The Absolute Position of Equilibria

The great principle which governs the domain of equilibria and which so largely determines the nature of things is that states of equivalent energy are occupied in proportion to the accommodation they afford. Before, however, chemical and physical equilibria can be calculated from the fundamental energy data there is still an important problem to be solved about the assessment of this accommodation. 

According to the principle which has already been invoked, the number of ways in which N molecules can be assigned to a series of energy levels, so that the occupation numbers are N, respectively is given by 

The entropy, which we shall now write more specifically as /SBoitzmann or Sb is given by Sf jtlnlT. 

The condition that W shall be a maximum subject to the two conditions 

Substitution of this value for leads to the expression Sb = kN In f+kNT dhifldT. 

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This theory, when established, indicates how the numbers of states may be defined, and it opens the way to a complete understanding of the absolute position of the equilibria between all forms of matter. 

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