Why Is Reversibility Essential for Using dS=δQ/T?

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SUMMARY

Reversibility is essential for using the equation dS=δQ/T because it allows for accurate calculation of entropy changes. While the change in entropy (S) is the same regardless of the path taken between states A and B, the integral TdS must be evaluated along a reversible path to ensure correctness. E. Fermi's book "Thermodynamics" illustrates that the integral for irreversible changes yields a lesser value than for reversible changes, emphasizing the importance of reversibility in thermodynamic calculations.

PREREQUISITES
  • Understanding of thermodynamic concepts, specifically entropy and state variables.
  • Familiarity with the first and second laws of thermodynamics.
  • Knowledge of integration techniques in calculus.
  • Basic comprehension of reversible and irreversible processes in thermodynamics.
NEXT STEPS
  • Study E. Fermi's "Thermodynamics" for a deeper understanding of entropy and its calculations.
  • Learn about the implications of irreversible processes on thermodynamic systems.
  • Explore the mathematical foundations of integrating thermodynamic equations.
  • Research the differences between reversible and irreversible transformations in detail.
USEFUL FOR

Students of thermodynamics, educators teaching thermodynamic principles, and professionals working in fields requiring thermodynamic analysis will benefit from this discussion.

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Homework Statement



In my book it says, "only if the transformation is reversible can we use dS=\frac{\delta Q}{T}", but I don't know why? I think even if it's not reversible we also use \delta Q=TdS to solve the thermo problems, don't we?

I'm looking forward to your ideas, thanks.
 
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Entropy is a state variable. That means that, no matter how we get from state A to state B, the change in S is the same. Doesn't matter if the change is reversible or not.

The point is that in order to CALCULATE the change in S, you must integrate along a reversible path.

In fact, the integral TdS from state A to B is always less for an irreversible change than for a reversible one. E. Fermi proves this in his Dover book "Thermodynamics' but I never followed the proof. Since the states are undefined for an irreversible change I don't lose too much sleep over it. But Fermi actually invokes that fact later in the book on a different topic.

If you want to get totally snowed, that is the book for you!
 

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