An ideal gas and the increasing (total) entropy principle: what is allowed in the PV plane and what is not

In a recent article in this journal, Brown and Singh present the results of an extensive in-class survey of student difficulties with the second law of thermodynamics. Here, we discuss in detail some issues identified by them in an attempt to resolve some of the problems. We do this by making clear the distinction between the 'system entropy', 'reservoir entropy', 'total entropy', and the 'entropy of the Universe'. We identify, without ambiguity, which quasistatic processes are 'internally reversible', which are 'totally reversible', and which are 'irreversible'. We discuss the meaning of quasistatic processes represented by curves in the PV plane. We show that the process P = P(V) that takes an ideal gas from initial state (PAVA) to final state (PBVB) always takes the gas away from the adiabat PV gamma = PAVA gamma. We establish the increasing (total) entropy principle as the quantitative expression of the second law of thermodynamics. This establishes the fundamental role of the total entropy in macroscopic thermodynamics. Expressing the increasing (total) entropy principle in the form (T-res - T-gas)d(PV gamma) > 0 reveals which processes are allowed, which are not, and which points in the PV plane are accessible from a given initial state. Students can now observe the limitations on individual processes mandated by the second law. Such second law analysis is suitable for the introductory physics course.

Automated summary

In this article, the authors discuss the difficulties students face with the second law of thermodynamics based on a survey. They address these issues by clarifying the concepts of system entropy, reservoir entropy, total entropy, and entropy of the Universe. They also differentiate between internally reversible, totally reversible, and irreversible processes. By establishing the increasing entropy principle as the quantitative expression of the second law, they highlight the importance of total entropy in macroscopic thermodynamics. This analysis helps students understand the limitations imposed by the second law.