Question on entropy in adiabatic phase change

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Discussion Overview

The discussion revolves around the concept of entropy in a closed, adiabatic system at equilibrium during a phase change, specifically focusing on a mixture of solid and liquid substance Z at its melting point. Participants explore the implications of entropy changes in relation to thermodynamic principles.

Discussion Character

  • Homework-related
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant suggests that the entropy change for a reversible process is zero at constant temperature, supporting answer choice E.
  • Another participant agrees that at equilibrium, the change in entropy over time is zero, prompting a consideration of the implications for the system's entropy.
  • Some participants propose that the entropy could be at a maximum or minimum, indicating uncertainty about the correct answer between A and B.
  • It is mentioned that the laws of thermodynamics state that the entropy of the universe increases for spontaneous processes, except at equilibrium where delta S equals zero.
  • Participants discuss that equilibrium represents a maximum entropy state, suggesting that reactions seek to increase entropy until reaching this point.

Areas of Agreement / Disagreement

There is no clear consensus on whether the entropy of the system is at a maximum or minimum, as participants express differing views on the implications of the second derivative and the laws of thermodynamics.

Contextual Notes

Participants do not fully resolve the implications of the second derivative in relation to entropy, and there are unresolved assumptions regarding the definitions of maximum and minimum entropy in this context.

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Homework Statement



Consider a closed, adiabatic system consisting of a mixture of liquid and solid substance Z at equilibrium at its melting point.

Z (solid) <---------> Z (liquid)

Which of the following statements is true regarding the system?

A) The entropy of the system is at a maximum
B) The entropy of the system is at a minimum
C) The entropy of the system will increase over time.
D) The entropy of the system is zero
E) the entropy of pure substances does not change if at a constant temperature.

Homework Equations



none

The Attempt at a Solution


[/B]
I put down my answer as being E. The entropy change for a reversible process is zero according to the second law of thermodynamics, so because my temperature is the same while melting, this answer choice makes sense.

However, my review book gave me A as being the correct explanation and then did not bother to explain this at all to me why the entropy of the system is at a maximum.

Could anyone please explain why this is the case and share their thoughts with me?

Thanks!
 
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You are correct that at equilibrium, the change in entropy over time is zero. From your knowledge of calculus, if dS/dt = 0, what does that tell you about the entropy (S) of the system?
 
Well it could be at a max or at a min. I could take the second derivative, but that is just complicating things.

So I can choose between A or B now. Thoughts?
 
What do the laws of thermodynamics say?
 
Entropy of universe always increases for a spontaneous process except for equilibrium. In that case delta S = 0.
 
Right, so if entropy always increases until the system reaches equilibrium, then equilibrium represents a...
 
Maximum. Right?
 
Yes. Reactions will always seek to increase the entropy of the universe until it reaches the point where the entropy is at its maximum and can't increase any more. At this point, the system is at equilibrium.
 
Aha that makes sense! Thanks!
 

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