Some years ago there was a claim that in Antarctica, you couldn’t dress warm enough to stay outdoors (-60C) indefinitely because merely breathing would slowly cool you down. I showed that this was not true:
Assume absolutely dry air is inhaled at ambient temp, and that air is then exhaled at body temperature (37C) and 100% relative humidity. Heat is lost from the body due to the warming and humidification of that air.
Assume typical parameters for an adult male at rest: 16 breaths per minute, 1/2-liter tidal volume.
Assume ambient temp of -60C. I calculated heat loss via respiration to be 29 watts. For reference, heat loss (via respiration) when ambient temp is 0C is 19.2 watts, so the heat loss at -60 is only an additional ten watts on top of that. (humidification requires an impressive 13.2 watts, no matter the ambient temperature; this is why the total power requirement doesn’t drop that rapidly with increasing ambient temp.)
Various web references indicate that a normal human bean at rest produces 60-90 watts of heat. If your body is perfectly insulated, you’ll eventually overheat since you’ll only be dumping 29 watts through respiration.
So assuming my clothing is perfectly adiabatic, how cold would it have to be before merely breathing is enough to remove all 60 watts of the heat that my metabolism produces?
In the above scenario, respiration is removing 29 watts, so I need to find an ambient temp that will remove an additional 31 watts. At -60C if humidification takes 13.2 watts, then 15.8 watts is required for heating the air from -60C to +37C. If I want an additional 29 watts of cooling, then my ambient temperature needs to be:
37- (29+15.8)/15.8 * (37+60) = -238C
Not only is this cold enough to damage the respiratory tract, it’s below the condensation temperature of oxygen. So in theory, no matter how cold it is, it’ll always be possible dress warmly enough so that something else kills you before hypothermia does.