Final answer:
The work equation W = -∫ P_{ext} dV is associated with quasi-static, reversible thermodynamic processes that can be represented as a well-defined PV curve. For irreversible processes, the path cannot be retraced without a net change, which typically involve rapid, non-equilibrium changes where the work integral is not directly applicable.
Step-by-step explanation:
The work done by or on a system during a quasi-static thermodynamic process can be represented by the equation W = -∫ P_{ext} dV, where P_{ext} is the external pressure and dV is the differential change in volume. This equation assumes the process is reversible and the system remains in thermal equilibrium, with pressure and volume changes occurring infinitesimally to maintain a defined state. Work done is interpreted as the area under the PV curve on a diagram, with positive values for gas expansion and negative for compression. When considering irreversible processes, conditions differ from the assumed equilibrium states, and the external pressure does not necessarily match the system's pressure at each state, making the integral not directly applicable.
In the context of the question asking about work being irreversible, the process would be irreversible if the path taken on the PV diagram cannot be retraced back without leaving a net change in the system or the surroundings. Often, irreversible processes involve non-equilibrium states, such as rapid compression or expansion, where the pressures and temperatures can vary significantly from point to point, not allowing for a well-defined PV curve.