# Residual Entropy

1. Aug 17, 2006

### Delzac

Hi all,

Do ALLl particles at absolute zero have a residual entropy?

Checked wiki, it didn't say anything about all particles haveing residual entropy, it only gave conditions for it to happen, most of which i do not understand.....

"residual entropy occurs if the material can exist in multiple different ground states that have the same zero-point energy. Residual entropy tends to occur in substances which have very weak tendencies to align into their energy ground state."

Any help will be appreciated

2. Aug 17, 2006

### lalbatros

Hi Delzac,

You will find on the web a paper on http://www.ifm.liu.se/~thoed/water/water-3.pdf" [Broken] that explains the "configurational degeneracy" of crystal water (page 4 & 5) and the "residual entropy" that results.

The hydrogen atoms in the cristalline structure can occupy different places without any difference in the total energy. Therefore, at 0K, the entropy cannot be zero because there are still many different possible configurations with the same energy (the ground level!). Remember the http://en.wikipedia.org/wiki/Ludwig_Boltzmann" [Broken] since the H and O atoms can be "mixed" on the lattice with some freedom. (mixing entropy also results directly from the Boltzmann formula but is more familiar from Physical Chemistry and basic thermodynamics)

This paper also mentions a good agreement of the experimental values with the residual entropy calculated from the Boltzmann formula. I am always surprised to see how -usually- the theory receives more attention than experience. The result is that most people (including myself) have no idea about how this could be measured (except the basic principle dS=dQ/t). If you had some hint, I would appreciate. See my question on this forum on the https://www.physicsforums.com/showthread.php?t=127793".

Michel

Last edited by a moderator: May 2, 2017
3. Aug 18, 2006

### cterence_chow

Ya, it does.All substances and elements have 0 entropy at absolute 0

4. Aug 20, 2006

### lalbatros

cterence_chow,

This is something to be checked experimentally and understood theoretically.
Ice at 0°K has an entropy of 3.41 J/mol/K .

The interpretation is simple: the ground state of cristalline water at 0K still has many possible configuration, because of a degeneracy. From the Boltzmann formula the value of the entropy is 3.28 J/mol/K, which is thus confirmed by experiment.

Most often the entropy at 0K is zero and this is understood theoretically on the assumption that in the ground state (minimum energy) only one configuration is possible. When this assumption is invalid, the theorem does not apply. Ice water is an example.

Michel

Last edited: Aug 20, 2006
5. Aug 21, 2006

### Delzac

But with a minimum energy(zero-point energy), this shows that all atoms and molecule would be vibrating and rotating, and in the case of helium(since is does not solidefy at 0 K) it will have translational energy isn't it? then ALL atoms have more that one way of arranging themself, all atoms should have some residual entropy isn't it?

quote
" Ya, it does.All substances and elements have 0 entropy at absolute 0"
does not appiled at all isn't it?

6. Aug 21, 2006

### lalbatros

Delzac,

For ice water there are different non-equivalent sites for protons which do have the same energy.
It does not mean they have more energy than what should be possible in the ground level.

For helium, I have difficulties to give you a precise answer.
But I would ask the question: what makes a difference between liquid and solid?
I would first say that the difference is the "fluidity". But fluidity can only be measured by an excitation of the system: applying an external force to see what happens. This means that it does not represent the atomic motions within the substance, but rather how the substance can react to external excitations. Another difference could be the crystalline order. But Helium is also known for some kind of order at low temperatures.

Michel

7. Aug 21, 2006

### Delzac

hm...... then do all atoms and molecules have a "different non-equivalent sites for protons which do have the same energy" ? i believe that this is the property that gives the non-zero entropy?

8. Aug 21, 2006

### lalbatros

Delzac,

Have a look in the reference on http://www.ifm.liu.se/~thoed/water/water-3.pdf" [Broken].

The title on page 5 is "Proton order and configurational degeneracy".
It explains exactly the freedom that the protons have to "relocate" on the ice water lattice at 0K. Deriving from the Boltzmann formula the entropy at 0K is rather simple. What is more difficult is to understand why this degeneracy happens. But we can easily accept that it may happen, and we can easily guess how this can be understood from radiocrystallogic data.

Note that I believe things may be more complicated.
For example, I doubt that it is an exact degeneracy, specially if the protons do really relocate at random. If it is only an approximate degeneracy, then we should conclude that S(0K) maybe zero but that it would be extremely difficult to prove it experimentaly. It would be necessary to record data in a very narrow range near the absolute zero. Outside this range, the degeneracy would increase the entropy. Moreover the system should have an opportunity to reach the equilibrium state, while it would probably prefer to stay (frozen) in a metastable state.

This is now far further than what I can deal with, both theoretically and even more experimentally: I really know very little about low temperature physics and the experimental aspects.

Michel

Last edited by a moderator: May 2, 2017
9. Aug 22, 2006

### Delzac

thx for the help