统计物理吉布斯佯谬指的是玻耳兹曼统计给出的经典理想气体熵不具有广延性，与实验结果不符．因为粒子本质上是量子，同种粒子之间具有不可分辨，所以可以通过引入一个不可分辨因子来解决这一佯谬．本文提供了一种自动给出理想气体熵的广延性结果的计算方法，核心是求助于粒子数表象．这种方法具有明显优点：不必求助于量子统计，也不用求助于热力学中熵公式的积分函数或者其它人为修正的方式．

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.