When an adiabatic irreversible expansion or compression becomes reversible

This paper aims to contribute to a better understanding of the concepts of a reversible process and entropy. For this purpose, an adiabatic irreversible expansion or compression is analysed, by considering that an ideal gas is expanded (compressed), from an initial pressure Pi to a final pressure P(f), by being placed in contact with a set of N work reservoirs with pressures decreasing (increasing) in a geometric or arithmetic progression. The gas entropy change Delta S is evaluated and it is clearly shown that Delta S > 0 for any finite N, but as the number of work reservoirs goes to infinity the entropy change goes to zero, i.e. the process becomes reversible. Additionally, this work draws attention to the work reservoir concept, which is virtually ignored in the literature, and to its analogy with the commonly used heat reservoir concept. Finally, it complements and reinforces an earlier study dealing with irreversible cooling or heating so that the synergy created by the two studies is important from both theoretical and educational standpoints.