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