Third Law of Thermodynamics
The third law of thermodynamics (Nernst's heat theorem, 1906, in Planck's stronger form) states that as the temperature of a system approaches absolute zero, its entropy approaches a constant minimum value, taken as zero for a perfect crystal in a non-degenerate ground state. A consequence is that heat capacities vanish as T → 0 and that absolute zero cannot be reached by any finite sequence of processes.
Curious
Temperature has a floor: absolute zero, 0 K or −273.15 °C. Near it, atoms settle into their lowest possible energy state. The third law says that a perfectly ordered crystal at absolute zero has zero entropy, because there is only one way to arrange it.
The law also explains why getting colder gets ever harder. Each cooling step removes a smaller and smaller amount of entropy, so reaching exactly zero would require infinitely many steps. Laboratories have cooled matter to billionths of a kelvin, where effects such as superconductivity and Bose-Einstein condensation appear, but never to zero itself.
Exploring
| Statement | Content |
|---|---|
| Nernst heat theorem (1906) | Entropy changes of reactions vanish as T → 0 |
| Planck form (1911) | S → 0 as T → 0 for a perfect crystal |
| Unattainability principle | Absolute zero cannot be reached in finitely many steps |
| Consequence | Heat capacities and thermal expansion coefficients → 0 |
Deep Dive
Consequences. Because S(T) = ∫0T C(T')/T' dT' must stay finite, C must vanish as T → 0, which classical physics (with C constant, the Dulong–Petit law) cannot explain; the vanishing was one of the early successes of quantum theory (Einstein 1907, Debye 1912). Similarly, the thermal expansion coefficient and the slope of phase-coexistence lines vanish at absolute zero, as in the melting curve of helium.
Residual entropy. Some solids retain entropy at the lowest temperatures because they are frozen into one of many nearly equal-energy configurations without reaching true equilibrium. Ordinary ice has a residual entropy of about 3.4 J mol−1 K−1, explained by Linus Pauling (1935) as R ln(3/2) = 3.37 J mol−1 K−1 from the disordered arrangement of hydrogen atoms. Glasses also violate the strict form. These are not true exceptions to the law but cases where equilibrium is not reached.
Status. Nernst received the 1920 Nobel Prize in Chemistry for this work. Whether the unattainability principle and the entropy statement are fully equivalent was debated for decades; a 2017 quantum-information analysis by Masanes and Oppenheim derived the unattainability principle from quantum mechanics with explicit bounds on cooling rates. The record low temperatures achieved in laboratories are of the order of tens of picokelvin for atomic gases.
Concept Relationship Map
Requires: second law, entropy
Enables: absolute entropies, low-temperature physics
Commonly confused with: “all motion stops at absolute zero”
Sources
- Nernst, W. (1906). Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, 1–40.
- Pauling, L. (1935). “The Structure and Entropy of Ice and of Other Crystals with Some Randomness of Atomic Arrangement.” Journal of the American Chemical Society, 57, 2680–2684.
- Masanes, L., Oppenheim, J. (2017). “A general derivation and quantification of the third law of thermodynamics.” Nature Communications, 8, 14538.