# Does the third law of thermodynamics apply to all compounds and elements?

According to wikipedia, the third law of thermodynamics is "The entropy of a perfect crystal, at absolute zero (zero kelvins), is exactly equal to zero.".

Then, theoretically, could all substances, including molecular compounds, attain absolute zero? Another way of thinking of this question is whether all compounds could become perfect crystals.

• Entropy would be zero but it can't be. – Mithoron Apr 18 '15 at 20:00
• @Mithoron So we can assume the law applies to all compounds? – Andy Apr 18 '15 at 20:31
• Laws of thermodynamics are universal, applicable beyond chemistry... – Mithoron Apr 18 '15 at 21:14
• – RE60K Apr 19 '15 at 10:31

No, because it is possible that perfect crystals cannot be formed for statistical reasons. A simple example:

The absolute Boltzmann entropy is defined as $S = k_\text{B} \ln \Omega$ per molecule, where $\Omega$ is the number of possible microstates.

Consider a crystal of carbon monoxide at absolute zero. Now consider exchanging the position of all C atoms with those of all O atoms. This structure will be equivalent in energy so $\Omega = 2$. Thus $S = k_\text{B} \ln 2 > 0$.

• Are you suggesting that if carbon monoxide is 2, monatomic atoms like He would be ln1, or 0? So it would be reasonable for elements in atomic state but not compounds? Or are you simply choosing 2 as a random number, but overlooking the electron cloud and its movement and even elements in atomic states would be unreasonable? I am curious to what cases the law would apply to. – Andy Apr 20 '15 at 1:50
• Yes, He would be theoretically be able to form a perfect crystal as there would only be one possible microstate. At absolute zero all the atoms/molecules are in their ground quantum states so there is no entropy associated with excitement. – J. LS Apr 20 '15 at 8:59

I strongly suggest you read this. From there:

The laws of thermodynamics dictate that absolute zero cannot be reached using only thermodynamic means, as the temperature of the substance being cooled approaches the temperature of the cooling agent asymptotically. A system at absolute zero still possesses quantum mechanical zero-point energy, the energy of its ground state. The kinetic energy of the ground state cannot be removed.

And:

An even stronger assertion is that It is impossible by any procedure to reduce the temperature of a system to zero in a finite number of operations. (≈ Guggenheim, p. 157)

And:

Perfect crystals never occur in practice; imperfections, and even entire amorphous materials, simply get "frozen in" at low temperatures, so transitions to more stable states do not occur.