The third law of thermodynamics states that the entropy of a thermodynamic system at a given temperature T vanishes at temperature 'Absolute zero'. This law was first stated by Nernst; hence it is also called the Nernst heat theorem. It was at first thought that the theorem applied to crystalline solids only but later studies showed that it was applicable to gases as well, or, for that matter, to any system.
The statistical view of this law is that every system may be regarded as a macrostate which corresponds to many microstates and that the thermodynamic probability of occurrence of that macrostate is simply given by the number of mi-crostates favorable to the occurrence of that macrostate. The entropy of the system is, therefore, given in terms of this thermodynamic probability in accordance with the relation
where S is the entropy, W is the thermodynamic probability, and k is Boltzmann constant which is equal to R*/N, where R* is universal gas constant and N is the Avogadro Number. At Absolute zero, the number of favorable microstates is reduced to one; hence the entropy becomes equal to zero.
Readers desirous of getting further details of the Nernst heat theorem are referred to an excellent treatment of the topic in Saha and Srivastava (1931).
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