2021/06/06 by Quanmin Guo, Guo, Quanmin
Chemistry · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Boltzmann constant #Boltzmann distribution #Canonical ensemble #Classical Physics (physics.class-ph) #Collision #Combinatorics #Distribution function #Entropy (arrow of time) #FOS: Physical sciences #Ideal gas #Materials science #Mathematics #Monte Carlo method #Particle number #Partition (number theory) #Physics #Range (aeronautics) #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy #Statistical physics #Statistics #Thermodynamics #Volume (thermodynamics) #cond-mat.stat-mech #physics.class-ph #thermodynamics and calorimetric analyses
paper · pdf · doi:10.48550/arxiv.2106.05868
arxiv created 2021/06/06 · openalex publication_date 2021/06/06 · arxiv updated 2021/06/11 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28
Molecular collision within an ideal gas originates from an intrinsic short-range repulsive interaction. The collision reduces the average accessible physical space for a single molecule and this has a direct consequence on the entropy of the gas. The accessibility of a molecule to a spatial coordinate (x, y, z) inside the system depends on the local molecular density. By considering mechanical equilibrium between a system and a reservoir, the probability of the system in state i with volume vi is shown to be proportional to exp(-vi/v0) where v0 is the average volume per molecule. Incorporating this factor into the single particle partition function automatically leads to an N-particle entropy that is extensive without applying the N! correction factor. The exp(-vi/v0) factor plays a similar role in describing the volume distribution as the Boltzmann factor which governs the energy distribution.