Work done under constant pressure
You can't do adiabatic reversible work at constant pressure.  The pressure has to change.  If you want to do adiabatic irreversible work at constant pressure, say by suddenly increasing or decreasing the pressure load to begin with, and then holding it constant during the process, this is sometimes referred to as adiabatic work at constant pressure, but it really isn't.  The final pressure will not be equal to the initial pressure that was present before you changed the applied load.