Question on entropy in adiabatic phase change

[RoboNerd]

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!

 

[Ygggdrasil]

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?

 

[RoboNerd]

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?

 

[Ygggdrasil]

What do the laws of thermodynamics say?

 

[RoboNerd]

Entropy of universe always increases for a spontaneous process except for equilibrium. In that case delta S = 0.

 

[Ygggdrasil]

Right, so if entropy always increases until the system reaches equilibrium, then equilibrium represents a...

 

[RoboNerd]

Maximum. Right?

 

[Ygggdrasil]

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.

 

[RoboNerd]

Aha that makes sense! Thanks!