# Applying ideal gas law to every day problems

Three classical examples of seeing the ideal gas law in action:

1. crumpled water bottle in cold car

2. crumpled water bottle after your flight lands

3. fridge door harder to open a second time after first.

I'm afraid I'm having trouble understanding all three, and I believe it stems from a single reason: the derivation of the ideal gas law is for a closed container subject to the conditions of temperature, pressure, volume, number of moles in THAT closed container. The explanations I see regarding these every day problems are either vague in regards to which quantities in the gas law are considered as being held constant, or vague in regard to describing the conditions IN the container; they always tend to talk about conditions outside the container. What am I missing here? Can someone elaborate, specifically telling me which variables are considered constant in each case, and which are fluctuating and why?

## 1. Crumpled water bottle in cold car

• System: air inside the closed bottle.
• Amount of gas is constant. (Bottle is closed.)
• Pressure is constant (atmospheric pressure on the outside of the bottle doesn't change, so at equilibrium the pressure inside the bottle must equal the external atmospheric pressure.)
• Temperature decreases. (You moved your bottle from room temperature to the colder car, so the air in the bottle will reach equilibrium with the environment at a lower temperature.)
• Therefore, volume decreases. (Your bottle is not rigid, so it crumples to decrease the volume in response to the other conditions.)

## 2. Crumpled water bottle after plane lands

• System: air inside the closed bottle.
• Amount of gas is constant. (Bottle is closed.)
• Temperature is constant. (Your plane cabin is heated for your comfort.)
• Pressure increases. (Although the cabin is pressurised, it isn't pressurised to the atmospheric pressure at ground level, and it isn't completely airtight. When the plane lands, it goes from the lower-pressure sky-level to the higher-pressure ground level. So the external pressure on the bottle increases, and at equilibrium the internal pressure must match that.)
• Therefore, volume decreases. (Your bottle is not rigid, so it crumples to decrease the volume in response to the other conditions.)

## 3. Fridge door harder to open second time after first

• System: air in fridge. After closing the door and powering on your new fridge, after some time you find it harder to open the door.
• Amount of gas is constant. (Up to the moment you open the fridge, the fridge is closed.)
• Volume is constant. (Fridges don't crumple.)
• Temperature decreases. (Your new fridge works.)
• Therefore, pressure inside the fridge decreases.
• As a result, the external pressure is greater than the internal pressure, which means there is a force on the fridge door acting inwards due to the pressure difference. So you will find it harder to open the door.
• Thanks. In #2, the pressure in the bottle is not changing; it's simply that the pressure outside the bottle increased, correct? Further, I'm guessing the decrease in this bottle's volume means the pressure inside the bottle has to increase in proportion, until it matches that in the cabin, correct? For #3 I'm less clear. The temperature in the fridge should increase with added hot air, shouldn't it? Also, people online mention a vacuum effect. – Nights Feb 8 at 9:11
• more issues: for example #2, a book I have shows the inverse relationship between P and V. But if this graph is referring to P outside the bottle (outside the system), this isn't the same P in the gas law, so I don't see this graph as accurate. Also, can you discuss a bubble rising from the sea floor? My impression is: P outside the bubble lessens as the bubble rises. But P inside the bubble (system) seems constant. So why increasing V inside the bubble? In terms of the gas law, the P that decreases is outside the system (bubble), so how can we use it in the gas law? – Nights Feb 8 at 9:26
• In #2, the pressure in the bottle is increasing. (My last sentence there: "at equilibrium, the internal pressure must match [the increased external pressure]".) So the bottle's volume decreases and the pressure increases together. For #3, the ideal gas law applies up until the moment the door opens and the airtight seal is broken. Once that happens you no longer have two well-defined inside/outside systems to talk about. The explanation I gave tells you that you will need to apply a larger force (compared to a non-working closed fridge) to open the door. – user194422 Feb 8 at 9:51
• @Nights For your second comment, P and V (and n and T) should always be talking about the same system (in our case, inside the bottle). The P outside the bottle is related to the P inside the bottle simply by the fact that they must be equal at equilibrium. For the rising bubble, the same logic applies. (Assuming T constant), n and T are constant, P inside needs to decrease to match the pressure outside, so V increases and the bubble expands. – user194422 Feb 8 at 9:59
• The "pressure moving toward equilibrium" concept is a result of what, or comes from where? – Nights Feb 8 at 10:15