32C with their ray-guns, but that's too hot to drink! So they drop in a sealed capsule of water (which is solid, because they keep their rooms at -50C). The boiling mercury heats the water, and the whole vessel quickly reaches an equilibrium; it's very easy to calibrate the size of the capsule so that that equilibrium is at 0C because getting the water from -1C to 1C takes much more thermal energy than getting it from room-temp up to -1C. But the bonus is more close to what you're after: The vessel of mercury will stay at 0C until it's lost enough energy to freeze all the molten water, which we've already mentioned is a lot!

Of course there are pretty firm limits on how well this can really work (you're not adding any heat), and it sounds like the effect is really only noticeable if the vessel is insulated and lidded.

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    $\begingroup$ The refinement is interesting. One of the problems with putting a too-hot drink into a thermos is that stays too-hot for even longer. The use of PCM (phase change material) not only resolves that problem but also retains the absorbed energy to keep the drink hot for longer (i.e., longer than if you'd cooled the drink by leaving the mug unsealed: the PCM is to absorb/retain heat, not to provide insulation). $\endgroup$
    – Brian
    Commented Oct 30 at 17:30
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    $\begingroup$ "The boiling mercury heats the water ..." - I don't think mercury boils at 32°C :P $\endgroup$
    – marcelm
    Commented Oct 30 at 22:16
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    $\begingroup$ You're quite right; I edited other parts of the analogy, and didn't fix that part to match. Nothing relevant to this question, but a good catch! $\endgroup$ Commented Oct 30 at 23:36
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Use parafin wax inside of some sort of enclosure (small rubber/plastic balls, or cubes).

Parafin wax solidifies at like 65°C (which is about the correct temperature for a hot drink). Paraffin/EG CPCMs wax releases 156J/g as it solidifies.. The specific heat of water is 4.18J/g-°C.

So as an example, one gram of wax can heat 1g of water by 37°C as it solidifies.

Since the process is based on a phase change it has the advantage of keeping your drink at a very specific temperature. Which also avoids wasting heat by initially starting hotter and gradually cooling (which would have a higher rate of heat loss initially since heat loss is based on temperature difference from surroundings).

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    $\begingroup$ I wonder if you could find something that solidifies around 4°C and boils around 65°C, so that you could use for both hot and cold $\endgroup$
    – bracco23
    Commented Oct 31 at 10:53
  • $\begingroup$ -7°C is a bit cold, You might want something closer to fridge temperatures, otherwise you risk very watery liquids freezing solid and being undrinkable. The hot temperature is pretty good though. $\endgroup$
    – bracco23
    Commented Nov 1 at 17:53
  • $\begingroup$ Benzene seems interesting. According to Wikipedia it's 5°C freezing point and 80°C melting point. A bit high on the high side but not too much $\endgroup$
    – bracco23
    Commented Nov 1 at 17:57
  • $\begingroup$ @bracco23: I don't want benzene or bromine anywhere near any substance I'm going to ingest, sealed or not. $\endgroup$
    – Kevin
    Commented Nov 1 at 20:48
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...a piece of fissile material...

No. A small lump of the same kind of "fissile material" that is used to fuel nuclear power stations will just sit there for many thousands of years without giving off any appreciable heat. If you want it to make heat, then you'd have to create the conditions for a nuclear chain reaction, which would require (among other things) more of it than you could fit into a coffee cup.

Also, you would receive a lethal dose of radiation standing anywhere near a nuclear chain reaction for more than a few seconds.

On the other hand, you might be interested in reading about radioisotope thermal generators (RTGs). They operate on the decay heat from a highly radioactive source, and AFAIK, there is no theoretical minimum size. Some sources can generate a lot of heat, but at the same time, the ionizing radiation they produce is relatively low energy, such that they require much less shielding than a fission reactor.

On the gripping hand, there's what @controlgroup said: Ingesting radioactive contamination (especially from an alpha source) can be bad for your health. Don't take chances with that stuff!

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    $\begingroup$ "ingesting any amount..." demonstrably not true. We ingest radioactive atoms in almost anything we eat; we inhale radioactive C14 every time we breathe, etc. Further, some types of radiation (e.g. slow particles or long-ish wave photons) are completely harmless. $\endgroup$ Commented Oct 30 at 16:07
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    $\begingroup$ @CarlWitthoft, Yeah, OK, I was thinking in terms of "hot particles" shed by an an alpha source. You're right. "Any amount" covers a lot of orders of magnitude, and "extremely bad" is a purely subjective description. $\endgroup$ Commented Oct 30 at 16:46
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    $\begingroup$ @CarlWitthoft Or what about bananas? $\endgroup$
    – Michael
    Commented Oct 31 at 14:15
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    $\begingroup$ @Michael yes, we have no bananas today $\endgroup$ Commented Oct 31 at 14:24
  • $\begingroup$ @Michael, I would not want to eat a banana if I thought a hot particle might have landed on it. Otherwise, no problem. Eating bananas does not increase your body burden of $\vphantom{K}^{40}\text{K}$. Potassium is essential for life, but it also is prevalent in nature, so your body does not store any more of it than it needs. If you ingest excess potassium, you will excrete it soon afterward. And, the ratio of potassium isotopes in a banana is the same as anywhere else in nature. $\endgroup$ Commented Oct 31 at 16:31

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