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Irreversible Quasistatic PV Work

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Hi

1) I am reading Pippard's Classical Thermodynamics and was confused by one of his examples in the attachment.

What I do not understand is the concept of using P' (I am thinking P' as = P_fric + P_interface) for work calculations. If I take the system as composed of just the gas inside the cylinder and assuming this system is insulated and the process quasistatic, pressure at the gas-piston interface should be equal (P_ interface) and the system only sees P_ interface applying work onto it during compressing and applying P_ interface during expansion. I get that P' is important because it includes friction, but the system/gas doesn't see this since it is happening outside its system boundaries.

2) For the same insulated piston cylinder system, if the compression-expansion process is quasistatic but the process contain irreversibilities like friction which is converted into heat and absorbed by the system since it is insulated, would first law become Qfric - W = E_2 - E_1 where W = P_ interfaceΔV and external applied pressure equal to P_interface + Pfriction?
I'm having trouble imagining how this system is irreversible since all of the applied energy in one form or another is added to the system; why wouldn't it be able to return to its initial state?

Thanks very much

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