Second Law of Thermodynamics

[Aki]

The second law of thermodynamics states that the entropy in the universe can only increase. A question came up to mind, would this law still hold if the universe stopped expanding and started contracting.

 

The formula for entropy is:

delta S = n* R *ln(Vf/Vi)

 

The final volume would be smaller than the initial volume if the universe were to contract, giving delta S a negative value, thus the entropy would be decreasing.

[lindagarrette]

The second law of thermodynamics states that the entropy in the universe can only increase. A question came up to mind, would this law still hold if the universe stopped expanding and started contracting.

 

The formula for entropy is:

delta S = n* R *ln(Vf/Vi)

 

The final volume would be smaller than the initial volume if the universe were to contract, giving delta S a negative value, thus the entropy would be decreasing.

Good point. That's why it can't happen.

[coldcreation]

The second law of thermodynamics states that the entropy in the universe can only increase. A question came up to mind, would this law still hold if the universe stopped expanding and started contracting.

 

The formula for entropy is:

delta S = n* R *ln(Vf/Vi)

 

The final volume would be smaller than the initial volume if the universe were to contract, giving delta S a negative value, thus the entropy would be decreasing.

 

Good topic.

A couple of points. Entropy either stays the same of increases with time. It depends on the type of system (the environment, properties, subsystems, interactions, open of closed, stable equilibrium, far from equilibrium, constituents, etc.). I take it you mean the entropy of the universe. Better topic. Cool.

 

Off the bat, the standard model of the universe you write about has problems across the board with entropy. Not just is the universe collapses, which seems unlikely since the 1990s high-z SNe Ia data.

 

From what I understand, according to BB cosmology, the entropy of the universe was very high to begin with, then decreased, then increased. Seems to me that that violates the second law. The same law would certainly be violated (again) if the cosmos were to shrink.

 

Coldcreation

[Qfwfq]

Good question Aki!

 

I too had thought of it recently but I haven't had time to work it out well at all. I was thinking along the lines that one must also consider what lets "the stuff" expand or makes it contract. The cosmic fluid and its gravity are somewhat like a gas inside a cylinder and piston. Have you tried working that out, physics book in hand? Thermodynamics isn't the part of physics I'm best at. :)

[coldcreation]

Good question Aki!

 

I too had thought of it recently but I haven't had time to work it out well at all. I was thinking along the lines that one must also consider what lets "the stuff" expand or makes it contract. The cosmic fluid and its gravity are somewhat like a gas inside a cylinder and piston. Have you tried working that out, physics book in hand? Thermodynamics isn't the part of physics I'm best at. :)

 

You're up mighty early Qfwfq, where are you writing from. My time is 12:12 pm (Greenwich mean time, in Barcelona).

 

A couple points: this was all discussed in a thread called Cosmology and Thermodynamics (thread by Coldcreation), but no problem.

 

Thermodynamics is not a part of physics (as you write). Physics is a part of thermodynamics.

 

It should not be underestimated the fundamental importance of thermodynamics with respect to the evolution of the universe. According to Gyftopopoulous and Beretta: “Physics is a science that attempts to describe all aspects of all phenomena pertaining to the perceivable universe. It can be viewed as a large tree with many branches, such as mechanics, electromagnetism, gravitation, and chemistry, each specialized in the description of a particular class of phenomenon. Thermodynamics is not a branch. It pervades the entire tree.” (Thermodynamics Foundations and Applications, 1991).

 

A note on expansion (or contraction): according to standard theory, it is space itself that expands (space is created between objects). The galaxies are not really moving. So if the universe collapse, I imagine that space itself would contract, shrink, be destroyed, disappear (?). And so too would entropy: a clear violation of the second law.

 

Incidentally, if space is created in an expanding universe, does that not violate the first law?

 

CC

[Erasmus00]

The second law of thermodynamics states that the entropy in the universe can only increase. A question came up to mind, would this law still hold if the universe stopped expanding and started contracting.

 

The formula for entropy is:

delta S = n* R *ln(Vf/Vi)

 

The final volume would be smaller than the initial volume if the universe were to contract, giving delta S a negative value, thus the entropy would be decreasing.

 

What you have there is the formula for the isothermal expansion of an ideal gas. However, as the universe expands, I would expect (though I'm not used to applying thermodynamics to cosmology, so I could easily be wrong)that it would cool down, on average, since space is actually being created. Hence the isothermal formula probably doesn't apply.

 

edit: There are also ways you could add or remove space form the universe without changing the entropy at all (called adiabatic processes).

-Will

[Erasmus00]

Thermodynamics is not a part of physics (as you write). Physics is a part of thermodynamics.

 

Actually, (though I suppose this is a bit off topic) thermodynamics is the direct consequence of applying the laws of physics (in statistical treatment) to large collections of particles. As such, thermodynamics is one particular application of physics, sometimes called many-body physics or statistical physics.

 

A note on expansion (or contraction): according to standard theory, it is space itself that expands (space is created between objects). The galaxies are not really moving. So if the universe collapse, I imagine that space itself would contract, shrink, be destroyed, disappear (?). And so too would entropy: a clear violation of the second law.

 

It actually entirely depends on the manner you shrink space. Consider a box with an ideal gas. If you squeeze the walls rapidly (shrinking the space) then the entropy of your system most certainly changes. However, if you shrink the space slowly, the number of states accesible to your particles doesn't change, and so the entropy remains constant. I see no reason why the expansion/contraction of the universe couldn't be adiabatic processes.

 

Incidentally, if space is created in an expanding universe, does that not violate the first law?

 

Depends on what the energy density of empty space is. If empty space has no energy, then no, creating or destroying it doesn't effect conservation of energy at all.

-Will

[Southtown]

I wonder if expanding space has any effect on the observed speed of light.

[Erasmus00]

I wonder if expanding space has any effect on the observed speed of light.

 

Under current theory (general relativity) it wouldn't at all. The speed of light would always have a constant local speed, c. Untill someone manages to unify quantum mechanics with general relativity, it seems increasingly unlikely that a new theory of gravity will emerge (though perhaps strong field tests of GR will fail), so I'd have to say probably not.

-Will

[Aki]

Good point. That's why it can't happen.

 

But why can't it happen? No one is sure that the Big Crunch won't happen. There might be a lot more dark matter out there than we think.

[Aki]

Good question Aki!

 

I too had thought of it recently but I haven't had time to work it out well at all. I was thinking along the lines that one must also consider what lets "the stuff" expand or makes it contract. The cosmic fluid and its gravity are somewhat like a gas inside a cylinder and piston. Have you tried working that out, physics book in hand? Thermodynamics isn't the part of physics I'm best at. :eek:

 

Well we just finished learning about thermodynamics at school, and I love it!:) I'm not sure what you mean by "working that out" though

[Aki]

What you have there is the formula for the isothermal expansion of an ideal gas. However, as the universe expands, I would expect (though I'm not used to applying thermodynamics to cosmology, so I could easily be wrong)that it would cool down, on average, since space is actually being created. Hence the isothermal formula probably doesn't apply.

 

edit: There are also ways you could add or remove space form the universe without changing the entropy at all (called adiabatic processes).

-Will

 

Erasmus,

You got a point there, I checked and that formula applies to isothermal processes only. The universe does cool down, so that formula wouldn't apply. But I then looked for another formula, and I found one that applies to any process, whether isothermal or not.

 

delta S = integral from Ti to Tf * dQ / T = mc ln (Tf/Ti)

since dQ=m*c* dT, where c is the heat capacity of the substance.

 

So in an adiabatic process, the change in heat is zero and therefore the change in entropy is zero.

[Snake]

maybe the law only applies in our cimcurstances. maybe the laws are different when the universe contracts. I mean the guy who figured it out lived in an expanding universe.

Snake

[insight]

Erasmus,

You got a point there, I checked and that formula applies to isothermal processes only. The universe does cool down, so that formula wouldn't apply. But I then looked for another formula, and I found one that applies to any process, whether isothermal or not.

 

delta S = integral from Ti to Tf * dQ / T = mc ln (Tf/Ti)

since dQ=m*c* dT, where c is the heat capacity of the substance.

 

So in an adiabatic process, the change in heat is zero and therefore the change in entropy is zero.

 

How about isentropic process that change in temp and pressure but not entrophy. Let see it....... as isentropic is Reversible Adiabatic process, Volume expands, Temperature and Pressure drops and the Universe is working!!!! But i'm not sure It is a Quasi-Equilibrium. :eek:

[insight]

What you have there is the formula for the isothermal expansion of an ideal gas. However, as the universe expands, I would expect (though I'm not used to applying thermodynamics to cosmology, so I could easily be wrong)that it would cool down, on average, since space is actually being created. Hence the isothermal formula probably doesn't apply.

 

edit: There are also ways you could add or remove space form the universe without changing the entropy at all (called adiabatic processes).

-Will

 

After i checked out from my text book, i found out some notes.

This is the second integral of entropy change

 

∆S >= 1∫2 δQ/T

 

For an isolated system (or simply an adiabatic closed system), the heat transfer( δQ/T) is zero, and becomes

 

∆S,isolated >= 0

 

The equation can be expressed as the entropy of an isolated system during a process always increases or, in the limiting case of a reversible process, remains constant. In other words, it never decreases. This is known as the increase of entropy principle.

[insight]

From what I understand, according to BB cosmology, the entropy of the universe was very high to begin with, then decreased, then increased. Seems to me that that violates the second law. The same law would certainly be violated (again) if the cosmos were to shrink.

 

Coldcreation

 

From what i understand, the increase of entropy principle doesn't imply that the entropy of a system can't decrease. The entropy change of a system can be negative during a process, but not entropy generation. Since Sgen is greater than 0, it's irreversible and the entropy of the Universe is larger and larger. So what you used in the para should be entropy change, not the entropy of the Universe itself. :eek:

[Aki]

After i checked out from my text book, i found out some notes.

This is the second integral of entropy change

 

∆S >= 1∫2 δQ/T

 

 

But would this equation still hold if the universe contracted?