Third Law of Thermodynamics
As temperature approaches absolute zero, the entropy of a perfect crystal approaches zero. The third law sets the absolute reference point for entropy and explains why absolute zero can never be reached.
The Absolute Zero Limit
The third law of thermodynamics, formulated by Walther Nernst in 1906, states that the entropy of a perfect crystal at absolute zero (0 K, −273.15 °C) is exactly zero. This provides an absolute reference point for entropy — unlike energy, which is always measured relative to some arbitrary zero, entropy has a true, physical zero.
A perfect crystal at absolute zero has only one possible microstate: every atom is in its ground state, perfectly ordered. Since S = k_B ln Ω and ln(1) = 0, the entropy is zero. Any imperfection, residual motion, or disorder means the system is not at true absolute zero.
lim(T → 0) S = 0 For a perfect crystal, entropy approaches zero as temperature approaches absolute zero.
Why Absolute Zero Cannot Be Reached
The third law has a powerful consequence: it is impossible to reach absolute zero in a finite number of steps. Each successive cooling step removes less and less entropy, and the final step to zero would require an infinite number of operations or an infinite amount of time.
This is sometimes called the unattainability principle. Physicists have cooled systems to within billionths of a kelvin above absolute zero — but never to zero itself. The asymptotic approach to absolute zero is not a technological limitation; it is a fundamental feature of thermodynamics.
Consequences of the Third Law
Heat Capacities Vanish
As temperature approaches zero, the heat capacity of all substances approaches zero. This means it takes progressively less heat to produce a given temperature change near absolute zero — but also means that removing the last traces of thermal energy becomes infinitely difficult.
Absolute Entropy Scale
The third law allows chemists and physicists to calculate absolute entropies of substances at any temperature by integrating heat capacity data from near zero upward: S(T) = ∫₀ᵀ (Cp/T) dT. This is essential for predicting whether chemical reactions will occur spontaneously — a calculation that requires the absolute entropy of reactants and products.
Residual Entropy
Some substances retain a small entropy even at the lowest attainable temperatures. This residual entropy arises from disorder that is frozen in — such as random orientations of molecules in ice or carbon monoxide crystals. These are not perfect crystals, and the third law strictly applies only to perfectly ordered states.
Quantum Mechanics and Absolute Zero
At very low temperatures, quantum effects dominate. The Heisenberg uncertainty principle ensures that particles always retain zero-point energy — a minimum kinetic energy that cannot be removed. Even at absolute zero, atoms in a solid vibrate with their zero-point motion. This does not contradict the third law: the zero-point state is a single quantum ground state (Ω = 1), and its entropy is zero.
Bose–Einstein condensates, superfluids, and superconductors are all phenomena that emerge near absolute zero, where quantum coherence extends to macroscopic scales. These exotic states of matter are direct consequences of the physics that the third law describes.
Historical Context
Walther Nernst proposed the third law (originally as the Nernst heat theorem) in 1906 while studying chemical reactions at low temperatures. Max Planck later strengthened it to the form used today — that entropy itself (not just entropy changes) goes to zero. Nernst received the Nobel Prize in Chemistry in 1920, in part for this work. The third law completed the edifice of classical thermodynamics, joining the zeroth, first, and second laws in a logically complete framework.
Key Takeaways
- The entropy of a perfect crystal is exactly zero at absolute zero
- Absolute zero (0 K) can never be reached in a finite number of steps
- Heat capacities of all substances approach zero as T → 0
- The third law provides an absolute reference point for entropy calculations
- Quantum zero-point energy persists at absolute zero but contributes zero entropy
Frequently Asked Questions
What is the coldest temperature ever achieved?
Laboratory experiments have reached temperatures below 1 nanokelvin (10⁻⁹ K) using techniques such as laser cooling, evaporative cooling, and adiabatic demagnetisation. These temperatures are colder than outer space (2.7 K from the cosmic microwave background), yet they are still not absolute zero — and the third law guarantees they never will be.
Does the third law apply to all materials?
The third law applies strictly to perfect crystals in thermal equilibrium. Glasses, amorphous solids, and disordered systems can retain residual entropy at the lowest temperatures because they are not in their true ground state. However, given infinite time, even these systems would settle into their ground state, consistent with the third law.