how to calculate work done in adiabatic irreversible process ?

For instance, an irreversible adiabatic compression of a gas would be one where the pressure force exerted on the gas exceeds the pressure of the gas. The work done is different than in a reversible process because the "P" that appears in the PdV expression for the work is actually the external pressure exerted on the gas and not the pressure of the gas itself, so the work would be greater than in the reversible case since the external pressure would need to be greater than the gas pressure to compress it.