# A Entropy and derivations - is my logic faulty?

1. Dec 27, 2017

### 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.?

2. Dec 27, 2017

### Arman777

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 cant 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.

Last edited: Dec 27, 2017
3. Dec 27, 2017

### Nick Prince

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

4. Dec 27, 2017

### Staff: Mentor

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.

5. Dec 27, 2017

### Staff: Mentor

Where? Please give a specific reference.

6. Dec 27, 2017

### Arman777

Yes as you said universe cant dump heat out of its boundry so there cant be change in dQ.

In adiabatic process heat transfers to work.

So In total theres no change in dQ.It just transforms to work.

7. Dec 27, 2017

### Arman777

8. Dec 27, 2017

### Nick Prince

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

9. Dec 27, 2017

### Staff: Mentor

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?

10. Dec 27, 2017

### Nick Prince

11. Dec 27, 2017

### Nick Prince

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

12. Dec 27, 2017

### Staff: Mentor

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?

13. Dec 27, 2017

### Staff: Mentor

Do you mean the CMB?

14. Dec 27, 2017

### Nick Prince

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

15. Dec 27, 2017

### Staff: Mentor

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.

16. Dec 27, 2017

### Nick Prince

Yes I mean the CMB.

17. Dec 27, 2017

### Nick Prince

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

18. Dec 27, 2017

### Staff: Mentor

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.

19. Dec 27, 2017

### Staff: Mentor

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"?

20. Dec 27, 2017

### Nick Prince

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.