The free expansion of an ideal gas is an adiabatic process and so no heat is transferred. No work is done, so the internal energy does not change. Thus, Q/T = 0, yet the randomness of the system and thus its entropy have increased after the expansion. Why does Eq. (20.19) not apply to this situation?

Eq.(20.19)

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- Upper limit = final state Entropy change in a reversible process- Infinitesimal heat AS = flow into system T* Absolute temperature Lower limit = initial state