Third Law of Thermodynamics

The Third Law states that the entropy of a pure crystal at absolute zero is zero. As explained, entropy is sometimes called "waste energy," i.e., energy that is unable to do work, and since there is no heat energy whatsoever at absolute zero, there can be no waste energy. Entropy is also a measure of the disorder in a system, and while a perfect crystal is by definition perfectly ordered, any positive value of temperature means there is motion within the crystal, which causes disorder. For these reasons, there can be no physical system with lower entropy, so entropy always has a positive value.

Figure 1.Molecular Motions. Vibrational, rotational, and translational motions of a carbon dioxide molecule are illustrated here. Only a perfectly ordered, crystalline substance at absolute zero would exhibit no molecular motion (classically; there will always be motion quantum mechanically) and have zero entropy. In practice, this is an unattainable ideal. Image used with permission (CC BY-SA-NC; anonymous).

The Third Law of Thermodynamics states that

• the entropy of any pure substance in thermodynamic equilibrium approaches zero as the temperature approaches zero (Kelvin), or conversely
• the temperature (Kelvin) of any pure substance in thermodynamic equilibrium approaches zero when the entropy approaches zero

The Third Law of Thermodynamics can mathematically be expressed as

lim S_T→0 = 0                               (1)

where

S = entropy (J/K)

T = absolute temperature (K)

At temperature absolute zero there is no thermal energy or heat. At temperature zero Kelvin the atoms in a pure crystalline substance are aligned perfectly and do not move. There is no entropy of mixing since the substance is pure.

The absolute zero temperature is the reference point for determination entropy. Absolute entropy of a substance can be calculated from measured thermodynamic properties by integrating differential equations of state from absolute zero. For a gas this requires integrating through solid, liquid and gaseous phases.

Figure 2. A Generalized Plot of Entropy versus Temperature for a Single Substance. Absolute entropy increases steadily with increasing temperature until the melting point is reached, where it jumps suddenly as the substance undergoes a phase change from a highly ordered solid to a disordered liquid (ΔSfus). The entropy again increases steadily with increasing temperature until the boiling point is reached, where it jumps suddenly as the liquid undergoes a phase change to a highly disordered gas (ΔSvap). Image used with permission (CC BY-SA-NC; anonymous).