How do you apply the formulae P(V2-V1) for work done in pushing the

How do you apply the formulae P(V2-V1) for work done in pushing the compressed charge out in reciprocating compressor? The process of pushing the compressed gas in to the compressor tank is not a non flow process. So we should not apply ⌠pdv. So you may think that it is flow process so we can apply⌠vdp. But its not a flow process if we consider that system is both tank and cylinder. And it is flow process when only cylinder is considered as a system. When it is non flow process, i.e, when system is both tank and cylinder: The piston is compressing the gas which is in both tank and cylinder by the amount equal to V2-V1. still the pressure in the tank is almost unaltered( because tank volume is more when compared with cylinder volume, v2-v1 is also negligible compared to tank volume). Hence the system is compressed by volume v2-v1 at constant pressure. Here we can apply the farmulae p(v2-v1) for workdone in compression. When it is flow process, i.e., when system is only cylinder: Here the piston is pushing the compressed gas against a force of P*A. where A is cross sectional area of cylinder. So the work done in overcoming the force is , (P*A)*(distance it moved), which is nothing but P*(v2-v1). Because the length * cross sectional area is nothing but the volume it displaced.