Monday, May 16, 2011

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 Pext. (It is important to remember that it is the external pressure, Pext. 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 = Pext. * A.
          Thus w = Pext. * 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 = –Pext. * ΔV
In case work is done on the system,
                     w = Pext. * ΔV

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