Entropy question: Does a substance at 0K have no entropy?

[Clovis]

Is it 0 K for a substance to have no entropy?Sorry. Just had to get that off my chest.

 

[fresh_42]

Nernst's theorem, the 3rd theorem of thermodynamics:
https://en.wikipedia.org/wiki/Third_law_of_thermodynamics
(note the graphic in the section "absolute zero")
and here's the math which directly answers your question
(Google translate isn't perfect, but it works)
https://de.wikipedia.org/wiki/Nernst-Theorem

If the basic state of the system is not degenerate, then $g = 1$ and thus
$$
\lim_{T\to 0}S(T,p,V,\ldots)=S(T=0)=S_ {0}= k_B\cdot \log g = 0
$$
Thus, the entropy of a system disappears when the temperature approaches zero.

 

[atyy]

As the link given above by @fresh_42 says, if there is ground state degeneracy, then the entropy need not be zero when the temperature is at absolute zero.

 

[hilbert2]

An imperfect crystal can have a non-zero entropy at 0 K, which I suppose is because there are many ways to distribute the same number of dislocations/defects in the lattice.

 

[Henryk]

The formula provided by fresh42 is correct. However, when the ground state of a system is degenerate, the entropy at 0 K is not zero, it is $k_B \cdot log (g)$ where g is the degeneracy of the ground state.

 

[Lord Jestocost]

Nernst's theorem, the 3rd theorem of thermodynamics...

A slight correction.
Nernst’s statement of the third law says:
Near absolute zero, all reactions in a system in internal equilibrium take place with no change in entropy.

That means: $$\lim_{T \rightarrow 0^+} {\Delta S}=0$$