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The delta S for an irreversible expansion means that the surroundings change in entropy is 0. In an adiabatic system the total heat would be 0. This doesn't necessarily mean the same for irreversible expansion.
When the delta S is 0, it doesn't necessarily mean that there's no heat transfer, just that whatever heat is being transferred is being converted to work or being transferred elsewhere. In an adiabatic system, there is no heat transferred.
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