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Pressure, volume and temperature of an ideal gas are related by \(pV=nRT\). Air at atmospheric pressure and room temperature (and above), very closely follows this relation. This experiment gives a situation to discuss this equation and also throws light on heat transmission through conduction.
In this experiment, heat exchange takes place between surrounding air, air inside the bottle and the plastic walls. The time scales of these exchanges are different and that should affect the shrinking rate.
Also the air inside will have high humidity, perhaps it will be saturated with vapour. As temperature goes down, some vapour might condense. That will also affect the shrinking pattern.
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