Here you go, Piston area and force.

This seems to be why p=f/a doesn't simply work for a gas in a sealed volume.


"It's the volume that determines the pressure (for a given amount of gas at a given temperature), so if you consider a rectangular container, increasing the surface area of two opposite sides and/or increasing the distance between those sides will increase the volume and therefor decrease the pressure. But increasing the total area while keeping the volume the same (in other words: changing the shape, not the volume) will have no effect.

To demonstrate this, assume the original container is a cube of 1 m³ (with each side a square of 1 m * 1 m) , and you change it to a rectangular box with width and length = 2 m and height = 0.25 m (top and bottom side become squares of 2 m * 2 m; left, right, front and back side become rectangles of 2 m * 0.25 m): now the average distance between particles and the top (or bottom) side of the box is reduced by a factor 4, so 4 times more particles hit the surface each second, but the surface area is also four times bigger (4 m²), therefor the pressure stays the same. The same is true for the sides of the box: the average distance has doubled, so the number of particles hitting them each second is halved, but the surface area is also reduced to half the original (0.5 m² instead of 1 m²), resulting in the same pressure."