Air is a relatively poor medium for transferring heat. Direct contact with metal, or submerging in water or something would be much quicker. That is what will burn in the short term, high heat over a short time.
Since air doesn’t transfer heat to our face very quickly, it doesn’t burn us much. Given enough time it certainly would, but a few moments will just be uncomfortable.
Air is a poor conductor of heat. I wouldn’t recommend it, but you can stick your hand into a 120 C oven for a few seconds and be totally fine whereas putting your hand into 100 C (boiling) water would cause serious injury. Water is a much better conductor of heat.
Conductivity is basically just a measure of how quickly one object can transfer heat to another.
An example on the cold end: dry ice is really really cold (-78 C) but can be handled briefly with nitrile exam gloves without causing any damage or even any significant discomfort.
Unless the oven is airtight, the hot air doesn’t “rush” out of it when it’s opened, because the pressure inside and out is the same. The heat you experience is from slight mixing of the air, plus infrared radiation from the hot surfaces. At no point are you blasted with 500°C air (which would definitely hurt you).
Air doesn’t hold much energy in the form of heat. It heats up and cools down very quickly. It also doesn’t conduct heat very well; air makes an excellent insulator, especially if you can keep it still (this is why foam and down make good insulation, they hold air still).
So when you open the oven door, the puff of hot air that comes out is cooling down quickly, and what heat it does have does not travel easily from the air into your skin. The combination of those two things keep you from getting burned due to brief exposure to hot air.
Air takes a long time to burn anything. It also doesn’t rush out very readily, if anything cold air is more likely to rush in due to the pressure difference.
Now if you had some sort of fan blasting the hot air towards you, then yeah you’d get burned pretty quickly, that’s basically how a convection oven or air fryer cooks food so quickly
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