Focus Problem for Entropy Change in Irreversible Adiabatic Process

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SUMMARY

The discussion centers on the analysis of an irreversible adiabatic process involving an ideal gas in a cylinder with a massless, frictionless piston. The initial state is defined by conditions To, Po, and Vo, and the process is initiated by dropping the external pressure to P1. The participants derive the new volume (V1) and temperature (T1) using the first law of thermodynamics and the ideal gas law, concluding that T1 and V1 can be expressed in terms of the initial conditions and P1. They also explore various reversible processes to achieve the same final state, emphasizing the importance of entropy changes in both irreversible and reversible processes.

PREREQUISITES
  • Understanding of the First Law of Thermodynamics
  • Familiarity with the Ideal Gas Law
  • Knowledge of entropy and its implications in thermodynamic processes
  • Basic concepts of reversible and irreversible processes in thermodynamics
NEXT STEPS
  • Study the derivation of the First Law of Thermodynamics in detail
  • Learn about the Ideal Gas Law and its applications in thermodynamic systems
  • Investigate the concept of entropy and how it applies to reversible and irreversible processes
  • Explore various thermodynamic cycles and their efficiency, focusing on reversible processes
USEFUL FOR

Students and professionals in thermodynamics, mechanical engineers, physicists, and anyone interested in understanding the principles of gas behavior under adiabatic conditions and the implications of entropy in thermodynamic processes.

  • #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.
 
Last edited:

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