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My friends and I were at a party last night and we were crushing empty water bottles until the cap popped off and water vapor came out. I have two questions regarding this phenomenon. From previous experience, I know that condensation forms when temperature is suddenly changed. Thus, I hypothesized that the reason for this phenomenon is that the temperature inside the water bottle is much higher than outside. But from the PV=nRT equation, I didn't expect the temperature to change. If we decrease the volume, shouldn't the pressure simply increase and the temperature remain constant?

In addition, why does a temperature difference cause this water vapor to form? It's not like it is freezing outside. Why does the air inside the bottle turn into misty vapor?

BTW this is the what I'm talking about: https://www.wikihow.com/Make-a-Water-Bottle-Cap-Pop-off-with-Air-Pressure

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For compression or expansion of any fluid, there is a corresponding thermodynamic cycle. For twisting the water bottle, the cycle causes a change in both pressure and temperature with the temperature dropping. See this prior answer for further info. Why is water vapor released when an empty water bottle is squeezed?

As to why water vapor forms, it is because you have saturated air with water vapor. When you oversaturate air, the water begins to condense. This is something you can observe on a cold morning on windows or the condensed water on the outside of a cold glass of water. The saturation of water in air at different temperatures can be found here: https://www.engineeringtoolbox.com/relative-humidity-air-d_687.html

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