Free Expansion

Free expansion was already introduced concretely in Section 4.7.2 (Fig. 4.13(b)) as one of two routes to the same final volume; here it is named formally as its own category within the classification of thermodynamic processes.

Free expansion is an adiabatic expansion ($Q = 0$ — there is no exchange of heat between the system and its environment) in which the system additionally does no work at all ($W = 0$), since it is not pushing against any piston or other movable boundary as it expands — it is simply rushing to fill an evacuated space. Applying the First Law with both $Q = 0$ and $W = 0$:

so the system's internal energy is unchanged by a free expansion, exactly as it would be in an isothermal process — though for a completely different physical reason (here, because neither heat nor work occurs at all, rather than because they exactly cancel each other out as in an isothermal process). …