# How long can you survive 1 million degrees?

I asked my Dad this once when I was about 14, and he said that no matter how short the amount of time you were exposed to such a great temperature, you would surely die. The conversation went something like:

Me:  What about a millisecond?
Me:  A nanosecond?
Me:  10^-247 seconds?


15 years later I still think that you could survive for some amount of time even though you'd surely get a few layers cooked. Thus, what's the longest period that you could theoretically withstand 1,000,000 degrees F heat and live to tell about it? Let's assume that you are wearing normal clothes (a t-shirt, jeans, sneakers, sunglasses, and a baseball cap), that the air around you is the only thing that is heated, and that after the time is up your friend sprays you with a fire extinguisher and the air magically returns to a nice 73 degrees F.

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"Well, he survived the plasma blast... but asphyxiated from the CO2 while Joey was putting out his clothes." –  Justin ᚅᚔᚈᚄᚒᚔ Mar 27 '13 at 17:27
By the way, there is no such thing as $10^{-247}$ seconds, as it would be much shorter than the Planck time. –  vsz Mar 27 '13 at 17:40
You should submit this to the "What If?" on XKCD. –  Joe Z. Mar 27 '13 at 20:21
@vsz, I don't believe there is a consensus that the Planck time is the shortest time interval. –  Mew Mar 27 '13 at 23:34
Does this apply to Chuck Norris? –  Clustermagnet Mar 28 '13 at 17:00

Let me mention that the air heated to 1 million degrees isn't a gas. It's probably plasma.

Just order-of-magnitude estimates. It takes seconds for your exterior skin temperature to drop or increase by 1 deg C if the body-air temperature difference is 10 deg C or so. If it were 1 million deg C, i.e. 100,000 times higher, the heating of the skin would be roughly 100,000 times faster but it seems likely to me that even microseconds would still be fine: that may be the time scale at which you would start to feel burns.

However, one would have to analyze the actual behavior of the "hot air", as you call it, namely the plasma. At a million of degrees, it is ionized and emits thermal X-rays. This is a very harmful, ionizing radiation. The plasma itself is ionized, too. These conditions probably lead to the creation of cancer more quickly than you get burned by the heat. So a more relevant calculation than heat answer would probably deal with the number of X-ray photons that you can "sort of non-lethally" absorb from the "air".

The thermal radiation is unavoidable and dominant. The first paragraph only discussed heat conduction. But the thermal radiation goes like $\sigma T^4$ so if the temperature is 160 times greater than the Sun's surface temperature, the radiation carries $(160)^4\sim 10^9$ times larger energy flux than if you're sitting next to the Sun's surface. And the energy fluxes near the Sun's surface are about $10^{5}$ times greater than on a sunny beach, so the thermal radiation is about $10^{14}$ times more intense than the solar radiation. So even if you only view this radiation as a non-carcinogenic heat, the safe time may be reduced to something like $10^{-14}$ seconds. When you realize that the energy counting heavily understates the harmful influence of the X-rays, you will get to a shorter timescale of safety, perhaps $10^{-20}$ seconds.

At any rate, I am confident that you will never get to something like $10^{-247}$ seconds. From a practical viewpoint, nothing happens at these extremely short time scales, they're really unphysical. You would probably not absorb a single thermal X-ray photon during such a ludicrously short timescale so such short exposures may be called "totally safe". They're also totally impossible, of course. You can never design a switch that would only "turn something on" for $10^{-247}$ seconds.

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Also, a lot would depend on the density of the super-hot plasma. I'm sure you could cook up a scenario where a sufficiently diffuse superhot plasma would be survivable for macroscopic times. –  Jerry Schirmer Mar 27 '13 at 15:08
+1 Nice answer... –  Killercam Mar 27 '13 at 15:12
Re: "the thermal radiation is about 10¹⁴ times more intense than the solar radiation. So even if you only view this radiation as a non-carcinogenic heat, the safe time may be reduced to something like 10⁻¹⁴ seconds": Doesn't this mean that the safe time on a sunny beach is something like 1 second? –  ruakh Mar 28 '13 at 0:39
Probably yes, it shows 1040 now... ;-) –  Luboš Motl Mar 29 '13 at 13:53
There's no way it's as short as $10^{-20}$ seconds, since any external effect would propagate only $3 \times 10^{-12}$ meters during that time (a good deal less than one atomic radius). –  Geoffrey Irving Apr 14 '13 at 0:58

The plasma you'd be in could be of extremely low density and pressure. It could be almost vacuum, just a few atoms, but with very high velocity. So it would have an extreme temperature, but the total thermal energy would be very low, and the gas would immediately cool down by contact with your skin. In such a case, you wouldn't be harmed by the temperature at all. The only factor would be how long could you survive in the vacuum. And since information about pressure change travels by the speed of sound, if the time were be sufficiently short, your body wouldn't actually notice he vacuum.

A similar phenomenon occurs in our solar system. Sun's corona has about one to three million kelvin, but since it's density is $10^{12}$ lower than Sun's photosphere, it radiates about one millionth of visible light compared to Sun's surface.

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Another similar phenomena occurs in out own atmosphere! "The highly diluted gas in this layer can reach 2,500 °C (4,530 °F) during the day. Even though the temperature is so high, one would not feel warm in the thermosphere, because it is so near vacuum that there is not enough contact with the few atoms of gas to transfer much heat."-en.wikipedia.org/wiki/Thermosphere –  raindrop Mar 28 '13 at 4:57

More than 5 minutes...

Any contact to a dense material at a million degrees would certainly be quite deadly as Lubos correctly pointed out. Try to estimate the thermal energy involved that would be absorbed if you "touched" a block of metal (i.e. high density plasma) at this temperature.

On the other hand adding on to Jerry's comment the time can be much longer if you only barely touch something that hot. It turns out that this is actually a nice medical application for plasmas: you can burn away the bacteria on your skin but not too much else happens: Plasma jet in Journal of Physics D, Plasma jet on geek.com.

The plasma is created from a 10kV voltage source, so the temperature of these gas molecules will certainly be quite high (but maybe not a million). On the other hand the density is so small compared to normal surrounding air that not much damage to the skin happens. It took five minutes to "burn" through 17 layers of bacteria, so it might take a long time until serious damage to your skin happens.

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That's kinda what I was wondering about. Here you have individual nuclei peppering your skin at enormous velocities. Wouldn't they easily penetrate and do damage at depth? –  Mike Dunlavey Mar 27 '13 at 20:50
@MikeDunlavey: that entirely depends on what the particles are. Different types of radiation penetrate the skin differently--some stuff will bounce off, some will be harmful, and some will pass through without interacting at all. And the penetration always depends on the energy regime. Wikipedia has a lot of discussion about this. –  Jerry Schirmer Mar 27 '13 at 20:58
some ion rays are even used for cancer therapy, because they actually do penetrate the skin, and transfer most of the energy only at a certain, well defined depth into the body! So yes, it entirely depends on the particles. (unlike most photons that transfer most energy to the skin) - correct me if i'm wrong, i'm only a computer scientist happening to live near a research institute that researches this kind of therapy. –  kutschkem Mar 28 '13 at 9:53
@kutschkem That form of radiation therapy uses ions, which get slower while traveling throu the body and release most of their energy only just before they get stuck at some depth. That's about the only kind of radiation problem that guy will not have, I guess :) –  Volker Siegel May 7 at 11:05

I'm with Luboš on that the radiation will kill you, but only if the pressure doesn't kill you first. 1,000,000 degrees Fahrenheit is about 500,000 degrees Celsius, so in proportions of absolute temperatures (Kelvin), that would be about 2,000 times room temperature. In a sealed room, that means that you're suddenly under 2,000 times as much air pressure. Since normal atmospheric pressure is about $10 \text{ N/cm}^2$, you'd be experiencing a sudden $20,000 \text{ N/cm}^2$. That's roughly equivalent to a car sitting on every square centimeter of your body. I don't know how quickly the body can implode, but I wouldn't expect you to last long.

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or, conversely, if you keep pressure constant, at such temperatures you have very little air around you, probably decreasing the thermal transfer capability of the air-skin interface layer. –  Javier Mar 27 '13 at 17:43
true, so I guess you would just suffocate. –  krs013 Jan 7 at 19:21

More heuristics:

1 million Kelvin corresponds to 86 electron volt, which is more, by a factor of 10, than any bond-dissociation energy for reasonable molecules.

The mean speed of the oxygen atoms coming for you should be in the range of 35000 m/s, i.e. 100 times the speed of sound (for the calculation, I plugged in "2*Sqrt[2*(Boltzmann constant)*10^6 (Kelvin) / (Pi 16 * proton mass)]" on WolframAlpha).

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## protected by Qmechanic♦Apr 7 '13 at 9:24

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