I actually went ahead and spent some hours experimenting. Used two 500ml aluminum beer cans filled with water at room temperature, 21.4°C. One can wrapped in a paper towel soaked with an additional 20ml of water, one left bare as control. Shoved both in my small, non-ventilated house freezer at -14°C and measured temperature and weight every twenty minutes until water in both cans started forming ice. These are the results.
Allowing for some error from my cheap digital food thermometer, the towel-wrapped can cooled quite a bit faster than the control one. In fact, it reached the 4°C serving temperature in about 50 mins, more than an hour earlier than the control can. Notably, by that time it had already lost some 6ml of water, I suppose through evaporation/minor dripping, and ended up losing a total of 10ml by the end of the experiment (the control only lost 2ml).
So yes, the wet paper towel trick does seem to work quite nicely. I'd expect it to work even better if one were to use a ventilated freezer (faster heat exchange) and smaller containers (greater surface/volume ratio).
I also had a properly sealed beer can in there with a wet towel, same starting temperature, and it cooled to serving temp at about the same rate as the other can. A little quicker, because it wasn't taken out of the freezer for measurements until the 1-hour mark, when it was ready to be in my tummy.
Not very academic maybe, but I hope this provides some useful info!
From a heat transfer perspective, steam is a lot more like air that it is like liquid water. The chemical makeup doesn't matter as much as the state.
As a gas, steam is a bunch of $H_2O$ molecules flying around at random, bashing into each other occasionally. The mechanism of conduction in that case is that the hot molecules will gradually bounce past the cold (and vice-versa), moving heat across a temperature gradient. The same is true for air, so their conductive properties are similar.
As a liquid, those molecules are much more tightly packed and are in contact (sort of) with each other all the time. When you heat up molecules in one place they can transfer that heat directly to their neighbors. At the molecular scale heat is just a lot of wiggling, spinning and vibrating motion (electrons get involved too if it's hot enough). Being in contact makes it easy for vibration in one molecule to make its way to others.
The pressure dependence in steam (an other gases) shows up at two extremes. At high pressure, the molecules will get closer together as they fly around and start to act a bit more like a liquid. At very low pressures, they'll collide so rarely that some of the molecules will go clear across the space in question without hitting any of the others. That the low pressure effect depends on both pressure and the size of the system
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Smoke isn't what you might think it is. What is referred to in layman terms as "smoke" or "fumes" or various similar terms is actually a mix of two distinct components:
Much of what you see in visible smoke (maybe all of it, actually) is solid particles. The only time I can think of being able to see gasses might be your breathe during the winter time and dry ice, and I'm pretty sure that's actually not vapours but just ice crystals which are solid particles.
Passing the air through a soaked material before you breathe it causes the solid particles to be removed from the air because they adhere to the liquid in the cloth via surface tension tension. It's the same as how rain removes dust from the air or how you use a wet cloth to wipe dust from a table. A good dry filter, like a HEPA filter, will do the same thing. So would a cloth soaked in something like mineral/baby oil.
But this type of mechanical filtering (or any type of mechanical filtering) won't protect you from the vapours. For a similar method to protect you from the vapours, something in the cloth must react with the vapour. The best example of this is breathing through a urine soaked cloth would protect you from mustard gas in World War 1.
And it obviously won't protect you from lack of oxygen.
This is why industrial respirators have both particulate filter cartridges and chemical vapour cartridges. And that's why there's many types of chemical vapour cartridges targeted for different substances but only only one or two particulate filter cartridges varying in particulate size. And why they say they are not for use in oxygen deficient environments.