Entropy question involving our Solar System

[gptejms]

TL;DR

Which is a higher entropy state: solar system as it is today with planets going around the sun at fixed distances in an orderly manner
OR
all the planets and sun bumping into one another forming a single body?

Which is a higher entropy state: solar system as it is today with planets going around the sun at fixed distances in an orderly fashion OR all the planets and sun bumping into one another and forming a single body?

If the entropy of the combined single body is higher, why doesn't the solar system move towards this direction. Should we even talk of entropy here as the concept is normally applied to a gas of free particles/ molecules?

 

[Dale]

It doesn’t really matter which of those two situations is higher entropy. The second situation doesn’t conserve angular momentum so it isn’t possible regardless of entropy. The second law of thermodynamics is not the only law that must be obeyed.

That said, everything collapsed to the center would probably be lower entropy since the energy would be more concentrated, the average temperature would be higher, and more gravitational work would have been done thus reducing entropy.

 

[russ_watters]

If the entropy of the combined single body is higher, why doesn't the solar system move towards this direction. Should we even talk of entropy here as the concept is normally applied to a gas of free particles/ molecules?

Entropy doesn't have goals and isn't a force. There's an infinite number of potential states of a system that may have different entropies, and there may or may not be anything even connecting the states, much less driving the system from one state to another*. So ask yourself what would cause the planets' orbits to be unstable and spiral into the Sun.

*Though now that I say that, I see it looks more like different systems that share similarities. Semantics.

 

[gptejms]

It doesn’t really matter which of those two situations is higher entropy. The second situation doesn’t conserve angular momentum so it isn’t possible regardless of entropy. The second law of thermodynamics is not the only law that must be obeyed.

That said, everything collapsed to the center would probably be lower entropy since the energy would be more concentrated, the average temperature would be higher, and more gravitational work would have been done thus reducing entropy.

Gravitational potential energy becomes more negative on collapse-- so energy should be released-- most of it going into the kinetic energy of the constituent particles and eventually into heat energy when these particles collide. So overall, the entropy of the universe will increase even though the entropy of the collapsed mass is low.

A question that follows is: why is the black hole thought to be such high entropy?

 

[anorlunda]

Gravitational collapse of a gas cloud is a difficult case. The collapse can not happen unless it radiates away a portion of its energy.

Conservation of energy needs to include those radiated photons.

Analysis of order/disorder entropy needs to include those radiated photons.

 

[Dale]

So overall, the entropy of the universe will increase even though the entropy of the collapsed mass is low.

Yes, exactly. The SLOT doesn't say that low entropy states cannot occur, just that the entropy of the universe as a whole increases. In this case, you would need to consider the entropy of the released thermal radiation as well as the entropy of the central body.

 

[gptejms]

Yes, exactly. The SLOT doesn't say that low entropy states cannot occur, just that the entropy of the universe as a whole increases. In this case, you would need to consider the entropy of the released thermal radiation as well as the entropy of the central body.

Someone needs to clarify!

 

[Dale]

Someone needs to clarify!

Clarify what?

 

[gptejms]

Clarify what?

Black hole entropy

 

[gptejms]

It doesn’t really matter which of those two situations is higher entropy. The second situation doesn’t conserve angular momentum so it isn’t possible regardless of entropy. The second law of thermodynamics is not the only law that must be obeyed.

That said, everything collapsed to the center would probably be lower entropy since the energy would be more concentrated, the average temperature would be higher, and more gravitational work would have been done thus reducing entropy.

So Is conservation of angular momentum at odds with the natural tendency of a system to move towards higher entropy? Or simply that bodies in circular/elliptical motion due to centripetal force resist changes in entropy? I know that seems a rather dumb way of putting it, but what I am trying to drive at is this: is the second law of thermodynamics not applicable beyond typical examples like 'gas of particles/molecules'?

 

[gptejms]

Entropy doesn't have goals and isn't a force. There's an infinite number of potential states of a system that may have different entropies, and there may or may not be anything even connecting the states, much less driving the system from one state to another*. So ask yourself what would cause the planets' orbits to be unstable and spiral into the Sun.

*Though now that I say that, I see it looks more like different systems that share similarities. Semantics.

It may not be a force, but a strong tendency of a system( specially a gas of molecules).

 

[Dale]

Black hole entropy

I cannot help you there.

So Is conservation of angular momentum at odds with the natural tendency of a system to move towards higher entropy? Or simply that bodies in circular/elliptical motion due to centripetal force resist changes in entropy? I know that seems a rather dumb way of putting it, but what I am trying to drive at is this: is the second law of thermodynamics not applicable beyond typical examples like 'gas of particles/molecules'?

The SLOT is applicable to any systems that have very many internal degrees of freedom that we want to ignore. The various conservation laws are applicable to all systems. I don't know what "at odds with" means in this context. Any real system satisfies all of the applicable laws together.

The SLOT doesn't say that systems must move towards higher entropy, nor that there is some force driving an increase in entropy. It says only that the entropy of an isolated system (or the universe) doesn't decrease. So the SLOT is perfectly happy with a gas cloud collapsing to a star or to a star + planets. In both cases the entropy of the universe doesn't decrease. So by the SLOT there is no particular preference for either outcome, regardless of the fact that they have different final entropies.

 

[russ_watters]

It may not be a force, but a strong tendency of a system( specially a gas of molecules).

"A strong tendancy" is not a mechanism. Entropy is not a verb. When someone asks, "why does a gas expand to fill a container?", the answer isn't "entropy", it's "because pressure pushes it to expand".

 

[gptejms]

"A strong tendancy" is not a mechanism. Entropy is not a verb. When someone asks, "why does a gas expand to fill a container?", the answer isn't "entropy", it's "because pressure pushes it to expand".

Ok, some systems have a strong tendency to increase their entropy or move towards configurations that have higher entropy, whatever be the driving mechanism. But some systems are just happy with a constant entropy, or decreasing entropy (if the total entropy of the universe increases). Right sir?

 

[gptejms]

I cannot help you there.

The SLOT is applicable to any systems that have very many internal degrees of freedom that we want to ignore. The various conservation laws are applicable to all systems. I don't know what "at odds with" means in this context. Any real system satisfies all of the applicable laws together.

The SLOT doesn't say that systems must move towards higher entropy, nor that there is some force driving an increase in entropy. It says only that the entropy of an isolated system (or the universe) doesn't decrease. So the SLOT is perfectly happy with a gas cloud collapsing to a star or to a star + planets. In both cases the entropy of the universe doesn't decrease. So by the SLOT there is no particular preference for either outcome, regardless of the fact that they have different final entropies.

How many degrees of freedom? Can you quantify it? Solar system with just nine planets and a sun won't qualify-- right?

 

[russ_watters]

Ok, some systems have a strong tendency to increase their entropy or move towards configurations that have higher entropy, whatever be the driving mechanism. But some systems are just happy with a constant entropy, or decreasing entropy (if the total entropy of the universe increases). Right sir?

Yes.

For example, there is a book sitting on my desk. The entropy of the book-earth system would be higher if the book were sitting on the floor. This tells us nothing whatsoever about how likely the book is to end up sitting on the floor.

 

[gptejms]

Yes.

For example, there is a book sitting on my desk. The entropy of the book-earth system would be higher if the book were sitting on the floor. This tells us nothing whatsoever about how likely the book is to end up sitting on the floor.

Why would it be higher on the floor?

 

[russ_watters]

Why would it be higher on the floor?

Because in the act of transferring the book from the table to the floor, I dissipate gravitational potential energy irreversibly as heat.

[Edit] I said the above quoted part wrong. Entropy of the system is lower, but heat is transferred out of the system, increasing the entropy of the universe.

Note: I'm an engineer and we don't think of entropy statistically like physicists do. For us it is more about low and high grade (usable) energy.

 

[gptejms]

Because in the act of transferring the book from the table to the floor, I dissipate gravitational potential energy irreversibly as heat.

[Edit] I said the above quoted part wrong. Entropy of the system is lower, but heat is transferred out of the system, increasing the entropy of the universe.

Right. Now a question that follows is: why is a black hole so high entropy when all of the gravitational potential energy should have been transferred out as heat?

 

[russ_watters]

Right. Now a question that follows is: why is a black hole so high entropy when all of the gravitational potential energy should have been transferred out as heat?

I'll leave that to a physicist, but a quick Google suggests this is still an active area of investigation for them.

 

[anorlunda]

but what I am trying to drive at is this: is the second law of thermodynamics not applicable beyond typical examples like 'gas of particles/molecules'?

From
https://en.wikipedia.org/wiki/Thermodynamics

Thermodynamics applies to a wide variety of topics in science and engineering, especially physical chemistry, biochemistry, chemical engineering and mechanical engineering, but also in other complex fields such as meteorology.
...
Classical thermodynamics is the description of the states of thermodynamic systems at near-equilibrium,

So equilibrium is part of it. For example, thermodynamics is not adequate to model an explosion inside of a room -- that is very non-equilibrium.

How many degrees of freedom? Can you quantify it? Solar system with just nine planets and a sun won't qualify-- right?

How many people does it take to meaningfully talk about the "average" person? The more the count, the easier it is to apply statistics.

The solar system did not begin as 9 planets plus a star. It began as a gas cloud with a huge number of particles. The gas cloud phase is where thermodynamics is most easily applied.

 

[gptejms]

From
https://en.wikipedia.org/wiki/ThermodynamicsSo equilibrium is part of it. For example, thermodynamics is not adequate to model an explosion inside of a room -- that is very non-equilibrium.

But you do have nonequilibrium thermodynamics/ statistical physics. We also talk of entropy of the early universe, and also at t=0.

 

[gptejms]

The solar system did not begin as 9 planets plus a star. It began as a gas cloud with a huge number of particles. The gas cloud phase is where thermodynamics is most easily applied.

Yes, solar system doesn't qualify as a thermodynamic system as it has very few degrees of freedom. But my point is even if it had a thousand planets and one giant star, it still wouldn't qualify as a thermodynamic system-- there is no random motion of the constituent particles/planets.

 

[Nugatory]

So Is conservation of angular momentum at odds with the natural tendency of a system to move towards higher entropy? Or simply that bodies in circular/elliptical motion due to centripetal force resist changes in entropy?

Neither.
The informal way of thinking about the relationship between dynamical laws and entropy increase is to start with the example of fifty coins placed heads-up and then shaken: we expect the system to evolve towards a mix of heads-up and heads-down (that's entropy increasing) but we still have fifty coins (that's a conservation law). Same thing with angular momentum: the entropy of a system can increase even though angular momentum is conserved.

what I am trying to drive at is this: is the second law of thermodynamics not applicable beyond typical examples like 'gas of particles/molecules'?

The second law is always applicable, but you'll have to unlearn the informal definition of entropy as "disorder" and learn the more precise definition in terms of accessible microstates. You'll encounter this fairly early in an undergraduate statistical mechanics class.

 

[Dale]

How many degrees of freedom? Can you quantify it? Solar system with just nine planets and a sun won't qualify-- right?

The more degrees of freedom you want to ignore the better. There isn’t a hard cutoff, but millions or more should be plenty for the various theorems of statistical mechanics to hold.

 

[gptejms]

Neither.
The informal way of thinking about the relationship between dynamical laws and entropy increase is to start with the example of fifty coins placed heads-up and then shaken: we expect the system to evolve towards a mix of heads-up and heads-down (that's entropy increasing) but we still have fifty coins (that's a conservation law). Same thing with angular momentum: the entropy of a system can increase even though angular momentum is conserved.The second law is always applicable, but you'll have to unlearn the informal definition of entropy as "disorder" and learn the more precise definition in terms of accessible microstates. You'll encounter this fairly early in an undergraduate statistical mechanics class.

Know this basic stuff very well! Reason for posing this question was to understand if the concept of entropy can be applied everywhere. My opinion is that a solar system with very few degrees of freedom (just 10 entities) and no random motion doesn't qualify for thermodynamic analysis-- you guys may have a different opinion.

 

[anorlunda]

My opinion is that a solar system with very few degrees of freedom (just 10 entities) and no random motion doesn't qualify for thermodynamic analysis-- you guys may have a different opinion.

Think ashes to ashes, dust to dust. (No religion intended.)

Our solar system began as dust which is well described by thermodynamics. At the moment, the sun and planets are in a state where thermodynamic analysis is less helpful. Sometime in the distant future, the remnants of our solar system may once again be best described by thermodynamics.

You should understand that physics is interested in what is useful, and less in what is true. Thermodynamics is more useful in some cases and less useful in others. Do you need more answer than that?

 

[gptejms]

Think ashes to ashes, dust to dust. (No religion intended.)

Our solar system began as dust which is well described by thermodynamics. At the moment, the sun and planets are in a state where thermodynamic analysis is less helpful. Sometime in the distant future, the remnants of our solar system may once again be best described by thermodynamics.

You should understand that physics is interested in what is useful, and less in what is true. Thermodynamics is more useful in some cases and less useful in others. Do you need more answer than that?

Not less helpful, it just doesn't apply.

 

[James Demers]

It may not be a force, but a strong tendency of a system

Its a statistically-favored outcome, not a physical tendency. As has been pointed out, there needs to be an energetically feasible path between two states, regardless of the magnitude of the entropy difference between them. There's no feasible path for the collapse of a solar system: the energy required to halt a planet in its orbit, so that it can fall into the central star (what a chemist would call the activation energy) is never going to be available.

 

[gptejms]

Its a statistically-favored outcome, not a physical tendency. As has been pointed out, there needs to be an energetically feasible path between two states, regardless of the magnitude of the entropy difference between them. There's no feasible path for the collapse of a solar system: the energy required to halt a planet in its orbit, so that it can fall into the central star (what a chemist would call the activation energy) is never going to be available.

In a way, we can say that the system is non-ergodic because of gravitational interactions(specific paths) and normal laws of statistical physics and concepts like entropy don't apply. The same would be true if we had a thousand planets going around the sun.So is it meaningful to talk of entropy of the universe as a whole?