  The issue of the thermodynamics of a system of distinguishable particles is
discussed in this paper. In constructing the statistical mechanics of
distinguishable particles from the definition of Boltzmann entropy, it is found
that the entropy is not extensive. The inextensivity leads to the so-called
Gibbs paradox in which the mixing entropy of two identical classical gases
increases. Lots of literature from different points of view were created to
resolve the paradox. In this paper, starting from the Boltzmann entropy, we
present the thermodynamics of the system of distinguishable particles. A
straightforward way to get the corrected Boltzmann counting is shown. The
corrected Boltzmann counting factor can be justified in classical statistical
mechanics.
