physics, science, silly, thought experiment

The Overkill Oven

As I was lying in bed last night, I started wondering: “What if I had an oven that could heat its contents up to nuclear-fusion temperatures?” This is why I have trouble sleeping: my brain is very badly-wired. But still, that’s a perfect question for this blog. But as I was preparing to write the article, I got to thinking: Why limit myself to nuclear-fusion temperatures? Nuclear fusion only requires a few billion Kelvin. There are processes (particle-accelerator impacts and cosmic-ray collisions) that reach a trillion trillion kelvin!

Overkill Oven 450 Kelvin

Here’s my new oven. You’ll notice it has quite a few temperature knobs. That’s because, if I tried to fit 10^24 Kelvin all on one knob, that knob would have to be the size of a galaxy before the 100-Kelvin interval marks were far enough apart to see with the naked eye. The cool thing about the decimal number system, though, is that I only (“only”) need 24 knobs, each only marked with 10 intervals, to set temperatures hot enough to melt protons.

This new oven has a couple of interesting features. The first is the patented ceramic bowl-schist lining. Bowl-schist is an exotic metamorphic rock I imported from a parallel universe. Its heat conductivity is so low you could put a block of it next to a supernova and it’d be just fine. The second important feature is the power supply. Naturally, I can’t plug a fancy oven like this into a standard 240-Volt U.S. oven socket. Instead, the cable passes through a very narrow wormhole into the Handwavium Universe, which is stuck mid-big-bang, and therefore is absolutely flooded with energy. With all that set up, let’s cook! To celebrate my new oven, I think I’ll make a big beef roast, with some potatoes, peas, carrots, onions, and herbs and spices.

0.001 Kelvin

The trouble with the Oven of Doom is that the controls are a little difficult to get used to. But hey, I play Dwarf Fortress, so I’m no stranger to shockingly opaque controls. Still, starting out, I accidentally set the oven almost to zero Kelvin. I didn’t realize this until I saw the fur of oxygen and nitrogen ice growing all over my roast. Luckily, the Death Oven is also completely hermetically sealed during operation, to prevent operator death, so I didn’t freeze out all the air in the house. And defrosting was easy.

450 Kelvin

Overkill Oven 450 Kelvin

After that initial hiccup, my roast is coming along nicely. I’m making a brisket roast, so I should probably cook it long and low and slow, so it gets nice and tender. I just hope I don’t run out of patience before

1,000 Kelvin

Overkill Oven 1000 Kelvin

Well that could have gone better. In my defense, this oven has a lot of knobs, and if there’s anything resembling a knob or switch, I am compelled to fiddle with it. The roast was on fire for a few minutes, but once most of the fat burned off, it settled down. Now I’m left with an oven full of glowing orange soot and carbonized meat and vegetables. I can probably find some creature willing to eat it…

5,000 Kelvin

Overkill Oven 5000 Kelvin

The trouble with having a fancy high-power oven is that it’s really tempting to turn it up unnecessarily high in the hopes of getting your food finished as quick as possible. I think there might be something to all this “slow food” stuff I keep hearing about. Trying to cook my roast at 5,000 Kelvin has reduced it to a cloud of white-hot soot with a pale yellow vapor of sodium, potassium, and iron simmering over it. Still, at least I can be sure it’s safe for the people who insist on having their beef well-done.

10,000 Kelvin

Overkill Oven 10000 Kelvin

You know, I should probably close the shutter over that porthole… It’s getting awfully bright in there. I’m pretty sure the roast hasn’t escaped, but truth be told, when I look in there, all I see is this screaming blue-white fog of ionized carbon. On the plus side, if I hurry up and buy a second roast, I can cook it with the light from the first one.

100,000 Kelvin

Overkill Oven 1e5 K.png

I think I’m starting to understand now why the oven’s window is more of a peephole. It’s only three inches across, but already I shouldn’t be able to stand in front of it without my legs evaporating. Actually, I shouldn’t be able to have the peephole open without my house exploding in a horrendous fireball. The oven’s emitting more power from radiant heat alone than the Three Gorges Dam. But I can hold my hand in front of the porthole, no problem. I think I’m starting to see why the department store I bought it from was called BS & Sons…

5,000,000 Kelvin

Overkill Oven 5e6 K.png

I don’t think I have the right to keep calling this thing a roast, do I? It’s really just a soup of highly-ionized carbon, oxygen, iron (from the myoglobin in the meat, and from what used to be my nice new roasting pan), nitrogen, sulfur, and trace metals. On the plus side, I’ve got my own pet solar flare now!

10,000,000 Kelvin

It’s not all bad news, though. The oven is now self-powering. All those hydrogen atoms that used to be part of things like fats, proteins and starches have long since evaporated into a searing plasma. Now, though, they’re colliding fast enough that they’re starting to fuse. Not only am I getting extra energy from this, but I’m making homemade helium, too! Cooking’s fun!

100,000,000 Kelvin

Well, I’ve gone and overdone it again. I burned up all the helium I just made! Now it’s gone and fused to make more carbon vapor. I should probably call somebody about this. Frankly, at this point, I’m afraid to turn the oven off. I mean, since the thermal conductivity is pretty much zero, it’s never going to cool down. And if I open the door, I’m going to release as much energy as detonating 30 tons of TNT. I think I’ll just wall off the kitchen and pretend none of this ever happened…

500,000,000 Kelvin

I am now essentially cooking my roast with a continuous nuclear explosion. Also, I’m pretty sure that, even if I managed to cool it down, not even a physicist with a mass-spectrometer would be able to identify what the roast used to be. That’s partly because, of course, it’s been thoroughly vaporized. But also, the carbon nuclei have started fusing to form weird stuff like neon. If you find an organism that likes to eat neon, send it my way. I’ve got a roast for it.

1,500,000,000 Kelvin

My oven now contains as much energy as a half-kiloton nuclear explosion. The oxygen nuclei are fusing to form things like phosphorus, magnesium, and silicon. If the peephole wasn’t made of pure handwavium crystal, it would be emitting more power (briefly) than the Sun.

3,000,000,000 Kelvin

The good news is that I got my roasting pan back, and then some! All the light atoms have pretty much fused into heavier elements, which have fused to form Nickel-56. If I opened the door, I would be violently vaporized, but after the fallout cooled, the Nickel-56 would decay into Cobalt-56 and then Iron-56, and I’d be able to re-cast my roasting pan!

12,000,000,000 Kelvin

All that brilliant blue-white death-light that filled the oven is finally starting to fade. The bad news is that that’s only fading because the thermal radiation is so intense that it’s actually spontaneously turning into matter and antimatter, forming electron-positron pairs. The other bad news is that I’ve lost my roasting pan again: the energy of the particles in the oven has exceeded the binding energy per nucleon of iron, which is the tightest-bound atomic nucleus. In other words, my stupid iron atoms are starting to melt and shed protons and neutrons. Oh well. Maybe I’ll make some really exotic elements and get them named after me. And if IUPAC won’t name them after me, I’ll threaten to open my death-oven, which has long since become a weapon of mass destruction.

5,900,000,000,000 Kelvin

By now, the iron nuclei should have melted. All I need to do is heat them a little more to get that nice gooey brown crust. Except, I just checked, and I’m pretty sure the protons and neutrons are also melting. It’s just a very thin soup of quarks and un-named nonsense particles in there. Just like the Standard Model, amirite? Sorry. I shouldn’t be joking about particle physicists. Actually, speaking of particle physicists, could somebody call one of them? Because I’ve got three kilograms of pure quark-gluon plasma that they’ll probably want to study. You know, if they’re obscenely brave and not concerned about the 1.9 megatons of thermal energy packed into my oven. To be fair, if the door was gonna fail, I’m pretty sure it would have done it by now.

I’m really glad I spent the extra money on the Handwavium Universe power connector. In the 15 minutes it took me to obliterate my roast and put the entire Earth in jeopardy, the oven was drawing 8,830 terawatts. I’ll have to check the electrical panel, but I’m pretty sure 37 billion amps is above the rating of the breaker for the kitchen. Now all I need to do is call BS & Sons customer service and see if there’s a way to dump what’s left of my roast back into the Handwavium Universe. I don’t think I’ll be hurting anything: the HU is way hotter than my oven can get. Actually, the HU is so hot that the laws of physics themselves are above their melting point.

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The Physics of Dragonfire

Last year, I wrote a post about the physics of the plasma-temperature dragonfire from Dwarf Fortress. Today, because my frontal lobes are screwed on backwards, I wanna work out whether or not biology could produce a plume of 20,000-Kelvin plasma without stretching credibility too far. I have a hunch that the answer will be disappointing, but my hunches are usually wrong. Must be those faulty frontal lobes.

The first thing we need to work out is how much power we’re going to need to heat all that air. Let’s say dragonfire comes out of the dragon’s mouth at 50 meters per second (111 mph, about as fast as a sneeze or a weak tornado). As a rough approximation, let’s assume that a dragon’s mouth has a cross-sectional area of about 0.0600 square meters (about the area of a piece of ordinary printer paper). This is one of those nice situations where we can just multiply our two numbers together and get what we’re looking for: a flow rate of 3.120 cubic meters per second.

So here’s what we know so far: we’ve got a dragon breathing 3.120 cubic meters of air every second. That air has to be heated from 300 Kelvin (roughly room temperature) to 20,000 Kelvin. The specific heat capacity of air is close to 1,020 Joules per kilogram Kelvin over a pretty wide range of temperatures, so we’ll assume that holds even when the air turns to plasma. That means that every second, our dragon has to put out 79.96 million Joules, or 22.2 kilowatt-hours. But we’re not talking about hours here. We’re talking per second. That’s 79.96 megawatts, which is almost twice the power produced by the GE CF6-5 jet engines that power many airliners. That’s a lot of power.

But, much to my surprise, there are some fuels that can deliver that kind of power. Compressed hydrogen burning in pure oxygen could do it. Except I’m basing that assumption entirely on the power required. There’s a lot more physics involved than that. The highest temperature that a combustion reaction can reach, assuming no heat loss, is called the adiabatic flame temperature, and although this is an impressive 3,500 Kelvin for a well-mixed oxy-hydrogen flame, that’s nowhere near the 20,000 Kelvin we need. The only fuels with higher energy densities than hydrogen are things like plutonium and antimatter, and for once, I’m going to be restrained and try not to resort to antimatter if I don’t have to. Let’s see if there’s another way to do it.

In my previous post on dragonfire, I described Dwar Fortress’s dragon’s-breath as a medieval welding arc. So to hell with it–why not use an actual welding arc to heat the air? Well, it turns out that something like this already exists. It’s called an arcjet. Like VASIMR, it’s one of those electric-thruster technologies that has yet to get its day in the spotlight. But arcjets have found another purpose in life: allowing space agencies to test their reentry heat shields on the ground. Here’s a strangely satisfying video of one such arcjet heater being tested on an ordinary metal bolt:

That certainly looks like how my brain tells me dragonfire should look, but from a little research, it seems that the Johnson Space Center’s arcjet only puts out something like 2 megawatts, thirty-five times less than the 79 we need. According to these people, the arc in an arcjet thruster can reach the 20,000 Kelvin we need, but it seems pretty likely that the actual plume temperature is going to be a lot lower.

And besides, our dragon’s powerplant has to be (relatively) biology-friendly, since it has to be inside a living creature. The voltages and currents needed to run an arcjet would probably make our dragon drop dead or explode or both.

So, as much as I hate to do it (I’m kidding; I love to do this) I’ve gotta turn to antimatter.

Antimatter is the ultimate in fuel efficiency. Because almost all of the universe is made of matter (and nobody really knows why), if you release antimatter into the world, it’ll very quickly find its matching non-anti-particle and annihilate, producing gamma rays, neutrinos, and weird particles like kaons. The simplest case is when an electron meets a positron (its antiparticle). The result is (almost) always two gamma rays with an energy of 511 keV, meaning a wavelength of 2.4 picometers, which is right on the border between really high-energy X-rays and really low-energy gamma rays.

This presents yet another problem: hard x-rays and soft gamma rays are penetrating radiation. They pass through air about as well as bullets pass through water (which isn’t an amazing distance, I’ll admit, but I’m still not about to sit in a pool and let someone shoot at me). At 511 keV and ordinary atmospheric density, the mass attenuation coefficient (which tells you what fraction of the radiation in question gets absorbed after traveling a certain distance) is in the neighborhood of 0.013 per meter, which means a beam of 511 keV photons will get 1.3% weaker for every meter it travels.

Working out just what fraction of these photons need to be absorbed is a bit beyond me. If the radiation has to be 1,000 times weaker, it’ll have to pass through 1.6 meters of air. That sounds to me like it’d be enough to burn our dragon’s tongue right off. And indeed, if we run the equation a different way, we see that, after traveling through 30 centimeters (about a foot) of air, the gamma rays will still have 25% of their original strength. I’m trying very hard not to imagine what burning dragon teeth would smell like.

But there’s no reason our dragon has to be making its death-dealing plasma out of air. Water is the most common molecule in biology, so why not use that instead? A 511 keV photon can still travel over 10 centimeters in water, but that’s a heck of a lot better than the 150 centimeters we were looking at before.

Of course, we can add a dash of metal atoms to the mix to absorb more of the x-rays and protect our poor dragon from its own flame. The heaviest metal found in organisms in large quantities is iron, usually in the form of hemoglobin. So let’s just throw some hemoglobin in that water, handwave away how the dragon is producing so many positrons, and call this experiment a success.

Well, it’s not a total success, since what I just described is essentially a dragon vomiting a jet of blood and then turning that into scalding-hot plasma. No wonder everybody’s scared of dragons…

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Dragonfire

So, I’ve been playing a lot of Dwarf Fortress lately (which goes a long way to explain the lack of new posts). If you don’t know, Dwarf Fortress is a bizarre and ridiculously detailed fantasy game where you send a squad of dwarves into the wilderness to dig for gems and ore and try to stay alive as long as possible. That’s harder than you might think, since all dwarves are born alcoholics who must have booze to function properly, they’re surrounded by horrible creatures that want them dead, the environment is harsh, and they’re…well, they’re a little dim.

I love Dwarf Fortress. I love it because the creators have put such an insane level of love and detail into it. For example, how many other fantasy games do you know where they actually use the specific heat of copper when calculating whether or not your armor is melting?

But one detail in particular caught my eye: Dwarf Fortress’s temperature system. Temperatures in Dwarf Fortress are, to quote the Wiki, “stored as sixteen-bit unsigned integers,” which means temperatures between 0 and 65,535. The cool thing is that Dwarf Fortress doesn’t use some wimpy unspecified temperature scale. There is a direct correspondence between Dwarf Fortress temperatures (measured in degrees Urist. Don’t ask.) and real temperatures. To convert from Dwarf Fortress temperatures to Kelvins, for instance, just do a little simple math: [Temperature in Kelvins] = ([Temperature in degrees Urist] – 9508.33) * (5/9) . As it turns out, the Urist scale is just the Fahrenheit scale shifted downward by 9968 degrees (which, incidentally, means you can go several thousand degrees below aboslute zero, but that’s an issue for another time).

Better yet, Dwarf Fortress has DRAGONS! I love dragons, far more than any twenty-six-year-old adult male probably should. I turn into a hyperactive eight-year-old boy when I think about dragons. And Dwarf Fortress combines two of my great loves: dragons, and being unnecessarily specific about things. Here’s a typical encounter between a human swordsman in bronze armor (the @ symbol; the graphics take some getting used to) and an angry dragon (the D symbol).

Dragon Fight 1

Round 1. FIGHT!

Dragon Fight 2

The dragon breathes fire. The human’s chainmail pants are now filled with poo.

Dragon Fight 3

The human is engulfed in dragonfire and begins burning almost immediately.

Dragon Fight Aftermath

To nobody’s surprise, the dragon wins. I’d also like to note that this dragon is a real jerk: while his poor prey was burning to death, it swooped in and knocked the human’s teeth out…

Dragon fights in Dwarf Fortress end very quickly. That’s because, as the wiki tells us, dragonfire has a temperature of 50,000 degrees Urist. Which translates to a horrifying 22,495.372 Kelvins (22,222.222 ºC, 40,032 ºF). That’s higher than the boiling point of lead. It’s higher than the boiling point of iron. It’s higher than the boiling point of tungsten, for crying out loud. In fact, it’s sixteen thousand degrees hotter than tungsten’s boiling point. Dwarf Fortress dragons don’t breathe fire like those wimpy Hollywood dragons. They breathe jets of freakin’ plasma. Plasma hotter than the surface of the sun. Plasma almost as hot as a lightning bolt.

With this in mind, we can take a scientific (and somewhat gruesome) look at what happened to our unfortunate human swordsman just now.

From the images above, let’s say the dragon’s plasma jet reached a maximum length of 10 meters before the dragon stopped spitting. Just before it struck our adventurer, it was spread out in a rough cone 10 meters long and 5 meters wide at the base. It was broiling away at a temperature of 22,500 Kelvin. When you’re working with absurd temperatures like this, the radiated heat and light do as much or more damage than the plasma itself. This kind of thing (unfortunately) also happens in more mundane circumstances: when high-voltage, high-current equipment shorts out, it can produce an arc flash, an electric discharge that produces a dangerous explosion, a deadly flash, a flare of plasma, and a shower of molten metal.

Arc flashes are horrifying. They’re a serious source of danger to electrical engineers. They’re also not terribly funny. But they give us an idea of the effects of dragonfire.

At a temperature of 22,500 Kelvin, the front surface of the fireball would radiate about 0.285 terawatts of energy. The formula for a blackbody spectrum tells us that the fireball will be brightest at a wavelength of 128.79 nanometers, which is in the far ultraviolet. That’s more energetic than the ultraviolet light from germicidal lamps, which is already more than enough to cause burns and damage the eyes. So our unlucky swordsman would be looking at instant UV flash-burns.

Lucky for him, he probably won’t have long to worry about those burns. The fireball is radiating at 1.453e10 watts per square meter. If we assume the swordsman knew he was about to fight a dragon and therefore put on some sort of bizarre medieval bronze spacesuit and polished it to a mirror finish. He’s still dead meat: copper, one of the main components of bronze (the other is most often tin) is a terrible reflector at the wavelengths in question here, bottoming out at around 30%. That means our foolish knight is still going to be absorbing 70% of the radiant heat, which will (given a long enough exposure) raise its temperature to around 20,500 Kelvin, more than hot enough to flash-vaporize the outer layers.

But if we’re nice and pretend the knight was smart enough to have his bronze armor coated with something decently reflective at all wavelengths (like ye olde dwarven electropolished electroplated aluminum), he would only absorb about 5% of the incident radiation. Well, bad news, sir knight: your armor’s still heating up to 7,600 Kelvin, which is much hotter than the surface of the sun.

Of course, producing a plume of 22,000-degree plasma takes a lot of energy (I’ll resist the urge to nitpick the biology of that), and even if we put that aside, according to the game’s own internal logic, dragonfire doesn’t hang around very long. Each in-game tick (in adventure mode or arena mode) lasts one second, and our bronze swordsman was only exposed to these ridiculous temperatures and irradiances for around 10 ticks, or 10 seconds. If we consider the fact that the plume of dragonfire is going to lose a lot of energy to radiation and thermal expansion, our knight probably wouldn’t evaporate right away. But he will probably wish to his randomly-generated deity that he did.

Metals are good conductors of heat, and copper is one of the most conductive metals, heat-wise. Therefore, although our knight only got exposed to that horrifying draconic welding arc for a few seconds, his armor’s going to soak up a lethal amount of heat from that exposure. Arc flashes, lightning, and nuclear explosions can cause second- and third-degree burns from just a few seconds’ exposure, so our night is going to be blind and scorched, and then he’s going to poach like an egg inside his armor.

Don’t worry, though–he probably won’t feel it. Unless he has superhuman willpower (and is therefore able to hold his breath while the rest of his body is bursting into flames), he’s going to take a panicked gasp, and that’ll put an end to his battle very, very quickly.

The inhalation of superheated gas kills very rapidly. The inhalation of gas at thousands of degrees (meaning: the dragon’s plume and every cubic centimeter of air in contact with it) kills instantly. So our knight would probably lose consciousness either instantly, or within 15 seconds, which is how long it takes you to pass out when your heart and/or lungs quit working. And what would be left? A knight cooked Pittsburgh rare, wrapped in a blanket of broken bronze welding slag.

So, if you think you’ve outgrown being scared of dragons, imagine this: a scaly reptilian horror older than a sequoia, fixing you with its piercing gaze and then spewing a jet of gas as hot and bright as a welding arc. That’s good–I didn’t need to sleep tonight, anyway…

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