Reversible and Irreversible Expansion

[bubblewrap]

What's the difference between reversible and irreversible expansion? I know how they are in formulas, (Irreversible-PV, reversible- integral over P in terms of V), but why are they expressed like this? What's the difference? And I would also like to get an exact formula of these two as I can't really find a page on the web about this, if there is it would be nice if you can put a link to the site.

 

[Bystander]

Reversible: at equilibrium at every point on a defined path, giving you an exact calculation of work done.
Irreversible: non-equilibrium at at least one point somewhere on the path, leaving you with an undefined and incalculable value for work done.