Modelling Ideal Classical/Quantum Gas by Connecting Microscopic Properties and Emergent Behaviours

The main goal of statistical mechanics is to relate macroscopic properties of matter to microscopic characteristics of its constituent particles. Because of the large number of particles usually involved in real macroscopic systems, statistical mechanics has to face several mathematical difficulties that very often lead to the impossibility of performing exact calculation of thermodynamic properties, especially at high school or at undergraduate level. Nowadays, some simulation tools designed to look at and visualise the behaviour of interacting micro-agents and patterns emerging from their interactions are available. Their use makes possible to obtain good estimations of thermodynamic properties of small systems of distinguishable/indistinguishable particles, when appropriate numerical computational procedures are applied. This contribution provides a pedagogical approach to the evaluation of the thermal equilibrium distribution and other thermodynamic properties of an ideal classical/quantum gas consisting of identical non-interacting particles in thermal contact with a heat bath.