How can we use bulk-phase thermodynamics when gravity disrupts a phase's uniformity?

Question

I am starting a course in thermodynamics, and two assumptions that the instructor listed for equations of state to apply is that:

the system is invariant with time; and
that the bulk physical properties are uniform.

However, if we consider a cylinder of ideal gas, the pressure is not uniform, is it?  I was taught that pressure in a cylinder of ideal gas would be greater at the bottom of the cylinder, just like how atmospheric pressure is higher at lower altitudes.

Question:  How can bulk-phase physical descriptions, e.g.
$$
PV = nRT
tag{ideal gas law}
,,
$$
be applied when a bulk-phase isn't actually uniform due to phenomena like gravity?

Martin Ueding · Answer

Gravity does affect the pressure distribution. This becomes more apparent when the medium is dense like water. Air pressure is also higher at ground than higher up, it decreases exponentially (if the temperature was constant, which it isn't). The change is rather low, though.

So in your class you can ignore gravity if it is not used explicitly and just assume that the pressure is uniform in the container of interest.

Deschele Schilder · Answer

In the previous answer, it is said:

This becomes more apparent when the medium is dense like water.

Not true. Just look at the (maximum) 11 kilometers deep waters around Japan.

It becomes more apparent there.

$$
PV = nRT
tag{ideal gas law}
,,
$$

still applies, but it is height-dependent.

How can we use bulk-phase thermodynamics when gravity disrupts a phase's uniformity?

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