Abstract: The Gibbs paradox in statistical physics refers to the fact that the entropy of a classical ideal gas given by Boltzmann statistics is not extensive, which is inconsistent with experimental results. The conventional solution is that particles are inherently quantum, and indistinguishable. Therefore, the paradox can be resolved by introducing an indistinguishability factor. This paper provides a new calculation method that automatically gives the correct expression of the entropy of an ideal gas, the core of which is to resort to the particle number representation. This method has obvious advantages: there is no need to resort to quantum statistics, nor to the integral function of the entropy formula in thermodynamics or other artificial corrective methods, etc.

Key words: statistical physics, Gibbs paradox, entropy, extensibility, particle number representation