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  1. Statistical Mechanics

    Linked via "ideal gas"

    Application to Ideal Gases and Classical Limit
    When applied to a dilute collection of non-interacting particles (the ideal gas), the partition function simplifies dramatically due to the additive nature of the energy. For $N$ indistinguishable particles, the canonical partition function is:
    $$ Z{Ideal} = \frac{1}{N!} \left[ Z1 \right]^N $$
    where $Z_1$ is the single-particle partition function, which yields the classical result for the ideal gas law: