Where is the resident WMT Physicist @sour_grapes when we need him...........
I call BS.
Rich ( @richmke ) has more or less nailed it. If the air is compressed at the bottleneck, it is heated. If it does not shed any of that heat, it will be the same temperature after expansion as it was beforehand.
I agree with Rich that I cannot see plastic soda bottles absorbing significant amounts of heat. And, let's say they did... where would that heat go? The necks would heat up; maybe a little of the heat would be passed to the outside air, but most would be passed back to the fast-moving airstream inside the bottle.
Furthermore, the amount of temperature rise expected from such a small compression is negligible.
Bottom line: guys and gals, this video was produced by an advertising agency, that was trying to win a humanitarian award fer cryin' out loud....
(Hmmm, why didn't they arrange the bottles in a hexagonal pattern to get more of them in the same area? )
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