Entropy Proof: Ideal Gas Expansion with Varying Temperature | Homework Question

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SUMMARY

The discussion focuses on proving that the change in entropy (ΔS) for an ideal gas expanding adiabatically and irreversibly from point 1 (at temperature TA and pressure PA) to point 2 (at temperature TB and pressure PB) is always greater than zero. Participants highlight the significance of varying temperature in this process, distinguishing it from typical adiabatic expansions that mirror isothermal processes. The conversation emphasizes the need for clarity in assumptions and calculations to validate the outcomes of the entropy change.

PREREQUISITES
  • Understanding of the first and second laws of thermodynamics
  • Familiarity with Helmholtz and Gibbs free energy equations
  • Knowledge of ideal gas behavior and properties
  • Concept of exact differentials in thermodynamic functions
NEXT STEPS
  • Study the derivation of the entropy change for adiabatic processes in ideal gases
  • Explore the implications of varying temperature on entropy calculations
  • Review the mathematical formulation of exact differentials in thermodynamics
  • Examine case studies of adiabatic irreversible expansions in thermodynamic systems
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Students and professionals in thermodynamics, particularly those studying ideal gas behavior, entropy calculations, and the implications of varying temperature in adiabatic processes.

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Homework Statement



Using the exact differential, state function characteristics of S prove that ΔS for step I is always > 0 for an ideal gas expanding adiabatically and irreversibly from point 1 at TA,PA to point 2 at TB,PB

can anyone help me with this one?
A key difference this one has over others is that temperature is varied and thus not a normal adiabatic process where it mirrors an isothermal one

Homework Equations



first law, second law, helmholtz and gibbs free energy equations? mayb

The Attempt at a Solution



I basically got the same outcome as a adiabatic irreversible expansion identical to a isothermal equation but have a feeling the assumptions leading up that are wrong
 
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Hi wangchungman, welcome to PF!:smile:

wangchungman said:
I basically got the same outcome as a adiabatic irreversible expansion identical to a isothermal equation but have a feeling the assumptions leading up that are wrong

We can't tell you whether what you did was wrong or or not unless you actually show what you did... Post your calculations and explain in detail any assumptions your are making.
 

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