Summary: A cubic inch sphere of oxygen plasma contains 10 kJ of energy. That makes a 12 cubic inch (~3 inch diameter) sphere hand grenade equivalent.
How I got there:
The original plan for the firepit (the scene that refuses to be written in chapter 19, in case you are just tuning in) was to have the Squad dig it. It occurred to me that we haven’t seen Marcy’s magic spheres as plasma, yet. We’ve seen liquid and solid water. A gas sphere might be useful if one is trying to breathe underwater, but seems generally useless (although steam explosions can be nasty). The plasma ball is my (sort-of) physics-based answer to the typical fireball spell.
Originally, the mana cost was based on size and element. I haven’t decided if the element is collected, summoned, or simply created. “collected” seems the cheapest option. “summoned” runs into the “summoned from where?” issue; it’s just collection with a longer reach. “created” runs into the E=mc2 issue, which at least sounds like it would require a lot of mana.
Oxygen is all over the place, so collecting some from the surrounding environment seems like an easy task (for magic). Generally speaking, one can just pull it out of the air. Should that not be possible, for whatever reason, almost every rock is something-oxide and the separation energy is far less the mc2.
The problem: I know next to nothing about plasma. It turns out that it is complicated. Who would have guessed? I like this part of the Wikipedia entry:
Although the underlying equations governing plasmas are relatively simple, plasma behaviour is extraordinarily varied and subtle
To some degree, I take that to mean I can make it do pretty much whatever I want and it will be a lot of work to prove me wrong. That’s acceptable.
The Quora post “what happens when you heat oxygen too much?” is much more practical. There’s even a “Practical Summary” section:
You do not get only a simple phase change; with increasing temperature O2 first thermally dissociates into atomic oxygen, and at still higher temperatures ionizes into a plasma. Along the way, excited species and strong chemical reactivity appear, and any contaminants or container materials will almost certainly undergo oxidation or vaporization, often producing further reactions well below full ionization temperatures.
The next question is the hard one: How much does one need to create a firepit and not blowup the entire farm?
Gas is annoying because everything involves pressure. I don’t see a problem with the initial plasma sphere having whatever pressure I want it to have. However, once it pops into existence, it’s at atmospheric pressure. If it’s created at higher pressure, it will immediately start expanding. For an AoE (area of effect) weapon, that’s a good thing.
Factibble: 100kPa is “standard atmospheric” pressure.
Let’s see if AI can be helpful now:
- What is the temperature of a cubic centimeter of oxygen plasma at 100kPa? Great. Yet another sort of plasma. The oxygen would be “room temperature” but the ionized electrons would be “much higher”. Not helpful.
- What is the minimum temperature and pressure… I already know the answer to this and it’s useless because temperature is not related to density (aka pressure). That’s why the gas clouds in space are so hot but space itself is not. The gas is moving very fast, but there is hardly any of it.
- At what temperature does oxygen become plasma at 1 atm?
- Significant Ionization: While trace ionization occurs at lower temperatures, significant thermal ionization generally becomes notable between 7,000 K and 10,000 K (approximately 6,727°C to 9,727°C).
- Molecular Dissociation: Before becoming a plasma, oxygen molecules ($O_2$) dissociate into individual atoms at roughly 3,000 K (approx. 2,727°C).
- Definition: Because “plasma” is defined by the degree of ionization and collective behavior rather than a fixed temperature, oxygen exists as a partially ionized plasma across a wide temperature range, becoming fully ionized only at much higher temperatures (millions of degrees).
I think that at the “mere” molecular dissociation point the heat alone is sufficient for massive destruction. Can we get joules?
How many joules of energy are in a cubic centimeter of 7000K oxygen at 1 atm? Heh. It’s too hot. It’s not in the data the AI has access to. Simple thermal expansion would be 0.101325 joules.
I need a benchmark: How many joules in a stick of dynamite? About 1 megajoule.
I’ve never seen dynamite, of any amount, in person (neither stable nor exploding). I’ve _heard_ of tree stumps being blown up with a stick of dynamite; it’s usually a cautionary trale. That leads me to think it’s somewhere more on the “firepit” side, but excessive.
I need a benchmark: How hot is an acetylene cutting torch? “The inner cone tip of the flame is the hottest part, generally cited at ~5,400°F to 6,000°F.”
While I use Fahrenheit daily, those numbers are too big. “Theoretical maximum temperatures can reach as high as 6,300°F (3,480°C) under ideal conditions.” Let’s call it 3000C, which is roughly the molecular dissociation point.
An oxygen plasma ball would be about three times as hot as an acetylene torch (which I have seen, although not used). That certainly seems hot enough. “any contaminants or container materials will almost certainly undergo oxidation or vaporization” certainly implies BOOM! I just need to know how much!! (which, of course, depends on pressure)
I wonder if energy goes up as the cube or the square of radius. Both make sense. The middle of the sphere isn’t reacting with anything; only the surface is. That says “square”. However, as the surface is eaten away via reactions, it moves inward (as the inside moves outward due to pressure differential). The amount of inwardness available is a function of volume. That says “cube”.
(4/3)pi(r^3) = 1, which means that (3/4pi)=r^3. 0.2387=r^3. r=0.62. I should probably do this in American units. A cubic inch of volume is ~5/8 inch radius. A cubic foot of volume is 5/8 foot radius, which is 7.5 inches. A 7.5 inch diameter (“a sphere the size of Luke’s dick” – I’m debating having Marcy say that), would be a 3.25 inch radius is 221 cubic inches. Huh? 12x12x12 is a cubic foot in inches. Oh, that’s the chilead; I was thinking gross. 1,728 cubic inches. Looking at a cubic foot shelf, that seems high, but the math works, so sobeit.
Anyway, assuming power scales by volume, a cubic foot is 1,728 times more than a cubic inch. That seems on the “blow up the farm” side of the scale.
I’m just going to wing it. A cubic foot will be 1.728 megajoules, about two sticks of dynamite. That means a cubic inch is: 1,728,000 / 1728 = 1 kilojoule. That will make for easy maths going forward.
I need a benchmark: What is 1 kj? “A fast-moving baseball thrown at high speed carries kinetic energy in the range of hundreds of joules; a particularly hard throw or a heavier object (like a small stone) moving at high velocity can approximate 1 kJ of kinetic energy upon impact.” That’s pretty lame. Joules are small.
This is helpful: “For context, 1 gram of TNT is defined as releasing 4,184 joules (4.184 kJ). Therefore, a 1 kJ event is about one-quarter the energy of 1 gram of TNT. A standard hand grenade (like an M67) contains about 0.1–0.2 kg of explosive, yielding roughly 100–200 kJ”
Slipping two digits: A cubic foot is 172.8 megajoules, which means a cubic inch is 100 kJ, which is a hand grenade equivalent. That seems too far the other way. The “Luke’s dick” sphere would be about 200 hand grenades. That’s definitely on the “blow up the farm” side.
Slip one digit and run the math the other way: A cubic foot is 17.28 megajoules, which means a cubic inch is 10 kJ, which means 12 cubic inches hand grenade equivalent. What’s the radius? 12(3/4pi)=r^3. 9/pi=r^3. 2.8658=r^3. 1.42025 = r. Say a 3 inch diameter, which is about the size of a hand grenade. That’s convenient. It does mean we’re not getting the “Luke’s dick” plasma sphere, though. That would be 2.20 mJ, which is two sticks of dynamite. Way too much for a firepit. I can live with that; it was a fleeting whimsy.
Marked Up 