# Question on entropy in adiabatic phase change

• RoboNerd
In summary, the conversation discusses a closed, adiabatic system at equilibrium consisting of a mixture of liquid and solid substance Z at its melting point. The question is which statement is true regarding the system's entropy. The correct answer is A, as at equilibrium, the entropy of the system is at a maximum, according to the laws of thermodynamics. This is because reactions will always seek to increase the entropy of the universe until it reaches a maximum at equilibrium.

## 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.

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!

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!

## What is entropy?

Entropy is a measure of the disorder or randomness in a system. It is a thermodynamic property that describes the distribution of energy in a system and the likelihood of different states occurring.

## How is entropy related to adiabatic phase change?

In an adiabatic phase change, there is no transfer of heat between the system and its surroundings. This means that the change in entropy is solely determined by the change in internal energy of the system. As the system undergoes a phase change, the distribution of energy within the system changes, resulting in a change in entropy.

## Why is entropy important in thermodynamics?

Entropy is important in thermodynamics because it helps to determine the direction and extent of energy transfer in a system. It is also a fundamental concept in the second law of thermodynamics, which states that the total entropy of a closed system will always increase over time.

## How is entropy calculated in an adiabatic process?

In an adiabatic process, the change in entropy can be calculated using the formula ΔS = q/T, where q is the heat transferred and T is the temperature of the system. Since no heat is transferred in an adiabatic process, the change in entropy is equal to zero.

## Can entropy be reversed in an adiabatic phase change?

No, entropy cannot be reversed in an adiabatic phase change. The second law of thermodynamics states that the total entropy of a closed system will always increase over time. This means that the entropy of a system can decrease in one process, but it will always increase in another process.