I'm fully aware of Gay-Lussacs Law, but when I was reading Feynman Lectures on Physics volume 1, sir said that the temperature and the speed of the gas (Ideal Gas) are proportional to each other. But if that's the case, shouldn't a fan never server its purpose if all that's happening is that its blades are imparting momentum to the adjacent air molecules, in turn increasing their speed and also increasing the temperature of the gas.
A.If we proceed with our last development so is it something like an AC, where the coolant is subjected to series of processes leading it to adsorb heat from the air from the place that it's serving?
B.Does it also have something to do with the moisture content of the skin (A person felling better under the fan.) And the moisture content of the air.
Please answer if you know the answers to anyone of the sections if not all.