What Is the Logic Behind Adding Pressure in the Derivation of PV=nRT?

[kidsasd987]

http://quantumfreak.com/derivation-of-pvnrt-the-equation-of-ideal-gas/please check eq.(7)

pressure equation is P=F/A which means, in any region over the surface, pressure will be the same.
for example, if we assume all the particles have the same mean squared velocity, pressure of one cube will be the same as the pressure of the whole container.

I wonder why we add up all the pressure we found for the small cubes, and what's the logic behind it?

 

[Drakkith]

You're not adding up the pressure of small cubes, you're adding up the pressure exerted on the cube's interior per particle to get the total pressure.