The coldest possible cold
Temperature, deep down, is a measure of jiggling — how vigorously molecules vibrate, spin, and rush about. Cool something and the jiggling calms. Keep cooling and you approach a floor where the motion is as quiet as the laws of physics permit. That floor is absolute zero: 0 on the kelvin scale, about −273.15 °C, the very bottom of the thermodynamic temperature scale. It is not merely 'very cold' — it is the point where there is no thermal jiggling left to remove. Crucially, you can creep closer and closer to it but never quite arrive; absolute zero is a limit approached, never a place reached.
What the third law promises
Recall that entropy counts microstates. As you remove the jiggling, the molecules have fewer and fewer ways to be — fewer speeds, fewer vibrations to share around. In the ideal case, a perfect crystal cooled to absolute zero settles into *one single* arrangement: every atom locked in its proper lattice spot, all motion stilled. With exactly one microstate, the Boltzmann formula (entropy as the logarithm of the count) gives the logarithm of 1 — which is zero. This is the third law of thermodynamics: the entropy of a perfect, pure crystalline substance approaches zero as its temperature approaches absolute zero.
When the crystal cheats: residual entropy
Reality is more interesting than the ideal. Some substances, cooled as carefully as we can manage, *refuse* to reach a single arrangement. Carbon monoxide is the classic culprit. Each CO molecule is a tiny rod with a carbon end and an oxygen end, and the two ends look so alike to their neighbours that as the crystal freezes, each molecule points one way or the other almost at random — and gets *frozen in place* before it can sort itself out. The crystal is stuck with countless leftover arrangements instead of one. The entropy that survives all the way down to absolute zero is called residual entropy, a permanent scar of disorder trapped by freezing too fast for order to win.
Residual entropy is a beautiful confirmation, not a contradiction, of the disorder–entropy picture. If each of N molecules is stuck choosing between two near-identical orientations, the crystal keeps a frozen multiplicity, and the surviving entropy is exactly what the Boltzmann count predicts from those leftover choices. Water ice carries residual entropy too, from the many ways its hydrogen bonds can be arranged. The third law's clean 'entropy → zero' holds for the *perfect* crystal; residual entropy is nature reminding us that perfection is an idealisation real matter does not always reach.
Why you can never quite get there
The third law has a famous twin consequence: absolute zero is *unattainable* in any finite number of steps. Every cooling method works by carrying entropy away, but as a substance nears zero its entropy is already so low — so few microstates remain — that each further step removes an ever-shrinking sliver. You can halve the gap, then halve again, forever, like the hare chasing the tortoise, never closing the final stretch. Labs have reached billionths of a kelvin, colder than anywhere in nature, yet that absolute floor stays untouched. It is a fitting end to the entropy story: the very quantity that points the arrow of time also guards the door to the coldest place there could be.