[Physics] Why does a bottle shrink when you pour hot water in it

Question

I think the title says pretty much. Last night I poured hot water in a half full bottle of water and closed the cap. The bottle immediately shrunk. Why? My girlfriend suggested that the hot water has less oxygen in it and thus consumes some of the oxygen in the bottle.

Answer 1

In an ideal gas

where P is the absolute pressure of the gas, V is the volume of the gas, n is the amount of substance of gas (measured in moles), T is the absolute temperature of the gas and R is the ideal, or universal, gas constant.

The capped gas in the bottle cools coming to a thermodynamic equilibrium , through conduction to the walls, and also according to the black body radiation # law everything cools at a certain rate. In the formula above the combined pressure times volume has to become smaller. If the walls are not rigid the imbalance of the inside pressure to the outside compresses the wall until pressure equilibrium is reached. The same is true if you put a capped half empty bottle in the freezer. - - - - - - -

#it has been pointed out in a comment air does not follow the black body radiation formula well , it has small emissivity and conduction has to be the main cooling mechanism.