Two identical empty plastic bottles were outside on a hotafternoon. They were in

Question

Two identical empty plastic bottles were outside on a hotafternoon. They were initially uncapped. At about threeo’clock, a physicist tightly capped one of the bottles,bottle A.
By midnight, the weather had turned very cold. When the physicistobserved the bottles at midnight, she found that the sides ofbottle A were caved in, but bottle B was the same shape it had beenin the afternoon.





A. Did the mass of air inside bottle A increase, decrease, orremain the same from 3 P.M. to midnight?
Explain.




B. Did the volume of air inside bottle A increase, decrease, orremain the same from
3 P.M. to midnight? Explain.




C. Did the volume of air inside bottle B increase, decrease, orremain the same from
3 P.M. to midnight? Explain




D. Did the mass of air inside bottle B increase, decrease, orremain the same from 3 P.M. to midnight?
Explain.

Explanation / Answer

B. The volume of the air inside a bottle is just the volume ofthe bottle itself, since the air completely fills the bottle. At 3PM, the bottle was not caved in. At midnight, the bottle was cavedin. A caved in bottle has less volume, so the volume of the airdecreased.
C. The bottle is exactly the same shape at 3 PM and atmidnight, so the bottle has the same volume. The air that fills thebottle just has the same volume as the bottle itself, so the volumeof the air inside the bottle stayedthe same.
D. This one is a little tricky. If two bottles are filled withair at the same temperature, then the one with more pressure has ahigher mass of air inside it, since it has more molecules pushingon the sides of the bottle. Since the sides of bottle A at midnightcaved in, it must have had less pressure than the outside air.Bottle B was uncapped, so the air inside it must have had the exactsame pressure as the air outside. Thus, the pressure inside bottleB was greater than the pressure inside bottle A at midnight, and soat midnight bottle B has a greater mass of air inside it thanbottle A. Now bottle A has the same mass as it did at 3 PM (as weshowed earlier), and at 3 PM bottles A and B had the same massinside of them. Thus, bottle B has a higher mass of air than it didat 3 PM. Thus, the mass of air inside bottle B increased.

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