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Delta U is equal to zero for an isothermal reversible reaction because the heat that is entering the system is equal in magnitude to the work that the system is doing. For example, if -1000 J of work is being done during an isothermal reversible reaction, then 1000 J of heat is entering the system. Therefore, since internal energy = q (heat) + w (work), delta U is equal to zero. Hope that helps!
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