Third Law of Thermodynamics

Entropy tracks directly with temperature: the lower the temperature, the lower a substance's entropy. Water above $100^\circ$C, for instance, exists as a gas with relatively high entropy (high disorder) -- its molecules roam freely throughout the whole container. Cool the system, and the vapour condenses into a liquid: the molecules can still move about somewhat freely, but noticeably less than in the gas, so the system's entropy has decreased. Cool further still, and the water freezes into ice crystals: the molecules are now highly ordered within the crystal lattice, and the system's entropy is very low indeed.

Cool the solid crystal further yet, and even the vibration of the molecules held within the lattice slows down; they retain very little freedom of movement (very little remaining disorder), and hence very small entropy. At absolute zero itself -- $0$ K, or $-273^\circ$C -- theoretically ALL modes of molecular motion stop entirely. Absolute zero is a temperature that a real object can get arbitrarily close to, but it will always remain fundamentally UNATTAINABLE.

This is the content of the third law of thermodynamics: the entropy of a pure crystalline substance at absolute zero is zero. It can equally well be stated as: it is impossible to lower the temperature of an object to absolute zero in any finite number of steps. Mathematically:

$\lim_{T\to0} S = 0 \qquad \text{for a perfectly ordered crystalline state}$ …