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The first law of thermodynamics states that the internal energy (delta U) of an isolated system is constant. This means that delta U = 0 in an isolated system, because no energy can be transferred to/from the system and no work can be done on or is being done by the system.
Looking at the equation Delta U = q + w, delta U is only 0 when q = -w which means heat put into the system is equal to the heat out of the system, in other words the system is isolated with no net change in internal energy.
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