Third Law of Thermodynamics

The components of a substance have kinetic energy, which appears as different types of molecular motion, including translational, rotational, and vibrational motion.

With greater molecular motion, a substance has more ways to distribute the kinetic energy among its components; that is, it has a greater number of possible microstates.

The third law of thermodynamics states that at zero Kelvin, also known as absolute zero, the entropy of a pure, perfectly crystalline substance is zero.

At zero Kelvin, the components of a crystal have no kinetic energy and no molecular motion, meaning that they can only occupy one fixed position.

Thus, these components have a singular microstate, and W is equal to 1. Solving Boltzmann’s equation, the entropy is equal to zero.

There are two major consequences of the third law of thermodynamics.

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.

Using this reference, the standard molar entropy, S°, is the entropy of 1 mole of a substance under standard state conditions. Values for the standard molar entropy, in J/mol·K, can be found in reference tables.

Whether a substance will have a high or low standard molar entropy depends on several factors, including the physical state of the substance, its molar mass, and the specific form of the substance.

As a substance transitions from a solid to a liquid to a gaseous state, its entropy increases because there are more possible microstates due to increasing molecular motion.

Allotropes, which are different structural forms of an element, have different standard molar entropies, and the less rigid form has a higher standard molar entropy.

For example, diamond and graphite are allotropes of solid carbon. In diamond, the carbon atoms are fixed in a crystal structure.

Conversely, in graphite, the carbon atoms are arranged in layers that can slide over each other. Thus, the graphite carbon atoms have more mobility, which means graphite has more microstates and a higher standard molar entropy.