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In a duel, one of the fighter is a fire mage who is capable of producing heat surges in a wave-like pattern. There are flames coming along with it, but it's purely for aethestics and has no physical impact whatsoever (as far as I know it's really hard to ignite air itself anyway). That way, you can imagine your favorite comic/movie/anime/book arsonist, so it's cooler. Well, sort of.

For the sake and accuracy of this question, this wave raises the air temperature almost instantaneously by 1 000 °C (~1 800 °F), then goes back down to the point it was as the wave fades away. Note that this heat peak only affects gas's temperature, not solid materials like an human body or their clothes. It can however "burn" the air inside one's lung if aimed properly at the mouth or nose. Solid components keep the heat they received through this surge, meaning they continue to burn if they have started to.

Of course, the longer you are under such heat, the more roasted you will smell if you haven't started to burn to ashes already, due to how heat transfer works. But if an human wearing cotton clothes is subject to a single fireball for 1 second of exposure, how bad would really be the damage? Would their clothes/skin start to burn? If not, how long/how many fireballs would you need to make this happen?

As a bonus question, and in order to make it more realistically dangerous, what would be the outcome if the heat spike also affects solid materials on that split second?

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    $\begingroup$ I don't actually know if this question falls more in reality-check or science-based tag. The source of the heat need not to be explained scientifically, but I'd like some accuracy on the effects it would produce ^^". $\endgroup$
    – Tortliena
    Nov 22, 2020 at 15:22
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    $\begingroup$ I'd worry about the clothing being set on fire. It's difficult to fight while your clothing is burning. $\endgroup$
    – NomadMaker
    Nov 22, 2020 at 16:39
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    $\begingroup$ Enough heat transfer has to occur to cause damage / ignition to the target. Ignoring the mechanics of the heat transfer itself, the available energy to transfer depends on the temperature (which you say is 1000 C) and the thermal mass of the transfer medium (gas = very low). Therefore, little energy is transferred over the 1 second duration. $\endgroup$
    – GrumpyYoungMan
    Nov 22, 2020 at 16:39
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    $\begingroup$ I guess the more interesting part would be that the air would expand by a factor of ~3.5 in volume. Depending on what "almost instantaneously" means that might do for a minor shockwave. $\endgroup$
    – user29956
    Nov 23, 2020 at 1:19
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    $\begingroup$ The answers diverge a lot. A big question is how much of the heat will be transferred in that 1 second or so. Air is a notoriously poor conductor and I'm inclined to go with Ash's answer, but if you want to be sure, you may want to reformulate the question and ask it on the physics SE. $\endgroup$
    – AI0867
    Nov 23, 2020 at 17:40

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If I understand you correctly, the atmosphere is heated to 1,000℃. That's the combustion temperature of gasoline. And you're exposing, not just your target, but everything in the path of the wave for a full second. You don't say, but let's assume the wave engulfs the target.

It would be valuable to describe the wave in all three dimensions from the point of emission at the spell caster to the end of the spell, whether it's at the target or beyond. For now, I'm going to assume that the wave engulfs the target but, magically (hah) doesn't touch anything else other than air. Which would be impossible in a forest. I'm just sayin'.

People can pass their hands through combustion without significant harm (other than, perhaps, burnt hair). My brother and I, when we were young and stupid, used to play "flaming tennis balls." We'd each have a bucket of gasoline. We'd thrust our hand holding the tennis ball into the bucket, draw it out, ignite it with a lighter (while still in our hand), and then bat it back and forth somewhat like handball until it extinguished. Then repeat. (It really was fun... I don't recommend it... You're an idiot if you try it...) The hair on the back of our hands was permanently burned off as a result, but we were unharmed. But we never held the ball for a full second. Not even close.

A full second is a very long time.

  • The target would experience 3rd degree burns.

What causes a third-degree burn? In most cases, full thickness, third-degree burns are caused by the following: A scalding liquid, Skin that comes in contact with a hot object for an extended period of time, Flames from a fire, An electrical source, A chemical source. (Source, emphasis mine)

That reference to a scalding liquid is important. Scalding liquids are much cooler than the temperatures you're talking about (~100℃). It causes a 3rd degree burn because the liquid rests on the skin, exposing it to boiling temperatures for, well, a full second. Consequently, I might be overly optimistic to suggest only 3rd degree burns. In fact, I could imagine the target losing his/her eyelids.

  • Loose clothing (not leather or tightly woven fabrics) would ignite.

  • Depending on the time of year and meteorological conditions, the foliage around the target would ignite. Obviously short-cut green grass would be hard to ignite. However, tall weeds in the fall or at high summer in a hot zone are trivial to ignite. Frankly, if you did this at the right time of year in California at the temperatures and duration specified, you'd trivially have a conflagration on your hands. One hopes the spell caster was smart enough to do this upwind.

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    $\begingroup$ I agree overall, but the other reason that liquids scald more than gasses is that they are more thermally conductive. Liquids like water or oil and solids like iron or steel can transfer their heat to your skin very quickly, which raises the temperature of your skin beyond the point where they burn. Gasses (especially dry air) transfer heat more slowly, so it takes a much higher temperature to burn you quickly. $\endgroup$
    – Kevin
    Nov 23, 2020 at 18:03
  • $\begingroup$ @KevinWells Agreed, but my concern is what "much longer" means? Hold your finger over a candle for the second-tick of a clock and it will burn. Hold cotton cloth over a candle for the second-tick of a clock and it will ignite. I'm afraid too many people here think a second is a short period of time and what they perceive as a brief (e.g. one-second) period is actually quite a bit less than a tenth of a second or enjoys conditions that are not equal to even a candle (much less the OP's spell). $\endgroup$
    – JBH
    Nov 23, 2020 at 18:18
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    $\begingroup$ Yeah, that I completely agree with. A full second of contact with high heat is much longer than people might think. I've touched an oven rack for a tiny fraction of a second and ended up with 2nd degree burns, if I had held it for a full second I would likely be looking at third degree burns, and an oven rack is only 350-400 degrees Fahrenheit. Even with the lower conductivity the hot air would be a huge problem, especially if it reached their lungs $\endgroup$
    – Kevin
    Nov 23, 2020 at 18:21
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    $\begingroup$ I broadly agree with this answer, but I want to add to the comments that one can sit in a sauna at well over 100℃ for 15 minutes or more without ill effect. (Though it might be uncomfortable if you're not used to it.) I definitely wouldn't want to try a 1000℃ sauna even for a second though. $\endgroup$
    – N. Virgo
    Nov 24, 2020 at 11:05
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    $\begingroup$ @Nathaniel In my youth, I regularly enjoyed sauna and have been in them at 100+℃ temperatures. Only idiots sauna at those temperatures and I've known only a couple of people who could stand it for more than 5-10 minutes. It's nowhere near as common or as safe as your comment might suggest. Based on my personal experience, a 125℃ sauna is as hot as a human can go without incredible health risks even for just 5 minutes and 150℃ would drive anyone from the room in seconds. $\endgroup$
    – JBH
    Nov 24, 2020 at 16:58
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As a fire dancer who routinely generates large fireballs in very close proximity to my body, and has hit myself in the face with fire, spraying fuel and getting a massive fireball engulfing me several times. Nothing will happen from a single direct hit.

No lung damage. No burns. Nothing.

Were flame present hair would be singed. That's it.

You need to transfer that heat into the skin to start burns. From air that takes a lot longer than from metal or some other conductive medium. A dozen hits minimum to overwhelm. 50 to permanently injure.

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    $\begingroup$ A fitting profile picture. $\endgroup$
    – Drake P
    Nov 23, 2020 at 4:06
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    $\begingroup$ Regarding the lung damage: is the Air inside your lungs also heated up? Because the Lung itself is very, very sensible and relies on everything before it to "prepare" the air. I think 1000 degree air in the lungs (not you breathing in such hot air to be cooled on the way down, the air inside the lungs being that hot directly!) would do major damage and maybe lead to suffocation even $\endgroup$
    – Hobbamok
    Nov 23, 2020 at 9:53
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    $\begingroup$ Aaah, I remember the smell of singed hair. Used to shave my arms expressly to avoid it during tap-heavy routines. $\endgroup$
    – Joe Bloggs
    Nov 23, 2020 at 16:09
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    $\begingroup$ I have also used fire poi, but I don't think it is comparable to the description by the OP. When hitting yourself or even engulfing yourself in fire it won't last as long as a full second, and while kerosine does burn at around 1000C, it doesn't heat all of the air around you to that temperature. Being surrounded by 1000C air for a full second isn't something I would want to risk $\endgroup$
    – Kevin
    Nov 23, 2020 at 17:59
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    $\begingroup$ @DrakeP That's because it is Ash himself pictured there $\endgroup$
    – val - disappointed in SE
    Nov 23, 2020 at 19:54
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  • In an ordinary cooking stove burning natural gas the flame temperature is between 900 °C and 1,500 °C (1650 °F to 2700 °F). The flame of an ordinary stearin candle is in the same range.

    You can cross the flame with your finger in about 0.1 seconds without getting burned. (This allows you to extinguish a candle by pinching the wick.) But if you hold your finger in the flame for 0.5 seconds you will get burned.

    Take a small piece of cloth and place it in the flame of your gas stove: it will catch fire almost instantaneously.

  • The flame of an ordinary match is between 600 °C and 800 °C (1100 °F to 1500 °F). Take a small piece of cloth and try to ignite it with a match; you will notice that it takes about one second for it to catch fire.

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The amount heat you are talking about here in air, as discussed in other answers, just isn't enough to burn someone. However, if you are willing to interpret the "almost instantaneously" as an arbitrarily small unit of time, you could inflict harm with the pressure changes.

Using \begin{equation} PV = nRT \end{equation} where P is pressure, V is volume, n and R are constants and T is temperature in absolute Celsius, we can calculate the change in volume the air undergoes when the temperature shifts from, say room temperature (20 C) to 1000 degrees more. Rough math pins that at (1000+273)/(20+273) = ~4.34, so roughly a fourfold increase in volume.

That won't be enough to knock people off their feet or anything, but that difference in volume could cause barotrauma - https://en.wikipedia.org/wiki/Barotrauma which could be quite damaging in some parts of the body.

If you allow for it to impact solid matter for a split second, the biggest change will be the flash-boiling of your opponent. Theoretically, it could also shatter certain solid matter like stone or bone depending on the shape of the wave. If the middle of the object was heated while the outside rapid cooled, the difference in volume could crack or shatter the object. How effective that would be depends on the material and how the wave works (Does it heat the whole object or just a thin band? Is speed constant? etc)

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  • $\begingroup$ While I disagree with your conclusions about heat, I'm delighted that you brought the issue of air pressure to light. Cheers and +1. $\endgroup$
    – JBH
    Nov 23, 2020 at 19:30
  • $\begingroup$ Better yet, superheat the air in an enclosed space, or let's say, in a barrel with appropriately thin walls. Sudden pressure will burst the walls, which turn into shrapnel, which may hurt somebody. $\endgroup$
    – user2510
    Nov 24, 2020 at 9:28
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If it were water 160 F would create 3rd degree burns in 1 second. That is 70 F differential from skin temperature of 90 F. Air has about 1/25th the thermal conductivity of water. Using this approximation 1840 air transfer at the same rate. So 3rd degree burns wherever that air touches.

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    $\begingroup$ air also has 1/4 of the heat capacity of water as well as lower conductivity, also it looks like you missed a word in your penultimate sentence $\endgroup$
    – jk.
    Nov 23, 2020 at 11:31
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    $\begingroup$ Also, that heat capacity is probably by weight, you'll need to add another factor of 1000 or so to account for the density. $\endgroup$
    – AI0867
    Nov 23, 2020 at 17:36
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    $\begingroup$ @jk. That will be relevant depending on how the magic works. The OP says that it raises the air temperature almost instantly to 1000C for a given time and then immediately cool off, so if the magic maintains the temperature for the full second the heat capacity won't matter $\endgroup$
    – Kevin
    Nov 23, 2020 at 18:06

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