When an adiabatic irreversible expansion or compression becomes reversible

Abstract

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 P i 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 S is evaluated and it is clearly shown that 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.

Reversible temperature exchange upon thermal contact

“…Replacing the sum in Eq. (A.5) with this expression, we obtain our main result (14). In principle, this should complete our solution.…”

“…The curves in Fig. 6 show the accuracy of this approximation: already for N = 5 the expression (10) overestimates the exact result (14) by only about 2%. We emphasize that while the final temperature of the hot water tends to zero asymptotically for N → ∞, it approaches zero rather slowly.…”

“…Note that a reversible process facilitated by an infinite number of thermal baths is well studied in the existing literature. [8][9][10][11][12][13][14][15][16] We emphasize, however, that the scenario described here is quite different: the reversibility does not rely on the presence of any auxiliary bodies as there are no thermal baths involved.…”

Evolution of ideal gas mixtures confined in an insulated container by two identical pistons

“…Miranda 2,3 also studied an ideal gas contained in an adiabatic cylinder, but with a slowly moving piston on one side, obtained the relation between temperature and volume using molecular considerations, and generalized his results to the irreversible case. Anacleto et al [4][5][6] provided further insights into the reversibility of adiabatic processes and demonstrated the equivalence of the microscopic and macroscopic descriptions of Miranda's adiabatic reversibility parameter.…”

The two-piston problem revisited: Generalization from reversible to irreversible expansion

“…[1][2][3][4][5] Recently, Amor and Esguerra 6 considered the adiabatic expansion of an ideal gas confined between two identical and frictionless pistons of mass M and cross-sectional area A, initially clamped at fixed positions separated by a distance L 0 (see Fig. 1).…”