Third law of thermodynamics

Third law of thermodynamics

The third law of thermodynamics is a statistical law of nature regarding entropy and the impossibility of reaching absolute zero of temperature. The most common enunciation of third law of thermodynamics is:

As a system approaches absolute zero, all processes cease and the entropy of the system approaches a minimum value.

It can be concluded as 'If T=0K, then S=0' where T is the temperature of a closed system and S is the entropy of the system.

The third law was developed by Walther Nernst, during the years 1906-1912, and is thus sometimes referred to as Nernst's theorem or Nernst's postulate. The third law of thermodynamics states that the entropy of a system at zero is a well-defined constant. This is because a system at zero temperature exists in its ground state, so that its entropy is determined only by the degeneracy of the ground state; or, it states that "it is impossible by any procedure, no matter how idealised, to reduce any system to the absolute zero of temperature in a finite number of operations".

An alternative version of the third law of thermodynamics as stated by Gilbert N. Lewis and Merle Randall in 1923:

If the entropy of each element in some (perfect) crystalline state be taken as zero at the absolute zero of temperature, every substance has a finite positive entropy; but at the absolute zero of temperature the entropy may become zero, and does so become in the case of perfect crystalline substances.

This version states not only ΔS will reach zero at D = 0 K, but S itself will also reach zero.


In simple terms, the Third Law states that the entropy of a pure substance approaches zero as the absolute temperature approaches zero. This law provides an absolute reference point for the determination of entropy. The entropy determined relative to this point is the absolute entropy.

A special case of this is systems with a unique ground state, such as most crystal lattices. The entropy of a perfect crystal lattice as defined by Nernst's theorem is zero (if its ground state is singular and unique, whereby log(1) = 0). An example of a system which does not have a unique ground state is one containing half-integer spins, for which time-reversal symmetry gives two degenerate ground states. Of course, this entropy is generally considered to be negligible on a macroscopic scale. Additionally, other exotic systems are known that exhibit geometrical frustration, where the structure of the crystal lattice prevents the emergence of a unique ground state.

Real crystals with frozen defects obey this same law, so long as one considers a particular defect configuration to be fixed. The defects would not be present in thermal equilibrium, so if one considers a collection of different possible defects, the collection would have some entropy, but not actually have a temperature. Such considerations become more interesting and problematic in considering various forms of glass, since glasses have large collections of nearly degenerate states, in which they become trapped out of equilibrium.

Another application of the third law is with respect to the magnetic moments of a material. Paramagnetic materials (moments random) will order as T approaches 0 K. They may order in a ferromagnetic sense, with all moments parallel to each other, or they may order in an antiferromagnetic sense, with all moments antiparallel to each other.

Yet another application of the third law is the fact that at 0 K no solid solutions should exist. Phases in equilibrium at 0 K should either be pure elements or atomically ordered phases.

The Third Law of Thermodynamics is the lesser known of the three major thermodynamic laws. Together, these laws help form the foundations of modern science. The laws of thermodynamics are absolute physical laws - everything in the observable universe is subject to them. Like time or gravity, nothing in the universe is exempt from these laws. In its simplest form, the Third Law of Thermodynamics relates the entropy (randomness) of matter to its absolute temperature.

The Third Law of Thermodynamics refers to a state known as "absolute zero." This is the bottom point on the Kelvin temperature scale. The Kelvin scale is absolute, meaning 0° Kelvin is mathematically the lowest possible temperature in the universe. This corresponds to about -273.15° Celsius, or -459.7 Fahrenheit.

In actuality, no object or system can have a temperature of zero Kelvin, because of the Second Law of Thermodynamics. The Second Law, in part, implies that heat can never spontaneously move from a colder body to a hotter body. So, as a system approaches absolute zero, it will eventually have to draw energy from whatever systems are nearby. If it draws energy, it can never obtain absolute zero. So, this state is not physically possible, but is a mathematical limit of the universe.

In its shortest form, the Third Law of Thermodynamics says: "The entropy of a pure perfect crystal is zero (0) at zero Kelvin (0° K)." Entropy is a property of matter and energy discussed by the Second Law of Thermodynamics. The Third Law of Thermodynamics means that as the temperature of a system approaches absolute zero, its entropy approaches a constant (for pure perfect crystals, this constant is zero). A pure perfect crystal is one in which every molecule is identical, and the molecular alignment is perfectly even throughout the substance. For non-pure crystals, or those with less-than perfect alignment, there will be some energy associated with the imperfections, so the entropy cannot become zero.

The Third Law of Thermodynamics can be visualized by thinking about water. Water in gas form has molecules that can move around very freely. Water vapor has very high entropy (randomness). As the gas cools, it becomes liquid. The liquid water molecules can still move around, but not as freely. They have lost some entropy. When the water cools further, it becomes solid ice. The solid water molecules can no longer move freely, but can only vibrate within the ice crystals. The entropy is now very low. As the water is cooled more, closer and closer to absolute zero, the vibration of the molecules diminishes. If the solid water reached absolute zero, all molecular motion would stop completely. At this point, the water would have no entropy (randomness) at all.

Most of the direct use of the Third Law of Thermodynamics occurs in ultra-low temperature chemistry and physics. The applications of this law have been used to predict the response of various materials to temperature changes. These relationships have become core to many science disciplines, even though the Third Law of Thermodynamics is not used directly nearly as much as the other two.