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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: