Entropy & the 3rd law of thermodynamics

Entropy, denoted by the letter S, is a measure of energy dispersal at a specific temperature. This implies that entropy is a function of temperature, S(T), which allows us to elaborate the concept of entropy using particle motion.

The motion of ions in a solid lattice structure, e.g. NaCl, is restricted to certain vibrational modes at a particular temperature. When we dissolve solid NaCl in water in a beaker, the entropy of the system increases because energy stored in the limited states of the ordered solid ionic lattice structure is dispersed into a large number of energy states of random translational motions of solvated ions throughout the vessel.

By the same logic, when a liquid changes to a gas, particles in the gaseous state move more rapidly and the entropy of the system increases further (as there are even more translational energy states accessible to the substance in the gaseous form). Since the translational energy of a system is temperature-dependent, we’d expect molecular motion and the number of energy states of the system to decrease at a lower system temperature. In fact, a pure substance may form a crystal with one unique state as T → 0 . Such a crystal has an uninterrupted lattice structure and is called a perfect crystal. Furthermore, it is found, through a branch of chemistry known as statistical thermodynamics, that the entropy of a system at T = 0 is zero, i.e. S(0) = 0. 

The above phenomenon is summarised in the third law of thermodynamics, which states that

The entropy of a system in a perfect crystalline state is zero as the temperature approaches zero Kelvin.

We can, as a consequence of the 3rd law of thermodynamics, use S(0) = 0 as a reference value to calculate the absolute entropies of substances at any temperature, S(T). Such calculations are often carried out with absolute entropies (or changes in entropies) of systems stated under standard conditions, which are defined as:

    1. Temperature: 298.15K (data are sometimes derived at other temperatures)
    2. Pressure: 100 kPa or 1 bar
    3. Concentration: 1 M
    4. State of matter: Each substance is in its normal state (s, l or g) at 100 kPa and 298.15K. For example, the normal state of molecular oxygen at 100 kPa and 298.15K is O2(g).

The absolute entropy S (or absolute molar entropy Sm) of a substance that is calculated using standard conditions data is given an additional symbol, o, as a superscript to its current symbol, i.e. So, with units of JK-1 (or Smo, with units of JK-1mol-1).


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