# Is the law of entropy radical or smooth?

One form of the third law of thermodynamics states that ; in absolute zero temperature,entropy is absolute that means it does not depend on any of the properties of the system.the question is ; is this a radical feature for absolue zero or absolute zero is only a limit i.e. the dependance of entropy on other properties goes to zero when temperature goes to zero ?
I want to use the answer of this question to discuss a more general idea concerning the study of ideal cases.

## Answers and Replies

I don't know much about the term radical feature but I'm pretty sure absolute zero is a limit, not something you can reach

btw I've never heard of your version of the third law, the one I'm accustomed to is "a perfect crystal with a single configuration at absolute zero has zero entropy"

According to http://en.wikipedia.org/wiki/Third_law_of_thermodynamics" [Broken], here is how the third law of thermodynamics is stated by Lewis and Randall:

If the entropy of each element in some (perfect) crystalline state be taken as zero at the absolute zero of temperature, every substance has a finite positive entropy; but at the absolute zero of temperature the entropy may become zero, and does so become in the case of perfect crystalline substances.​

I don't know if this should be called radical or smooth, but at least it is rather clear.
On the same wikipedia page the third law is related to the Boltzmann definition of entropy. You can also read this:

The entropy of a perfect crystal lattice as defined by Nernst's theorem is zero (provided that its ground state is unique, whereby ln(1)k = 0).

An example of a system which does not have a unique ground state is one containing half-integer spins, for which time-reversal symmetry gives two degenerate ground states (an entropy of ln(2) k, which is negligible on a macroscopic scale). Some crystalline systems exhibit geometrical frustration, where the structure of the crystal lattice prevents the emergence of a unique ground state. Ground-state helium (unless under pressure) remains liquid.

In addition, glasses and solid solutions retain large entropy at 0K, because they are large collections of nearly degenerate states, in which they become trapped out of equilibrium. Another example of a solid with many nearly-degenerate ground states, trapped out of equilibrium, is ice Ih, which has "proton disorder".

This shows some examples where the entropy at 0K may be larger than zero.

Last edited by a moderator:
My question is not about the state of absolute zero itself but the states near absolute zero... Is the small difference of temperature above absolute zero negletable regarding the application of the law of entropy (this is what I mean by radical and smooth)
As for the third law of thermodynamics, it is clear and real and cannot be a topic of discussion in forums

What do you mean by negligible?
What do you mean by "the law of entropy"? Do you mean the third law?
What do you mean by "radical"? Would you mean discontinuous?

What does the third law imply if you are close to 0K but not exactly at 0K?
Have a look at the Debye theory for http://en.wikipedia.org/wiki/Debye_model" [Broken].
You will see that the specific heat tends to zero as the temperature tends to 0K.
This is related to the thrid law: the specific heat must be zero at 0K.
The specific heat goes smoothly to 0 when the temperature goes to 0K since there is no phase transition in the Debye model.

I don't see why there could sometimes be a phase transition precisely at 0K, but it could happen.
Would it be the case for "Ground-state helium" ?
Anyway, a phase transition at precisely at 0K could never be verified experimentally.
Therefore, such a phase transition would remain a purely theoretical concept.

Last edited by a moderator:
What do you mean by negligible? I mean that is it a good approximation if we apply the third law in a system of small temperature above 0K.

What do you mean by "the law of entropy"? Do you mean the third law?
I mean the fact that entropy at 0K does not affected by any change in other properties of the system this is one form of the third law( do not seach for it in wikipeadia)

What do you mean by "radical"? Would you mean discontinuous?
No .. changes can be continouus and radical .. the transition to 0K is radical if the the law cannot be applied even in approximation at any other temperature however near to zero is it ...[/QUOTE]

I don't see why there could sometimes be a phase transition precisely at 0K, but it could happen.
Would it be the case for "Ground-state helium" ?
Anyway, a phase transition at precisely at 0K could never be verified experimentally.
Therefore, such a phase transition would remain a purely theoretical concept.

Thanks ! this is what am searching for

Now I want someone who is specialized in Biomedical Engineering to add something..

Dale
Mentor
2020 Award
One form of the third law of thermodynamics states that ; in absolute zero temperature,entropy is absolute that means it does not depend on any of the properties of the system
I have never seen that form. Can you provide a citation?

the question is ; is this a radical feature for absolue zero or absolute zero is only a limit i.e. the dependance of entropy on other properties goes to zero when temperature goes to zero ?
As lalbatros said, the entropy of an ideal crystal goes smoothly to 0 as the temperature becomes arbitrarily close to 0 K. I would suspect that most "other properties" that you may consider would disrupt the crystalline state so that it would no longer be a perfect crystal. Other substances may theoretically have non-zero entropy at 0 K.

Last edited: