Does gravity defy the 2nd Law?

[Gerinski]

Summary: Trying to understand the relationship between gravity, thermodynamics and entropy, thank you.

Gravity can take a diffuse cloud of gas filling a given volume of space at equilibrium density and temperature, and turn it into a burning star surrounded by empty space. Does this mean that gravity can defy the 2nd Law? Is a burning star really a higher entropy state than the original cloud of diffuse hydrogen and helium gas?
Thank you.

 

[Orodruin]

Does this mean that gravity can defy the 2nd Law?

No. The second law holds for an isolated system. Your system is not isolated. A lot of entropy is removed from the system in the form of radiation.

 

[Gerinski]

Thanks, so you mean that if we took a huge space container full of hydrogen and helium gas, isolated from everything else, a star would never form by gravitational collapse? Because of the impossibility to radiate to any external environment?

 

[Orodruin]

I don’t know what a ”huge space container” implies so I cannot answer that question.

 

[Chestermiller]

The 2nd law says that the entropy of an isolated system cannot decrease. It can, of course, increase.

 

[Demystifier]

Is a burning star really a higher entropy state than the original cloud of diffuse hydrogen and helium gas?

Yes. After all, the star has a higher temperature, so it should not be strange that it also has a higher entropy. You probably thought that the star could have a lower entropy because it has a lower spatial 3-volume than the initial gas. But you should really think in phase space, not in the 3-space. Larger temperature means that particles have larger average momenta, which also implies that the momenta span over a larger set of values. As a result, the total coarse-grained volume in phase space is larger for the star than for the initial gas.

 

[erobz]

So is the star a more disordered state of matter than the gas cloud?

 

[Demystifier]

So is the star a more disordered state of matter than the gas cloud?

Yes.

 

[Demystifier]

Let me also present a simple analog without gravity. Consider two metal balls at zero temperature, one positively charged and another negatively charged. Due to zero temperature, the initial entropy is essentially zero. But due to charge they attract each other, so they accelerate and eventually collide. In the collision, a part of their kinetic energy transforms into thermal energy, which increases temperature and entropy of the balls.

 

[erobz]

Let me also present a simple analog without gravity. Consider two metal balls at zero temperature, one positively charged and another negatively charged. Due to zero temperature, the initial entropy is essentially zero. But due to charge they attract each other, so they accelerate and eventually collide. In a collision, a part of their kinetic energy transforms into thermal energy, which increases temperature and entropy of the balls.

The charge is a form of entropy, correct? I assume that is why you say the entropy is "essentially" zero in the initial state.

EDIT: I guess the charge asymmetry would be a low entropy state. But this leads me to now asking what orders the initial charge? If we count that, it isn't as clear what the total change in entropy was in this scenario.

 

[Chestermiller]

Yes. After all, the star has a higher temperature, so it should not be strange that it also has a higher entropy. You probably thought that the star could have a lower entropy because it has a lower spatial 3-volume than the initial gas. But you should really think in phase space, not in the 3-space. Larger temperature means that particles have larger average momenta, which also implies that the momenta span over a larger set of values. As a result, the total coarse-grained volume in phase space is larger for the star than for the initial gas.

In addition to this, a chemical reaction has taken place.

 

[erobz]

But was there spatially a decrease in entropy in the collapse of a star or not? It seems like all the matter was there in the cloud, and the chemical reaction @Chestermiller speaks of are toward increased entropy, which only begins after the collapse.

 

[anorlunda]

Thanks, so you mean that if we took a huge space container full of hydrogen and helium gas, isolated from everything else, a star would never form by gravitational collapse? Because of the impossibility to radiate to any external environment?

Yes. That's right.From The Potato Radius: a Lower Minimum Size for Dwarf Planets

Gravity alone cannot make things collapse. To collapse “gravitationally”, material has to get rid of energy and angular momentum. Only when dissipative structures and/or processes (accretion disks, viscosity, friction, magnetic breaking, inelastic collisions, dynamical friction) act to export energy and angular momentum, can an object collapse

 

[Demystifier]

The charge is a form of entropy, correct? I assume that is why you say the entropy is "essentially" zero in the initial state.

EDIT: I guess the charge asymmetry would be a low entropy state. But this leads me to now asking what orders the initial charge? If we count that, it isn't as clear what the total change in entropy was in this scenario.

Well, thermal entropy is zero despite the charges. Some kind of statistical entropy can be nonzero due to charges, but it depends on how exactly do you define entropy. Hence it's hard to quantify it.

 

[Gerinski]

In addition to this, a chemical reaction has taken place.

You probably meant a nuclear reaction.

 

[Gerinski]

Yes. That's right.

Well I was assuming a volume of space full of hydrogen and helium at stabilized pressure and temperature, in principle without any angular momentum. So, a star would never form from such a cloud of gas right?

Also, and more speculatively, does that mean that stars could not form in a contracting universe? Because of such impossibility of radiating heat away?

Thanks,

 

[Lord Jestocost]

Well I was assuming a volume of space full of hydrogen and helium at stabilized pressure and temperature, ...

How will you stabilize the temperature in your volume of hydrogen and helium? If $T$ and $V$ are conserved, then the Helmholtz (free) energy of your system is minimal in equilibrium.

 

[PeroK]

Well I was assuming a volume of space full of hydrogen and helium at stabilized pressure and temperature, in principle without any angular momentum. So, a star would never form from such a cloud of gas right?

Unless you change the laws of physics, I don't see how a cloud of ordinary matter would not collapse.

Also, and more speculatively, does that mean that stars could not form in a contracting universe? Because of such impossibility of radiating heat away?

Thanks,

Why would radiation be impossible in contracting universe?

 

[Vanadium 50]

First, a lot of people in this thread are treating entropy as a qualitative thing - one where we tall ourselves a story about what seems ordered and disordered to us. Nope. It's a quantitative...um...quantity.

Second, the heat capacity of an object undergoing gravitational collapse is negative. As it loses energy, the temperature goes up, not down.

Third, a photon bath at temperature T is emitted from the collapsing cloud. That's how we see it. Ignoring this in our calculations or even our stories is as wrong as wronng can be. Let's ignore the only part of the system we catually observe" is not very smart.

 

[Gerinski]

Thanks to all, I'm just trying to improve my understanding, but I seem to receive contradictory answers. Anorlunda says such an hypothetical cloud of gas will never undergo gravitational collapse (if I understood him/her correctly, because it could not radiate heat away to any "external environment"). PeroK on the other hand says "unless you change the laws of physics, I don't see how a cloud of ordinary matter would not collapse".

Even if we dismiss the star's ignition (and therefore the nuclear reactions involved) and look only at gravitational aggregation of ordinary matter, intuitively one would think that a small and dense clump of all the gas concentrated in a small region of space and surrounded by empty and colder space, is a lower entropy state than a diffuse could of the same gas spread evenly across all the volume of available space at even temperature and pressure, which (perhaps naively) seems to me to be thermodynamical equilibrium. I know that "intuitively" speaking of entropy is likely to be misleading, but again, I'm just trying to better educate myself.

So perhaps to refine the original question, "starting from a cloud of hydrogen and helium gas at thermodynamical equilibrium, would gravitation cause it to gradually collapse?". And if so, is that collapse an increase in the entropy of the system?

Thank you.

 

[256bits]

Thanks to all, I'm just trying to improve my understanding, but I seem to receive contradictory answers. Anorlunda says such an hypothetical cloud of gas will never undergo gravitational collapse (if I understood him/her correctly, because it could not radiate heat away to any "external environment"). PeroK on the other hand says "unless you change the laws of physics, I don't see how a cloud of ordinary matter would not collapse".

There is the jean's instability for gas clouds.
https://en.wikipedia.org/wiki/Jeans_instability

Even if we dismiss the star's ignition (and therefore the nuclear reactions involved) and look only at gravitational aggregation of ordinary matter,

Think of a star as a high temperature dense gas cloud. Stars are stable for quite some time with the Qin from reactions = Qout from the radiation from the surface. The ignition prevents further collapse.

 

[256bits]

Yes. After all, the star has a higher temperature, so it should not be strange that it also has a higher entropy. You probably thought that the star could have a lower entropy because it has a lower spatial 3-volume than the initial gas. But you should really think in phase space, not in the 3-space. Larger temperature means that particles have larger average momenta, which also implies that the momenta span over a larger set of values. As a result, the total coarse-grained volume in phase space is larger for the star than for the initial gas.

I was under the impression that as a gas cloud contracts, the entropy of the cloud decreases. The increase in velocity can't keep up with decrease in position of the constituent particles.

 

[Algr]

So is the star a more disordered state of matter than the gas cloud?

The correct comparison includes the star, but also all the light and energy it has already radiated. So the original gas cloud system isn't contracting, it is expanding in every direction at the speed of light. Since the star alone is only a fraction of the original gas cloud, it can be more ordered then the cloud as a whole because the disorder is elsewhere.

 

[PeroK]

Thanks to all, I'm just trying to improve my understanding, but I seem to receive contradictory answers. Anorlunda says such an hypothetical cloud of gas will never undergo gravitational collapse (if I understood him/her correctly, because it could not radiate heat away to any "external environment"). PeroK on the other hand says "unless you change the laws of physics, I don't see how a cloud of ordinary matter would not collapse".

Ordinary matter interacts electromagnetically, which allows matter to clump. Whereas, dark matter does not clump so cannot form stars, planets or potatoes.

 

[Algr]

Whereas, dark matter does not clump so cannot form stars, planets or potatoes.

I don't think anyone was discussing dark matter. Dark matter stars don't form because you need friction to turn the momentum energy of particles into heat, thus slowing them down and giving them all similar physical locations.

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a huge space container full of hydrogen and helium gas, isolated from everything else

Doesn't the universe as a whole fit this description? I suspect that stars would form even if the universe was not expanding. Having every particle gravitationally balanced against the others reminds me of a pencil balancing on it's tip.

 

[Gerinski]

The correct comparison includes the star, but also all the light and energy it has already radiated. So the original gas cloud system isn't contracting, it is expanding in every direction at the speed of light. Since the star alone is only a fraction of the original gas cloud, it can be more ordered then the cloud as a whole because the disorder is elsewhere.

Forget the ignited star then, let's consider only the collapsing cloud of gas before it has ignited. It has not yet released any huge radiation except for thermal photons.

 

[Vanadium 50]

Anorlunda says such an hypothetical cloud of gas will never undergo gravitational collapse (if I understood him/her correctly, because it could not radiate heat away to any "external environment").

Wait a second.

You yourself posed a scenario where there was a cloud of gas was placed into a situation where - as part of the problem - could not radiate. @anorlunda correctly replied that it could not collapse (and by the way, this has nothing to do with entropy. Just energy).

Now you turn around and apply his answer to the situation where it can radiate energy.

Complaining that it is "contradictory" when it is all your doing is a little like the old joke where the criminal kills his parents and asks for leniency on the grounds that he's an orphan.

 

[PeroK]

I don't think anyone was discussing dark matter. Dark matter stars don't form because you need friction to turn the momentum energy of particles into heat,

Dark matter is relevant because it exemplifies the point that gravity alone is not enough for star and planet formation. Electromagnetic interaction is also required. And, crucially, ordinary matter does interact.

This point appears to have been missed by OP.

 

[Gerinski]

Wait a second.

You yourself posed a scenario where there was a cloud of gas was placed into a situation where - as part of the problem - could not radiate. @anorlunda correctly replied that it could not collapse (and by the way, this has nothing to do with entropy. Just energy).

Now you turn around and apply his answer to the situation where it can radiate energy.

Complaining that it is "contradictory" when it is all your doing is a little like the old joke where the criminal kills his parents and asks for leniency on the grounds that he's an orphan.

I never stated that the cloud of gas could or could not radiate, that came only in some of the answers such as Anorlunda's.

Personally, even now I do not see why such a gravitationally coalescing cloud of gas could not radiate to its immediate environment in the rest of the container.

 

[256bits]

Now you turn around and apply his answer to the situation where it can radiate energy.

I beg to differ.
The reason the core reaches a temperature of 15 million K to initiate ignition for a 1M star is because the core cannot radiate away the energy as heat. If the energy was radiated away the collapse would be an isothermal process.