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For how long can a human sustain a temperature of 180 degrees Fahrenheit (82oC) without damage in a confined place?

For instance, suppose a person is sitting in a steam-filled room, without external air flow (but with enough oxygen) - how long could one resist the heat before permanent physical damage would occur?

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Short answer
Water of 180 oF (82 oC) causes immediate scalding (thermal burn wounds).

Background
The severity of a scald injury depends on the temperature to which the skin is exposed, and for how long. Residential water heaters warm up tap water typically to 120 oF (48 oC). At this temperature, the skin of adults requires an average of five minutes of exposure for a full thickness burn to occur. When the temperature of a hot liquid is increased to 140 oF (60 oC)) it takes only five seconds or less for a serious burn to occur. Coffee, tea, hot chocolate and other hot beverages are usually served at 160 to 180 oF (71 - 82 oC), resulting in almost instantaneous burns that will require surgery (American Burn Association).

How these numbers apply to steam I am not sure, but I think they will be comparable, given that steam is essentially made up of a dense mass of water droplets. Further, the amount of steam obviously matters. Consider these numbers: The temperature in a sauna typically ranges from 160-200 oF (71 - 93 oC) with a low level of humidity (ranging from 5 - 30%). Steam rooms provide moist heat from a water-filled generator pumping steam into the enclosed room. The temperature in a steam room typically ranges from 110-114 degrees Fahrenheit (43 - 46 oC) with a humidity level of 100%.

There is anecdotal evidence of the Russia-born Ivan Ivanitz Chabert (1792-1859), who supposedly entered an iron oven in Paris with a few trays of meat, and stayed there unscathed for 5 minutes at a temperature of 380 degrees F (193 oC). When he re-emerged from the oven the meat was cooked, while the only noticeable effect on him were profuse sweating and a dramatic increase in heart rate (from 98 to 168 bpm).

This experiment shows the remarkable capacity of the human body to reduce overheating by means of evaporative cooling (sweating). However, the effects of steam are far more devastating to the human body than dry heat. Not only does it carry much more energy than hot air, it also prevents perspiration by saturating the air with water vapor.

References
- American Burn Association Educator's Guide

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    $\begingroup$ AFAIK the main difference in steam's behavior comes from "latent heat", in which the energy absorbed by the liquid as it changes into gas is released when it changes back into a liquid. But that'll only happen above 100 deg C -> scienceline.ucsb.edu/getkey.php?key=1322 $\endgroup$
    – Gaurav
    Commented Jun 9, 2015 at 6:38
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Depends highly on the amount of steam in the room. Most if the heat energy does not come from the air, but from the steam that is condensing on your skin. I can tell from my own experience that I regularly spend 20-30 minutes in 80c sauna while pouring more water to the stove every few minutes without getting too uncomfortable (as long as I have water to drink). 100c sauna maybe 10-20 minutes and 120 c sauna 5-10 minutes. If you don't throw any water, you can stay in much longer. It is also worth to mention that people normally are NOT used to this kind of temperatures and will feel uncomfortable much earlier if they are not used to the heat.

I can take an example from the last Finnish Sauna Championships: a Russian guy died and a finnish guy burned 70% of his skin after spending only 6 minutes in 110c sauna. However, a few years back the same guy lasted for 16 minutes in the same 110c temperature without burns. Again, the difference was made by the humidity. In the final, half liters of water was poured every 30 seconds. Half liter per 30 seconds in a small sauna means the air is constantly over saturated with water and it is constantly condensing on the skin without a moment of relief.

Around 50 people die annually in the sauna in Finland. Most of them are either very old (70+), very drunk or/and have an existing disease. Normally you cannot get burns in the sauna as long as you are hydrated enough to sweat and your body is not completely messed up by alcohol. If you pass out in the sauna, your body does not function properly with managing the heat stress. Dehydration in people under the influence of alcohol heightens the risk of hypotension which impairs skin blood circulation.

Here one article claims A 30-minute stay in a sauna with a temperature of 80 degrees C increases rectal temperature by about 0.9 degrees C in adults. If the rise stays constant, a fatal level of hyperthermia (about 5 c increase in body temperature) is reached in around 2.5 hours. This estimation is probably based on a relatively dry sauna.

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