Pressure-Volume Work

Pressure – Volume Work or PV work is also known as Expansion Work. Consider a gas contained in a cylinder fitted with a frictionless piston. The pressure of gas, P exerts a force on the piston. This can be balanced by applying an equal but opposite pressure from outside on the piston. Let it be represented as P_ext. (It is important to remember that it is the external pressure, P_ext. and not the internal pressure of gas itself, which is used in calculating work done either due to expansion or contraction).
If gas expands at constant pressure through a distance of ‘l’ then,
         Work, w = force * l.
                    w = f * l.
          But f/A = P.
          ∴ f = P_ext. * A.
          Thus w = P_ext. * A * l.
          Where, A is area of cross – section of piston.
                    w = Pext. * ΔV.
Where ΔV is increase in volume.
Since work is done by system, then
                     w = –P_ext. * ΔV
In case work is done on the system,
                     w = P_ext. * ΔV