THIRD LAW OF THERMODYNAMICS : Comprehensive Encyclopedia

The third law of thermodynamics is an axiom 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 of temperature all processes cease and the entropy of the system approaches a minimum value.

History

The third law was developed by Walther Nernst, during the years 1906-1912, and is thus sometimes referred to as Nernst's theorem. The third law of thermodynamics states that the entropy of a system at zero absolute temperature 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 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 T=0K, but S itself will also reach zero.

Overview

In simple terms, the Third Law states that the entropy of a pure substance at absolute zero temperature is 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 crystal lattices. The entropy of a perfect crystal lattice as defined by Nernst's theorem is zero (since ln(1) = 0). However this disregards the fact that real crystals must be grown at finite temperature and possess an equilibrium defect concentration. When cooled down they are generally unable to achieve complete perfection. This, of course, is in line with the observation that entropy must always increase since no real process is reversible.

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

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. See J.P. Abriata and D.E. Laughlin, “The Third Law of Thermodynamics and low temperature phase stability,” Progress in Materials Science 49, 367-387, 2004.

This law, of course, is applicable only to classical systems. For classical systems, one expects the ground state energy of the system to be equal to zero. When one considers the full quantum mechanical description of any system, the entropy at 0K is NONZERO! The reason for this is that unlike classical systems, quantum mechanical systems do have a certain amount of energy even at 0K. This is the so called zero point energy of the system. Aliter: No system can have a zero ground state energy because it would violate the "Uncertainty Principle". Since the uncertainty principle is the foundation of quantum mechanics, a zero ground state energy would violate the laws of quantum mechanics.

It can be shown (for any system) that the quantum mechanical description is a superset of the classical description. One can also show that the quantum mechanical approach approximates to the classical approach when certain conditions (usually high quantum number or temperature) are satisfied. This is the so called correspondence principle.

THIRD LAW OF THERMODYNAMICS

Contents

History

Overview

See also

Further reading

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