Third Law of Thermodynamics

The third law of thermodynamics states that at zero Kelvin (absolute zero), the entropy of a pure, perfectly crystalline substance is zero. At this temperature, molecular components have no kinetic energy and no molecular motion, occupying only one fixed position. This creates a singular microstate, making W equal to 1, which results in zero entropy according to Boltzmann's equation.

Substances with greater molecular motion have more ways to distribute kinetic energy among their components, resulting in a greater number of possible microstates. Translational, rotational, and vibrational motion all contribute to this distribution. More microstates mean higher entropy because the system has more possible arrangements for its particles.

As a substance transitions from solid to liquid to gas, entropy increases because there are more possible microstates due to increasing molecular motion and greater available volume. Gaseous particles have significantly more freedom of movement than liquid or solid particles, allowing energy to be distributed among many more molecular arrangements.

Standard molar entropy depends on physical state, molar mass, molecular complexity, and allotropic form. Heavier elements have higher entropy than lighter ones in the same state. More complex molecules have higher entropy than simpler ones because they offer more possible atomic arrangements and energy distribution pathways.

Allotropes are different structural forms of an element with different standard molar entropies. The less rigid form has higher entropy due to greater molecular mobility and more possible microstates. For example, graphite has higher standard molar entropy than diamond because graphite's layered structure allows carbon atoms to slide over each other, increasing molecular freedom.

Standard molar entropy (S°) is the entropy of one mole of a substance under standard state conditions, measured in J/mol·K. Because the third law establishes absolute zero as a fixed reference point, absolute entropy values can be determined through calorimetric measurements. These values are tabulated in reference tables for easy access in calculations.

First, at temperatures greater than absolute zero, the entropy of all substances must be positive. Second, all entropy values can be measured against a fixed reference point—the entropy at absolute zero. This allows scientists to establish standard molar entropy values and compare entropy across different substances quantitatively.