Why is the Entropy of the Universe (total entropy) a path function?

[Jimyoung]

Homework Statement

The question of the problem is "What if Delta S_{univ} was a state function? How would the world be different?"

Relevant Equations

Delta S_univ = Delta S + Delta S_sur

I understand that S (S_sys) is a state function but I can't understand why S_surr and S_univ (or S_tot) are a path function.

 

[jbriggs444]

Homework Statement:: The question is "What if Delta S_univ was a state function? How would the world be different?"
Relevant Equations:: Delta S_univ = Delta S + Delta S_sur

I understand that S (S_sys) is a state function but I can't understand why S_sur and S_univ are a path function.

Can you give us a little context on what you have been studying?

To me, "the Entropy of the universe" is not a well defined thing to begin with. If the universe is spatially infinite then surely the total entropy for some particular spatial slice (probably using the co-moving foliation) would be infinite as well?

So, instead, perhaps we are talking instead about entropy density on a sufficiently large scale that local variations are averaged out. But now are we talking about entropy density per fixed unit volume (say per cubic megaparsec)?

Or are we talking about total entropy in a fixed co-moving spatial volume. Say entropy per what is a cubic megaparsec now, was a smaller volume in the past and will be a larger volume in the future?

Or are we talking about a hypothetical "universe" that is a much more restrictive region to which we are restricting our attention. Like the "universe of this beaker" where we are performing a reaction?

Then we get to the meat of your homework. What is meant by $\Delta S_\text{univ}$? What does it mean when you assert that $\Delta S_\text{univ}$ is path function rather than a state function?

Are you asking, for instance, about the difference between the irreversible free expansion of a gas (e.g. a blowout of a tire) and a reversible expansion (e.g. deflating the same tire through a pump and a generator in order to charge a battery).

 

[Jimyoung]

I'm studying a book named "Chemistry" written by Zumdahl.
It said that $\Delta S_{univ} = \Delta S + \Delta S_{surr}$ and "In any spontaneous process there is always an increase in the entropy of the universe. This is the second law of thermodynamics."
I saw some books telling $\Delta S_{tot}$ rather than $\Delta S_{univ}$
In the isothermal, isobaric process, $\Delta S_{surr} = -\frac {\Delta H} T$ so $\Delta S_{univ}=-\frac {\Delta G} T$
My homework is, what will the world be if $\Delta S_{univ}$ is a state function, but I can't understand why it is a path function.

 

[jbriggs444]

I'm studying a book named "Chemistry" written by Zumdahl.
It said that $\Delta S_{univ} = \Delta S + \Delta S_{surr}$ and "In any spontaneous process there is always an increase in the entropy of the universe. This is the second law of thermodynamics."

Ahhh, very good. So he has in mind a classical model. A large, but not infinite, isolated system in a stationary space-time so that total entropy is well defined. i.e. a thermo problem, not a cosmology problem. With that, I have to step back and let someone competent in thermodynamics step forward.

 

[Chestermiller]

Why does the professor think that it is not a state function?

 

[Jimyoung]

Why does the professor think that it is not a state function?

I think he said that since $\Delta S_{surr} = \frac {q_{surr}} {T_{surr}}$ so $\Delta S_{surr}$ isn't a state function and that makes $\Delta S_{tot}$ a path function.
I'm not convinced by this explanation.

 

[Chestermiller]

I think he said that since $\Delta S_{surr} = \frac {q_{surr}} {T_{surr}}$ so $\Delta S_{surr}$ isn't a state function and that makes $\Delta S_{tot}$ a path function.
I'm not convinced by this explanation.

You shouldn't be convinced by this silly explanation. The equation you wrote for $\Delta S_{surr}$ applies to an ideal isothermal reservoir (which is typically how the surroundings are modeled). Assuming that the reservoir fluid is incompressible (also typical), $q_{surr}=\Delta U_{surr}$. In short, this means that $\Delta S_{surr}$ is always considered a function of state. In fact, S of the surroundings would be a function of state even if this limited model did not apply. Entropy is always a state function, since it is a physical property of the material under consideration.

 

[Jimyoung]

You shouldn't be convinced by this silly explanation. The equation you wrote for $\Delta S_{surr}$ applies to an ideal isothermal reservoir (which is typically how the surroundings are modeled). Assuming that the reservoir fluid is incompressible (also typical), $q_{surr}=Delta U_{surr}$. In short, this means that $\Delta S_{surr}$ is always considered a function of state. In fact, S of the surroundings would be a function of state even if this limited model did not apply. Entropy is always a state function, since it is a physical property of the material under consideration.

Ok, so your talking that $\Delta S_{surr}$ is a function of state, so the The problem itself doesn't work. Right?

 

[Chestermiller]

Ok, so your talking that $\Delta S_{surr}$ is a function of state, so the The problem itself doesn't work. Right?

I'm saying that entropy is always a function of state.