Entropy and derivations - is my logic faulty?

[Nick Prince]

It is assumed that entropy increases in the universe. However, the fluid and acceleration equations are derived assuming that.

TdS=dE+pdV where dQ = TdS.

But dQ is usually set equal to zero to derive these equations. Hence since T is non zero, dS should be zero and so there would be no increase in entropy. This seems to conflict with the initial assumption. Can anyone fault my logic here.?

 

[Arman777]

It is assumed that entropy increases in the universe. However, the fluid and acceleration equations are derived assuming that.

TdS=dE+pdV where dQ = TdS.

But dQ is usually set equal to zero to derive these equations. Hence since T is non zero, dS should be zero and so there would be no increase in entropy. This seems to conflict with the initial assumption. Can anyone fault my logic here.?

I found this,

"The expansion of a homogeneous universe is adiabatic, as there is no place for “heat” to come from,
and no “friction” to convert energy of bulk motion into

It makes sense since T is not zero but its almost zero (2.73K).

Since the universe is homogeneous the energy density will be uniform for all the places. One place is not hot then the other place in example. So there can't be any heat transfer also CMB confirms that.

In the early universe this will be no longer true cause there particles are heavily interacting with each other.

 

[Nick Prince]

I found this,

The expansion of a homogeneous universe is adiabatic, as there is no place for “heat” to come from,
and no “friction” to convert energy of bulk motion into random motions of particles.

It makes sense since T is not zero but its almost zero (2.73K).

In early universe I am not sure about the answer...

But adiabacity requires dQ = 0 (the universe can't dump heat out of a boundary, hence dE= - pdV. Most textbooks derive the fluid equation from this. T is proportional to 1/a and that means in the early universe T is High!

 

[PeterDonis]

It is assumed that entropy increases in the universe.

Can you give a reference? It is helpful to see the specific sources you are using.

the fluid and acceleration equations are derived assuming...

Same comment here: please give a reference for this derivation and its assumptions.

dQ is usually set equal to zero to derive these equations.

Same comment.

 

[PeterDonis]

I found this

Where? Please give a specific reference.

 

[Arman777]

But adiabacity requires dQ = 0 (the universe can't dump heat out of a boundary, hence dE= - pdV. Most textbooks derive the fluid equation from this.

Yes as you said universe can't dump heat out of its boundry so there can't be change in dQ.

In adiabatic process heat transfers to work.

So In total there's no change in dQ.It just transforms to work.

 

[Arman777]

Where? Please give a specific reference.

I tried but it gave me wrong url I guess so I edited and deleted. I ll try again.

https://www.google.com.tr/url?sa=t&...JCl4QFghFMAI&usg=AOvVaw0xjZcR1b8OcNFbrriXGEr2

 

[Nick Prince]

Can you give a reference? It is helpful to see the specific sources you are using.
Same comment here: please give a reference for this derivation and its assumptions.
Same comment.

Try Barbara Ryden p52-53, or Ray D'inverno p322.

 

[PeterDonis]

adiabacity requires dQ = 0 (the universe can't dump heat out of a boundary, hence dE= - pdV. Most textbooks derive the fluid equation from this.

Most textbooks on cosmology that I'm aware of derive the Friedmann equations from the Einstein Field Equation. They don't make any assumptions of the sort you're describing; their only assumption is a homogeneous and isotropic universe.

T is proportional to 1/a

Temperature of what? And in what model?

 

[Nick Prince]

Try Barbara Ryden p52-53, or Ray D'inverno p322.

See also Liddle - An introduction to modern cosmology p26.

 

[Nick Prince]

Most textbooks on cosmology that I'm aware of derive the Friedmann equations from the Einstein Field Equation. They don't make any assumptions of the sort you're describing; their only assumption is a homogeneous and isotropic universe.
Temperature of what? And in what model?

The temperature of the background in a model based on the Friedmann equations. a is the scale factor.

 

[PeterDonis]

I ll try again.

Looks ok, I was able to get to the URL and see the quote you gave.

Since the universe is homogeneous the energy density will be uniform for all the places.

Yes, but this still doesn't say how energy density is related to temperature.

It makes sense since T is not zero but its almost zero (2.73K).

This T is the T of the CMB. It's not the same as the T of other components of the universe. The link you gave discusses two kinds of components: radiation (of which the CMB is an example) and cold non-relativistic matter. What is the T of the latter?

 

[PeterDonis]

The temperature of the background

Do you mean the CMB?

 

[Nick Prince]

Most textbooks on cosmology that I'm aware of derive the Friedmann equations from the Einstein Field Equation. They don't make any assumptions of the sort you're describing; their only assumption is a homogeneous and isotropic universe.
Temperature of what? And in what model?

Not talking about Friedmann derivations. I'm talking about continuity equation and acceleration equations.

 

[PeterDonis]

Try Barbara Ryden p52-53, or Ray D'inverno p322.

In my copy of Ryden this talks about redshift, not thermodynamics. A chapter/section reference would be helpful. I don't have a copy of D'Inverno.

See also Liddle - An introduction to modern cosmology p26.

In my copy this doesn't talk about thermodynamics at all, it just talks about spherical geometry. Again, a chapter/section reference would be helpful.

 

[Nick Prince]

Not talking about Friedmann derivations. I'm talking about continuity equation and acceleration equations.

Yes I mean the CMB.

 

[Nick Prince]

In my copy of Ryden this talks about redshift, not thermodynamics. A chapter/section reference would be helpful. I don't have a copy of D'Inverno.
In my copy this doesn't talk about thermodynamics at all, it just talks about spherical geometry. Again, a chapter/section reference would be helpful.

In my copy it is section 3.4 p 26 Ryden is section 4.2.

 

[PeterDonis]

Not talking about Friedmann derivations. I'm talking about continuity equation and acceleration equations.

I don't know what you mean by these. "Continuity equation" to me means the covariant divergence of the stress-energy tensor is zero, which doesn't add any information if I already have the Friedmann equations. "Acceleration equation" to me means the second Friedmann equation.

 

[PeterDonis]

In my copy it is section 3.4 p 26

Ok, got it. This specifically says it assumes a reversible expansion $dS = 0$, so obviously it rules out by fiat any entropy increase. But it's just an assumption, not a proof.

Ryden is section 4.2.

Same comment here: it is explicitly assumed that entropy does not increase.

So now I'm confused; you said in your OP:

It is assumed that entropy increases in the universe.

But so far you've given two sources that make precisely the opposite assumption. So what source are you getting the assumption from that "entropy increases in the universe"?

 

[Nick Prince]

I don't know what you mean by these. "Continuity equation" to me means the covariant divergence of the stress-energy tensor is zero, which doesn't add any information if I already have the Friedmann equations. "Acceleration equation" to me means the second Friedmann equation.

Ok Ryden has for section 4.2 THE FLUID AND ACCELERATION EQUATIONS she derives the fluid equation first then uses the ist F'man equation to get the 2nd accn eqn. I call the fluid equation the continuity equation.

 

[Nick Prince]

Ok, got it. This specifically says it assumes a reversible expansion $dS = 0$, so obviously it rules out by fiat any entropy increase. But it's just an assumption, not a proof.
Same comment here: it is explicitly assumed that entropy does not increase.

So now I'm confused; you said in your OP:
But so far you've given two sources that make precisely the opposite assumption. So what source are you getting the assumption from that "entropy increases in the universe"?

Do you think that entropy does not increase in our universe?

 

[Chestermiller]

dS=dQ/T only for a reversible process. The processes taking place in the universe are not reversible. So entropy is being generated in the universe even though dQ is equal to zero.

 

[Nick Prince]

Ok, got it. This specifically says it assumes a reversible expansion $dS = 0$, so obviously it rules out by fiat any entropy increase. But it's just an assumption, not a proof.
Same comment here: it is explicitly assumed that entropy does not increase.

So now I'm confused; you said in your OP:
But so far you've given two sources that make precisely the opposite assumption. So what source are you getting the assumption from that "entropy increases in the universe"?

Do you think that entropy doesn't increase in the universe?

 

[Nick Prince]

dS=dQ/T only for a reversible process. The processes taking place in the universe are not reversible. So entropy is being generated in the universe even though dQ is equal to zero.

Can you elaborate?

 

[Chestermiller]

Can you elaborate?

Are you not aware that you can determine the entropy change between two states of a system only by determining the integral of dq/T for a reversible path?

 

[Nick Prince]

Can you elaborate?

dS=dQ/T only for a reversible process. The processes taking place in the universe are not reversible. So entropy is being generated in the universe even though dQ is equal to zero.

The entropy of sub systems is additive so the overall entropy of the universe must be greater than zero. This must be equal to T dS hence dS of the whole universe must be positive not zero?

 

[Chestermiller]

The entropy of sub systems is additive so the overall entropy of the universe must be greater than zero. This must be equal to T dS hence dS of the whole universe must be positive not zero?

I have no idea what you're saying here. Here is a link to a Physics Forums Insights article I wrote a couple of years ago on Entropy and the 2nd Law of Thermodynamics: https://www.physicsforums.com/insights/understanding-entropy-2nd-law-thermodynamics/

Hope this helps.

 

[Nick Prince]

The entropy of sub systems is additive so the overall entropy of the universe must be greater than zero. This must mean Tds non zero so dq must be non zero. Thanks Chestermiller will look at this link
.

 

[PeterDonis]

Ryden has for section 4.2 THE FLUID AND ACCELERATION EQUATIONS she derives the fluid equation first then uses the ist F'man equation to get the 2nd accn eqn. I call the fluid equation the continuity equation.

Yes, I agree that is the terminology she is using.

 

[PeterDonis]

Do you think that entropy does not increase in our universe?

No. But that does not mean I think entropy is increasing in the idealized models of a homogeneous, isotropic universe based on the Friedmann equations. Your references make it obvious that it is not. So, if entropy is in fact increasing in our universe, it is obviously doing so as a result of some process that is not included in those idealized models.

 

[Chestermiller]

For an isolated system like the universe, the Clausius inequality reduces to $$\Delta S\gt\int{\frac{dq}{T}}=0$$This means that, even with no heat transfer to the system (dq=0), entropy is generated with the system itself, and thereby increases.

 

[PeterDonis]

The entropy of sub systems is additive

There are no "subsystems" in the Friedmann models, or in the thermodynamics based on them that you referenced. There is just one homogeneous, isotropic universe.

so the overall entropy of the universe must be greater than zero

For our actual universe, yes, I agree. For the idealized universe in the Friedmann models, however, you might want to rethink this statement.

This must be equal to T dS

No, $T dS$ is the change in entropy as a result of some process. If the process is adiabatic, as the expansion of the homogeneous, isotropic universe is in the Friedmann models, then $dS = 0$. Your references make that clear. What they do not discuss at all is what other processes might be taking place in the actual universe (as opposed to the idealized universe in the Friedmann models) that might increase entropy.

 

[Nick Prince]

No. But that does not mean I think entropy is increasing in the idealized models of a homogeneous, isotropic universe based on the Friedmann equations. Your references make it obvious that it is not. So, if entropy is in fact increasing in our universe, it is obviously doing so as a result of some process that is not included in those idealized models.

So the implicit starting assumptions are wrong and hence the friedmann's accn and continuity equation are not complete?

 

[PeterDonis]

So the implicit starting assumptions are wrong and hence the friedmann's accn and continuity equation are not complete?

Do you think the equations in the references you gave are complete models of everything that happens in the universe?

 

[Arman777]

Looks ok, I was able to get to the URL and see the quote you gave.
Yes, but this still doesn't say how energy density is related to temperature.
This T is the T of the CMB. It's not the same as the T of other components of the universe. The link you gave discusses two kinds of components: radiation (of which the CMB is an example) and cold non-relativistic matter. What is the T of the latter?

Thats nice then

Well I mean to radiation energy density. And radiation energy density has a relationship with tempature.

I mean the CMB.