Focus Problem for Entropy Change in Irreversible Adiabatic Process

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    Cylinder Ideal gas
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Discussion Overview

The discussion centers on the entropy change in an irreversible adiabatic process involving an ideal gas in a cylinder with a piston. Participants explore the implications of the first law of thermodynamics, the ideal gas law, and the nature of reversible versus irreversible processes. The scope includes theoretical analysis, mathematical reasoning, and conceptual clarification regarding entropy changes in different processes.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants question the definition of "adiabatic" in the context of an irreversible process, noting that entropy change cannot be zero.
  • Others propose that the change in internal energy can be expressed using the first law of thermodynamics, leading to equations relating temperature and volume.
  • Several participants derive relationships for the new temperature and volume after the irreversible expansion, with some expressing concerns about algebraic errors in earlier calculations.
  • Multiple reversible processes are suggested to transition from the initial to final states, including isobaric and isothermal steps, with participants discussing the work done and heat added in each case.
  • There is a discussion about the conditions under which a process can be considered reversible, with some participants expressing uncertainty about how to determine reversibility without invoking the second law of thermodynamics.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the definitions and implications of adiabatic and irreversible processes, as well as the calculations related to temperature and volume changes. There are competing views on the nature of reversibility and the correctness of derived equations.

Contextual Notes

Participants express uncertainty regarding the assumptions made in their calculations, particularly concerning the relationship between initial and final states in adiabatic processes. Some equations are noted to depend on specific conditions that may not hold in all scenarios.

Who May Find This Useful

This discussion may be useful for students and professionals interested in thermodynamics, particularly those exploring the nuances of irreversible processes and entropy changes in ideal gases.

  • #61
Lollo said:
@Chestermiller I am very surprised that there are cases where, in reversible adiabatic processes, the work is less than in the corresponding irreversible path.
There exists no reversible adiabatic process between the same two end states as for an irreversible adiabatic process. We know this because the entropy change for an adiabatic irreversible process is positive and the entropy change for an adiabatic reversible process is zero. So if we have an adiabatic irreversible process, all reversible processes between the same two end states must be non-adiabatic.
Lollo said:
I always thought that the work carried out on the system in irreversible adiabatic compression is greater than the work carried out on the system in reversible adiabatic compression, and that the work carried out on the system in irreversible adiabatic expansion is always less than the work carried out on the system in reversible adiabatic compression. Is this not so? I have seen several answers on StackExchange saying this, and they have never been refuted. See for example https://chemistry.stackexchange.com...rreversible-adiabatic-compression-greater-tha.
As I showed in the examples in the present thread, this is not correct.
Lollo said:
"the entropy change is the same for all the reversible paths as for the irreversible path." How to prove that? It seems to me that point (c) has been left open. Can you post a solution for the benefit of the forum?
If the two end states are the same for all the paths and, if entropy is a state function, what other possibility is there?

If you think you have found any errors in the analysis that I have done in this thread, please articulate them.
 
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