How Do We Calculate Entropy Change for Non-Isothermal Points on a PV Diagram?

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SUMMARY

The calculation of entropy change (ΔS) for non-isothermal points on a PV diagram can be achieved by designing an isothermal reversible process connecting the initial and final states. This method is valid regardless of the actual process being non-isothermal or irreversible. The key is to conceptualize a reversible path where heat flows are easily determined, allowing for the calculation of ΔS through the integral of dq/T along that path. This approach ensures accurate entropy change determination based solely on the system's initial and final states.

PREREQUISITES
  • Understanding of PV diagrams and thermodynamic processes
  • Knowledge of the concept of entropy and its significance in thermodynamics
  • Familiarity with reversible processes and their characteristics
  • Ability to perform integrals involving heat transfer and temperature
NEXT STEPS
  • Study the principles of reversible thermodynamic processes in detail
  • Learn how to calculate integrals of dq/T for various thermodynamic paths
  • Explore the implications of non-isothermal processes on entropy change
  • Investigate the use of software tools for simulating PV diagrams and entropy calculations
USEFUL FOR

This discussion is beneficial for thermodynamics students, engineers working with heat engines, and researchers focused on entropy calculations in non-isothermal processes.

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how do we find change in entropy for two points on a P V diagram which are not an isotherm
 
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Since the change in entropy of the system only depends on the initial and final states of the system, you can design an isothermal reversible process which goes from the intial point to the final point indicated by the diagram and easily calculate its ΔS. It will be the same even if the actual process you are studying is not isothermal or reversible.
 
MexChemE said:
Since the change in entropy of the system only depends on the initial and final states of the system, you can design an isothermal reversible process which goes from the intial point to the final point indicated by the diagram and easily calculate its ΔS. It will be the same even if the actual process you are studying is not isothermal or reversible.
The temperature at the initial state may not be the same as the temperature in the final state. So the path may not be totally isothermal. But you have the right idea.

The OP needs to "dream up" a reversible path between the initial and final states (any reversible path will suffice) for which the heat flows are easy to determine, and then calculate the integral of dq/T for that reversible path. That will give the change in entropy.

Chet
 
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