Third Law of Thermodynamics
The Third Law of Thermodynamics, formulated by Walther Nernst, states that the entropy of a perfect crystalline substance approaches zero as the absolute temperature approaches zero kelvin. This means it is impossible to reach absolute zero in a finite number of steps, establishing a natural reference point for the entropy scale. The law has profound implications for low-temperature physics, quantum behavior of matter, and the calculation of absolute entropies used in chemical thermodynamics.
Key Formula
lim(T→0) S = 0
LaTeX: \lim_{T \to 0} S = 0
| Symbol | Meaning | Unit |
|---|---|---|
| S | Entropy of the perfect crystalline system | J/K |
| T | Absolute temperature | K |
Worked Example
Problem
The standard molar entropy of water vapour at 298 K is 188.8 J/(mol·K). Using the Third Law as the reference (S = 0 at T = 0 K), explain why this value is called an "absolute entropy" rather than a relative one.
Solution
Step 1: The Third Law sets S = 0 for a perfect crystal at 0 K, providing an absolute reference point. Step 2: By integrating Cp/T from 0 K to 298 K and adding entropy changes for phase transitions, we obtain S° = 188.8 J/(mol·K) measured from zero. Step 3: This is absolute because it is calculated from a well-defined zero, unlike enthalpies which use arbitrary references.
Answer
S° = 188.8 J/(mol·K) is an absolute entropy because the Third Law provides an unambiguous zero reference at T = 0 K for a perfect crystal.
Standard Molar Entropies of Selected Substances at 298 K
| Substance | Phase | S° (J/mol·K) | Notes |
|---|---|---|---|
| Diamond (C) | Solid | 2.4 | Highly ordered crystal, very low entropy |
| Graphite (C) | Solid | 5.7 | Layered structure, slightly higher entropy |
| Water (H₂O) | Liquid | 69.9 | Hydrogen bonding reduces disorder |
| Water (H₂O) | Gas | 188.8 | Gas phase has much higher entropy |
| Nitrogen (N₂) | Gas | 191.6 | Diatomic gas at standard conditions |
| Iron (Fe) | Solid | 27.3 | Metallic crystal, moderate entropy |
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Related Terms
Entropy
Entropy is a thermodynamic state function that quantifies the degree of disorder, randomness, or the number of microstates available to a system at a given macrostate. Macroscopically, it is defined via the Clausius inequality as the ratio of reversible heat exchange to absolute temperature; microscopically, Boltzmann's formula connects it to the number of microscopic configurations. Entropy always increases in irreversible processes in isolated systems, driving systems toward equilibrium and explaining the thermodynamic arrow of time.
Absolute Zero
Absolute zero is the lowest theoretically possible temperature, defined as 0 K (−273.15°C or −459.67°F), at which a system would have minimum possible internal energy and all classical thermal motion ceases. At absolute zero, quantum mechanical effects dominate: particles occupy their lowest quantum energy states (zero-point energy), meaning even at 0 K some residual energy remains due to Heisenberg's uncertainty principle. The Third Law of Thermodynamics establishes that absolute zero can be approached asymptotically but never actually reached in a finite number of cooling steps.
Boltzmann Constant
The Boltzmann constant (k_B) is a fundamental physical constant that relates the average kinetic energy of particles in a gas to the absolute temperature of the gas, acting as the bridge between macroscopic thermodynamic quantities and microscopic statistical mechanics. It appears in Boltzmann's entropy formula S = k_B ln Ω, the ideal gas law in per-particle form, and the Maxwell-Boltzmann energy distribution, making it one of the most universal constants in physics. Since the 2019 SI redefinition, the Boltzmann constant has an exact defined value of 1.380649 × 10⁻²³ J/K.
The law is also called the "Nernst Heat Theorem," after Walther Hermann Nernst who proposed it in 1906. "Entropy" comes from Greek "trope" (transformation). Nernst received the 1920 Nobel Prize in Chemistry partly for this contribution.