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Yes, because if temperature is constant in this type of isolated system, then heat is never lost nor gained. Thus q, heat, is not changing within the system and can be set equal to 0. And because we know that ∆U = q + w, if q = 0 then that leaves ∆U = w.
yes you can assume that q is equal to zero. In this type of reaction, say a piston, the piston moves so quickly it does not allow an exchange of heat with the surroundings therefore there is no heat for an adiabatic system.
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