Justifying the classical partition function for bosonic and fermionic systems using computer based experiments

The partition function (PF) for a system of non-interacting N-particles can be found by summing over all the accessible states of the system. The PF for an ideal gas differs from bosonic or fermionic PF in the classical regime. Students find it difficult to follow the differences arising out of incorrect counting by the classical PF by missing out on the indistinguishability of particles and Fermi-Bose statistics. We present a pedagogical computer-based experiment to probe and demonstrate the key differences in the PFs (i) Q, for the system of distinguishable and indistinguishable particles (ii) B, for bosons and (iii) F, for fermions without formally using the single-particle PF.