We all use deodorant and they always feel cold, why is that?
Is it because it is liquid inside the bottle and a gas when it is released?
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Yes, the deodorant contains a mixture of low boiling point alkanes, such as butane, that form a liquid under pressure but evaporate when the pressure falls to one atmosphere as they leave the can. It's primarily the latent heat of vaporisation that reduces the temperature and makes it feel cold.
In addition to this, deodorants (as opposed to antiperspirants) contain ethanol - they are essentially just a solution of perfume in ethanol plus propellant. The ethanol evaporates on the skin and again the latent heat of vaporisation cools the skin.
In a can of deodorant the dip tube goes down into the liquid propellant. When you press the button the pressure in the can forces liquid alkane up the dip tube and out. The alkane mostly evaporates in the tube and nozzle, but if you hold the can very close to your skin you can get liquid alkane on the skin. This evaporates very rapidly, and it's really cold!
I think that might not be the reason related to physics the actual reason is the perfume bottle consists of compressed gas that means which is unstable at normal temperature and hence when the liquid is sprayed on the skin it quickly absorbs the temperature of the body and evaporates hence we feel cold at that instance due to loss of heat from our body