[Araconan]

The following is how my textbook derives the equation for PV work:

Suppose we have a gas confined to a cylindrical container with a movable piston, where F is the force acting on a piston of area A. Since pressure is defined as force per unit area, the pressure of the gas is P = F/A. Work is defined as a force applied over a given distance, so if the piston moves a distance Δh, then the magnitude of the work is: l work l = l force x distance l = l F x Δh l. Since P = F/A, or F = P x A, then
l work l = l F x Δh l = l P x A x Δh l. This is then simplified to: l work l = l PΔV l, and after consideration is given to the signs, w = -PΔV.

What I don't get:

Following the explanation, the textbook states that it's important to keep in mind that when dealing with PV work, the "P" in "PΔV" always refers to the external pressure - the pressure that causes a compression or that resists an expansion. Why is this so? Why isn't the pressure of the gas being considered? When deriving the equation, the equation "P = F/A" was the equation given for the pressure of the gas, and since it was then used to derive the work equation, shouldn't the "P" always refer to the internal, or the pressure of the gas? Furthermore, does this mean that when dealing with questions regarding PV work, the pressure of the gas, besides being used to calculate the volume (PV = nRT), is irrelevant during calculations? Is there any time when dealing with PV work, in which I also have to consider the pressure of the gas?