Pressure at different altitudes

[Sp4rk]

Hi, I was wondering if the pressure in an airtight container changes with different altitudes?

For example, I seal an empty bottle of water (just air in it) at sea level so no air can leave or enter it. I then send the bottle to an altitude of 100km above Earth, will the pressure change in it? How come if it does and what equations are used?

Thanks!

 

[Matterwave]

The pressure inside the bottle will probably chance since at higher altitudes the temperature changes.

For an ideal gas (for which air is a pretty good fit) we have PV=NkT where P is the pressure, V is the volume, N is the number of particles contained in the volume, k is the Boltzmann constant, and T is the temperature.

So one see that P will not change if V,N, and T remain fixed. In this case, V and N can remain fixed, but T probably changes between the altitudes. If you kept the container at a constant temperature, then probably the pressure wouldn't change inside the bottle.

The pressure outside the bottle definitely changes (it is simply the pressure of the ambient air) and therefore the total pressure differential between the inside and outside of the bottle changes.