Entropy

[RichIsnang]

If you take a large cloud of gas in space (nebula), it has very high entropy.

Once it starts to attract itself through gravity, its entropy decreases.

When it gets hot enough to form a star, does it have even lower entropy?

and at the end of its life cycle does, lets say this particular star turns into a neutron star, neutron stars have extremely low entropy right?

so gravity lowers entropy, so why is it proposed that black holes have maximum entropy?

it seems to me, even if you took all the possible combinations of particles inside the event horizon, this would still be lower entropy than if all the mass in the form of a star.

Edited April 26, 2012 by RichIsnang

[swansont]

If you take a large cloud of gas in space (nebula), it has very high entropy.

 

I don't think this is inherently true, but can be taken as an initial condition.

 

Once it starts to attract itself through gravity, its entropy decreases.

When it gets hot enough to form a star, does it have even lower entropy?

 

In order to form a star, it needs to radiate away energy in order to form a bound system. That radiation is going to have entropy, which leaves the system.

 

and at the end of its life cycle does, lets say this particular star turns into a neutron star, neutron stars have extremely low entropy right?

so gravity lowers entropy, so why is it proposed that black holes have maximum entropy?

it seems to me, even if you took all the possible combinations of particles inside the event horizon, this would still be lower entropy than if all the mass in the form of a star.

 

Gravity by itself doesn't lower entropy. This is just a guess, but since the mass inside a black hole cannot radiate away any energy, this has something to do with the high entropy of the black hole.

[studiot]

I don't see why a cloud of gas, small or large, has very high entropy.

 

 

 

What is high entropy?

 

 

 

Would a better measure be specific entropy?

[Fuzzwood]

A high entropy means nothing more than the number of possible states a given system can take. Every particle that can exchange information with another adds to the number of states. I'm talking statistic thermodynamics here.

[juanrga]

If you take a large cloud of gas in space (nebula), it has very high entropy.

 

Very high relative to what?

 

Once it starts to attract itself through gravity, its entropy decreases.

 

Really? Who showed that?

 

When it gets hot enough to form a star, does it have even lower entropy?

and at the end of its life cycle does, lets say this particular star turns into a neutron star, neutron stars have extremely low entropy right?

so gravity lowers entropy, so why is it proposed that black holes have maximum entropy?

 

The hypothetical 'entropy' associated to black holes is not the entropy of thermodynamics but a mere formal analogy. How could the black hole 'entropy' was a maximum when its 'heat capacity' is negative.

[RichIsnang]

correct me if i am wrong on any of this.

the nebula has higher entropy as a neutron star. we know the position of the particles in a neutron with relative precision, but in a nebula this will be much harder to know.

this means the nebula has higher entropy.

we can know the positions of particles in a star with more precision than we can in a nebula simply because they occupy a smaller amount of space.

quote from Brian Greene's book: 'hence black holes have maximum entropy'

the schwarzschild radius for a non-rotating black hole of the mass of the sun is ~2950m

the radius of the sun is~ 695500000m

seems to me there are any less possible combination of particle positions inside the schwarzschild radius than in the radius of the sun.

so why is he saying it has higher entropy?

 

everything has entropy, we defined it that way, so weather or not it as a negative heat capacity it irrelevant?

Edited April 29, 2012 by RichIsnang

[juanrga]

we can know the positions of particles in a star with more precision than we can in a nebula simply because they occupy a smaller amount of space.

quote from Brian Greene's book: 'hence black holes have maximum entropy'

 

Their 'heat capacity' is negative, which implies there is no maximum in their 'entropy'.

[RichIsnang]

how is heat capacity related to entropy?

[juanrga]

how is heat capacity related to entropy?

 

[math]\frac{d^2S}{dE^2} = -\frac{1}{T^2 C}[/math]

 

Thus the black hole 'entropy' cannot be a maximum.

[RichIsnang]

What does that mean?

Sorry my knowledge is a little lacking

Edited May 1, 2012 by RichIsnang

[juanrga]

What does that mean?

Sorry my knowledge is a little lacking

 

It is saying that if the heat capacity C is negative the second derivative of the entropy with energy is positive. This means that the entropy function has form of "U" and there is not maximum entropy corresponding to equilibrium. For any material the heat capacity is positive and the entropy function has form of inverted U

_
/ \

with a maximum corresponding to equilibrium.

Edited May 2, 2012 by juanrga

[RichIsnang]

Ok, thanks

black holes are so strange