Why is 0 degrees K unattainable?

[Kakashi]

At constant pressure we have:

$$ dq_{p}=dH=C_{p} dT $$ which implies

The enthalpy change dH reflects the increase in internal energy associated with molecular motions such as rotational and vibrational modes. The atoms, molecules or ions that compose a system can undergo several types of motion including translation, rotation, and vibration. The greater the motion (the higher the temperature), the greater the number of possible microstates and therefore the higher the entropy. A perfectly ordered system with only a single microstate would have 0 entropy. The only system that meets this criteria is a perfect crystal at 0 K in which each component is fixed in place within a crystal lattice and exhibits no motion.

Near absolute zero, the heat capacity approaches zero:

$$ Cp \to 0 $$ as $$ T→0 $$

$$ dT = \frac{dq_{p}}{C_{p}} $$

Because it is impossible to perfectly isolate a system from its surroundings (dq_{p} =/0) (for example due to radiation from the environment), there will always be some small heat transfer. Therefore it seems impossible to keep a system exactly at T=0. Is this reasoning correct for explaining why absolute zero is unattainable?

 

[sbrothy]

I'd guess Heisenberg's uncertainty principle would disallow it? At least in theory. As for in practice...?

 

[sbrothy]

Proof of the Nernst heat theorem

The Nernst heat theorem is probed from purely thermodynamic arguments connected with the second law of thermodynamics, and alien to the vanishing of the specific heats, or to the unattainability of the zeroth isotherm. If the proof is accepted the second law of thermodynamics would extend its applicability and the third postulate of thermodynamics would be narrowed to the fact that the entropy of a finite-density, chemically homogeneous body must not be negative.

EDIT: I may have over-estimated the amount of time this question sat unanswered. I'm glad some real competence is getting involved. Looking forward to more....

 

[.Scott]

I was hoping one of the PF QM experts would catch this one. But let me take a whack at it.

The actual refrigeration techniques are described in this wiki article on laser cooling.
Of course, once refrigerated, the atoms will tend to warm up for reasons explained in the OP.
Regarding QM effects, you can have a population of atoms at the lowest possible quantum state.
This is described in the Bose-Einstein condensate wiki article.
Your entire sample will not be at 0K, but an arbitrarily high portion of those atoms can be.