Work done in expansion of a gas

The work might be calculated from the average pressure, but not the difference.

The work done by expansion of a gas can be evaluated using $int P_{ext} enspace dv$ where $P_{ext}$ is the external pressure and $v$ is the specific volume of the gas. If $P_{ext}$ is fixed, for example expansion against atmospheric pressure, this becomes $P_{ext} Delta v$.

For a reversible process, the work is also $int P enspace dv$ where $P$ is the pressure in the gas, and the integral depends on the path taken between the initial and final equilibrium states of the gas.

For an irreversible process, the gas does not necessarily move through a series of equilibrium states and the work is not $int P enspace dv$; we do not know the path taken between the intial and final states.

See a good text on Thermodynamics, such as one by Sonntag and Van Wylen.