Looking for a physics explanation of this observation

[LennoxLewis]

I have cola-bottle (1.5L) that is half-filled with water. The other half was air, of course. I put it in the fridge (~ -14 C) and after about an hour, before i could see ice formation but when it was very cold nonetheless, i saw that the bottle hull was deformed to the inside, the same way if you smash it (the Dutch for it is a "deuk", don't know how to translate that, "indentation"?).

So, the pressure inside has become smaller than the pressure outside. According to the gas law, the pressure should drop as the temperature goes down and the volume remains constant. But the temperature of the air around it was -14 degrees Celsius, so that pressure would have been smaller also.

Can anyone explain this "indentation" ?

 

[jack action]

But the temperature of the air around it was -14 degrees Celsius

Yes, but the temperature of the air IN the bottle was NOT at -14 °C. So the initial conditions were:

P_bottle = P_fridge = P_atm

T_bottle = 20°C (or whatever is the ambient temperature)
T_fridge = -14°C

Then the temperature of the air in the bottle finally goes down to -14°C, and so the pressure goes down too. The difference between the outside and inside pressure created that force that the bottle couldn't handle.

 

[Lsos]

The pressure in the fridge is NOT smaller. The fridge is not perfectly sealed. It is open to the atmosphere, and therefore it is at atmospheric pressure.

 

[jack action]

The pressure in the fridge is NOT smaller. The fridge is not perfectly sealed. It is open to the atmosphere, and therefore it is at atmospheric pressure.

That' what I said: P_bottle = P_fridge = P_atm

But the temperature of the air in the bottle is higher than the temperature in the fridge.

When the air inside the bottle cools down, the pressure INSIDE the bottle decreases. The pressure in the fridge remains the same, i.e. the atmospheric pressure.

There is a vacuum formed inside the bottle, hence "pulling" the bottle in.

 

[Lsos]

I know, but I'm not sure the OP does (who my response was aimed at). You appear to have agreed with his claim that "pressure would have been smaller also." while simultaneously saying that Pbottle = Pfridge = Patm. I just wanted to clear it up.

 

[LennoxLewis]

Thanks guys, that explains it well.

One more thing: since the frigde is at lower temperature, is the particle density (N/V) higher than say, in the kitchen? I'm asking because if you look at PV = NRT, and you decrease T but P remains constant, something's got to give..

 

[Lsos]

Yes the air in the fridge is denser than in the kitchen. It's why warm air rises and cold air drops...

 

[LennoxLewis]

Yes the air in the fridge is denser than in the kitchen. It's why warm air rises and cold air drops...

Turning this around, do you think it's possible to leave the bottle opened in the freezer for a while, then opening the freezer and quickly fastening the lid, in a hope to capture the denser, at atm. pressure, -14 degrees Celsius air? Now if one leaves this bottle at RT, the bottle should become very hard or even explode, right?

Do you think this will work in practice, or will the air density of the freezer drop relatively quick when opening the door?

 

[jack action]

Turning this around, do you think it's possible to leave the bottle opened in the freezer for a while, then opening the freezer and quickly fastening the lid, in a hope to capture the denser, at atm. pressure, -14 degrees Celsius air? Now if one leaves this bottle at RT, the bottle should become very hard or even explode, right?

Do you think this will work in practice, or will the air density of the freezer drop relatively quick when opening the door?

If you open the bottle in the freezer, the pressure will equalize to atm pressure because air from the fridge will enter the bottle (hence increasing the density inside the bottle). Doesn't matter how slow or fast you do it, as long as the temp of the air in the bottle doesn't drop too much.

And when you're going to take it out, let it warm up to RT, yes the pressure will increase inside the bottle.

Air density in the fridge has nothing to do with it.