# Pressure in a bottle

## Homework Statement

Maria has an empty bottle with a cork in her backpack. One cold winter day when she had been out skiing, she opened the backpack and she saw that the bottle had been crumpled together. What happened and why?

## The Attempt at a Solution

My first thought was that the molecules in the bottle didn't get enough energy so they didn't exert a high pressure on the bottle so the pressure outside was bigger. But then I realized that the temperature outside the bottle and inside is the same so why didn't all the molecules in the atmosphere have a smaller pressure on the bottle?

Orodruin
Staff Emeritus
Homework Helper
Gold Member
Where do you think Maria filled the bottle?

at home maybe :)

billy_joule
So how do the conditions differ between her home and up a cold mountain?

there are less molecules in the bottle because the have a higher energy so they take up more space

Chestermiller
Mentor

## Homework Statement

Maria has an empty bottle with a cork in her backpack. One cold winter day when she had been out skiing, she opened the backpack and she saw that the bottle had been crumpled together. What happened and why?

## The Attempt at a Solution

My first thought was that the molecules in the bottle didn't get enough energy so they didn't exert a high pressure on the bottle so the pressure outside was bigger. But then I realized that the temperature outside the bottle and inside is the same so why didn't all the molecules in the atmosphere have a smaller pressure on the bottle?
Does the pressure of the atmosphere really change when the temperature gets colder outside, or is it determined by the weight of the overlying atmosphere?

I don't know, but the pressure is lower in the mountains and so is the temperature :P

Chestermiller
Mentor
I don't know, but the pressure is lower in the mountains and so is the temperature :P
Who says she was skiing on a mountain? Maybe she was doing cross country skiing at sea level. What then?

Chet

Why doesn't the atmospheric pressure decrease in colder temperatures?

Chestermiller
Mentor
Why doesn't the atmospheric pressure decrease in colder temperatures?
What are your thoughts on this?

there will be less gas in the atmosphere maybe :P cuz if I look at pV=nRT
R is constant, T decreases, V is constant and if p doesn't change then n has to increase

Chestermiller
Mentor
there will be less gas in the atmosphere maybe :P cuz if I look at pV=nRT
R is constant, T decreases, V is constant and if p doesn't change then n has to increase
Does atmospheric pressure vary with altitude? Does atmospheric temperature vary with altitude? If so, what value of these parameters do you use in the ideal gas law (since the atmosphere is not uniform)? Do you really think that, for purposes of solving your problem, changes in n (the total number of moles of gas in the atmosphere) on a day-to-day basis can be significant?

Chet

I don't know why the atmospheric pressure is the same everywhere

I don't know why the atmospheric pressure is the same everywhere
Again, look at Chet's post. Does atmospheric pressure vary? If so, how?

well, I have read about winds and there is something called low pressure and high pressure. So the atmospheric pressure shouldn't be the same everywhere but maybe the difference isn't high enough to affect the bottle

Chestermiller
Mentor
well, I have read about winds and there is something called low pressure and high pressure. So the atmospheric pressure shouldn't be the same everywhere but maybe the difference isn't high enough to affect the bottle
The atmosphere is not in a solid container like the air in bottle, so the pressure is much more free to readjust to local temperature changes. In addition, gravity strongly affects the pressure of the air, so that the pressure decreases substantially with altitude. The ideal gas law cannot be applied to the entire atmosphere as a whole, because, if pressure and temperature vary, what values do you use in the equation? Even though the air pressure at ground level varies somewhat as a result of weather changes, the variations are typically pretty small (usually, not more than about 5%). Look up on Google the daily atmospheric pressure variations in your local area. The average pressure of the atmosphere at sea level (per square meter) is basically determined by the average weight of the 1 square meter column of air above that location.