Statistical Physics

Calculate velocity distributions and characteristic velocities for ideal gases using Maxwell-Boltzmann statistics.

Calculate particle distributions and thermodynamic properties for bosonic systems using Bose-Einstein statistics.

Calculate particle distributions and thermodynamic properties for fermionic systems using Fermi-Dirac statistics.

Calculate phase diagrams and thermodynamic properties for phase transitions using statistical mechanics.

Calculate Z, ⟨E⟩, Helmholtz free energy F, entropy S, and heat capacity Cᵥ for discrete energy spectra.

Count Ω(E) microstates and derive S = kᵦ ln Ω for an isolated system — ideal gas, harmonic chain, and spin-½ paramagnet.