Entropy change for reversible and irreversible processes

[vcsharp2003]

TL;DR

Change in entropy for reversible and irreversible processes

I came across the following statement from the book Physics for Engineering and Science (Schaum's Outline Series).

I cannot seem to find a satisfactory answer to the questions.

1. Is the statement in above screenshot talking about entropy change the statement of Second Law of Thermodynamics or is it a conclusion based on definition of entropy?
2. If the statement of entropy change is the Second Law of Thermodynamics, then the entropy change truth needs to be accepted without any questions and we don't need to bother about the reasons why entropy changes occur in the way described. But, I still wonder how can entropy change for an irreversible process increase as per the statement in above screenshot, when this change depends only on the end points of the irreversible process that when joined by a reversible process will yield a 0 change in entropy as per the same statement for the system and it's surroundings.

 

[Chestermiller]

TL;DR Summary: Change in entropy for reversible and irreversible processes

I came across the following statement from the book Physics for Engineering and Science (Schaum's Outline Series).
View attachment 321092
I cannot seem to find a satisfactory answer to the questions.

1. Is the statement in above screenshot talking about entropy change the statement of Second Law of Thermodynamics or is it a conclusion based on definition of entropy?
2. If the statement of entropy change is the Second Law of Thermodynamics, then the entropy change truth needs to be accepted without any questions and we don't need to bother about the reasons why entropy changes occur in the way described. But, I still wonder how can entropy change for an irreversible process increase as per the statement in above screenshot, when this change depends only on the end points of the irreversible process that when joined by a reversible process will yield a 0 change in entropy as per the same statement for the system and it's surroundings.

The statement is messed up, and I disagree with the last sentence in the statement all-together.

When looking at the change in entropy for an irreversible process, you need to separate the system from the surroundings and subject each of them to new reversible paths separately. The reversible path for the system will be different from the reversible path for the surroundings.

See my Physics Forums Insights Articles
https://www.physicsforums.com/insights/understanding-entropy-2nd-law-thermodynamics/
and
https://www.physicsforums.com/insights/grandpa-chets-entropy-recipe/

 

[vcsharp2003]

The statement is messed up, and I disagree with the last sentence in the statement all-together.

When looking at the change in entropy for an irreversible process, you need to separate the system from the surroundings and subject each of them to new reversible paths separately. The reversible path for the system will be different from the reversible path for the surroundings.

See my Physics Forums Insights Articles
https://www.physicsforums.com/insights/understanding-entropy-2nd-law-thermodynamics/
and
https://www.physicsforums.com/insights/grandpa-chets-entropy-recipe/

As per the first article provided by you, it seems that the entropy change for any real process is less than or equal to the entropy change for a reversible process joining the end points of the real process. Is that what the article is saying? And furthermore, the entropy change is only for the thermodynamic system undergoing the real process and excludes it's surroundings.

 

[Chestermiller]

As per the first article provided by you, it seems that the entropy change for any real process is less than or equal to the entropy change for a reversible process joining the end points of the real process. Is that what the article is saying?

Basically, yes.

And furthermore, the entropy change is only for the thermodynamic system undergoing the real process and excludes it's surroundings.

The surroundings experiences a change in entropy too.. But that has to be calculated as ii the surroundings were a separate system.

It is important to recognize that entropy is a physical property of the material(s) comprising the system, defined at thermodynamic equilibrium. In this sense, it is analogous to internal energy U and enthalpy H. None of these depend directly on the manner (path) by which the material arrived at that state.

There are only two ways that the entropy of a system can change:

1. By heat transfer through the boundary between the system and its surroundings, at the boundary temperature $T_B$, such that the entropy transferred to the system is the integral of $dQ/T_B$. This mechanism is present in both reversible- and irreversible processes.

2. By entropy generation within the system $\sigma$. This mechanism is present only in irreversible processes.

So the entropy change a system for an irreversible process is $$\Delta S=\int{\frac{dQ}{T_B}}+\sigma$$

 

[vcsharp2003]

The surroundings experiences a change in entropy too.. But that has to be calculated as ii the surroundings were a separate system.

It's very confusing when it comes to Second Law of Thermodynamics. I have seen in some online sources that this law applies to a closed system, while other sources/textbooks say it applies to an isolated system. Who's correct is a big question mark.

But if we include system alongwith it's surroundings, we end up with an isolated system across whose boundary neither matter nor energy is exchanged. So, the system + surroundings is also another system. On the other hand, a closed system allows energy exchanges across it's boundary but no matter exchange. So, the fact that some books/online sources say this law applies to only closed systems while some say it applies to only isolated systems gets very, very confusing for a student studying this law for the first time.

I thought there would be one and only one statement for Second Law of Thermodynamics since a law must be uniform. It's like different sources are giving different interpretations for this law unlike the Newton's Laws of Motion which are so beautifully stated that there is zero chance of any confusion.

 

[DrClaude]

I thought there would be one and only one statement for Second Law of Thermodynamics since a law must be uniform. It's like different sources are giving different interpretations for this law unlike the Newton's Laws of Motion which are so beautifully stated that there is zero chance of any confusion.

The 2nd law is not a "law" in the common sense of the word in physics. It is fundamentally a statement about probabilities, a "statistical law" if you want. Small systems can (at least temporarily) break the 2nd law.

 

[vcsharp2003]

Small systems can (at least temporarily) break the 2nd law.

I see. I need to figure this out.

Do you know of an example where this law is violated?

 

[DrClaude]

I see. I need to figure this out.

Do you know of an example where this law is violated?

Some links:
https://www.nature.com/articles/news020722-2
https://www.scientificamerican.com/article/second-law-of-thermodynam/

Textbooks on statistical physics should give a description of how the second law emerges from statistical principles.

 

[vcsharp2003]

Some links:
https://www.nature.com/articles/news020722-2
https://www.scientificamerican.com/article/second-law-of-thermodynam/

Textbooks on statistical physics should give a description of how the second law emerges from statistical principles.

That's a surprising revelation for something that's called a law in Physics. I guess knowledge is always evolving.

 

[DrClaude]

That's a surprising revelation for something that's called a law in Physics. I guess knowledge is always evolving.

It is a question of domain of application. For any sufficiently big system (which in practice is actually quite small) the 2nd law applies. Not much different from Newton's laws that only apply if speed is low compared to c.

 

[256bits]

It's very confusing when it comes to Second Law of Thermodynamics. I have seen in some online sources that this law applies to a closed system, while other sources/textbooks say it applies to an isolated system. Who's correct is a big question mark.

But if we include system alongwith it's surroundings, we end up with an isolated system across whose boundary neither matter nor energy is exchanged. So, the system + surroundings is also another system. On the other hand, a closed system allows energy exchanges across it's boundary but no matter exchange. So, the fact that some books/online sources say this law applies to only closed systems while some say it applies to only isolated systems gets very, very confusing for a student studying this law for the first time.

While it is being taught to you in a lecture it is kinda like that makes sense and understandable.
And then they give you a problem to solve and you are, wait, what, let's go over this again.

 

[vcsharp2003]

It is a question of domain of application. For any sufficiently big system (which in practice is actually quite small) the 2nd law applies. Not much different from Newton's laws that only apply if speed is low compared to c.

Yes that makes a lot of sense. It's like saying that a law in Physics can have limitations but still is true in many situations.

 

[Chestermiller]

It's very confusing when it comes to Second Law of Thermodynamics. I have seen in some online sources that this law applies to a closed system, while other sources/textbooks say it applies to an isolated system. Who's correct is a big question mark.

The form of the equation I wrote applies to a closed system: $$\Delta S=\int{\frac{dQ}{T_B}}+\sigma$$
When we consider a system and surroundings, we can regard "the system" as System A,, and its surroundings as a separate system, System B. System B is the surroundings for System A, and system A is the surroundings for System B. So we have, $$\Delta S_A=\int{\frac{dQ_A}{T_{BA}}}+\sigma_A$$and$$\Delta S_B=\int{\frac{dQ_B}{T_{BB}}}+\sigma_B$$But, since Systems A and B are a complementary system and surroundings, $$Q_B=-Q_A$$and$$T_{BB}=T_{BA}$$we have $$\Delta S_A+\Delta S_B=\sigma_A+\sigma _B$$So for an isolated system consisting of System A (system) and System B (surroundings), the entropy change is positive.

But if we include system alongwith it's surroundings, we end up with an isolated system across whose boundary neither matter nor energy is exchanged. So, the system + surroundings is also another system. On the other hand, a closed system allows energy exchanges across it's boundary but no matter exchange. So, the fact that some books/online sources say this law applies to only closed systems while some say it applies to only isolated systems gets very, very confusing for a student studying this law for the first time.

So there are two versions of the law, depending on whether we are talking about a closed system or an isolated system. Big deal!!

I thought there would be one and only one statement for Second Law of Thermodynamics since a law must be uniform. It's like different sources are giving different interpretations for this law unlike the Newton's Laws of Motion which are so beautifully stated that there is zero chance of any confusion.

The version I always work with is the closed system version, which is easier to use in solving problems.