The reservoir concept: entropy generation and lost work

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 (P_A V_A) to final state (P_B V_B) always takes the gas away from the adiabat PV^γ=P_A V_A^γ. 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^γ)>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.

Section: The Pv Diagram and Quasistatic Processesmentioning

confidence: 99%

“…Their figure 7 of [10] demonstrates these results graphically. But, generally, students are not aware of the importance of the d (PV γ ) term in equation (7).…”

Section: Allowed Processes In the Pv Planementioning

confidence: 99%

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

Marcella¹

2022

“…Applying the above equation to surroundings and using the energy conservation principle, a thermodynamic process viewed as a series of infinitesimal processes can be described by the fundamental equation [11] T dS − P dV = −T e dS e + P e dV e ,…”

Section: How To Distinguish Heat From Work?mentioning

confidence: 99%

“…Thus, (2) does not depend on which of the interacting parts is labelled as system or as surroundings. Any equation or quantity exhibiting this property is a process invariant [11].…”

Section: How To Distinguish Heat From Work?mentioning

confidence: 99%

“…We also have a different view from that stated in references [8,9], which is that it is not always convenient or even possible to cleanly distinguish Q from W in irreversible processes. The difficulties arise because the discussions on the heat and work concepts found in the literature do not give due importance to the reservoir concept, which cannot be dissociated from the former [11].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

How to distinguish heat from work in irreversible processes?

Anacleto

2022

Self Cite

The theoretical foundations of the reservoir concept are presented and then applied to the discussion of two irreversible processes. As an alternative to what is stated in the literature, it is shown that heat and work can be clearly distinguished in irreversible processes, provided that the reservoir concept is considered. This discussion, which is expected to be both theoretically and instructively relevant, is intended primarily for graduate students and teachers, although it may also be of interest to undergraduate students with a solid background in thermodynamics. By covering specific examples of irreversible processes in which heat and work turn out to be controversial concepts, this article will also be useful in the introductory or upper-level undergraduate curriculum.

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

Anacleto¹

2023

Self Cite

This comment deals with an issue in Marcella’s paper, 2022 Eur. J. Phys. 43 045104. We point out that the statement that quasistatic processes are necessarily free of dissipative effects is wrong, which led to an incorrect expression for entropy generation. We derive the correct expression, our aim being to remove persistent misconceptions in thermodynamics, in a constructive and pedagogical spirit.