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Isothermal systems have delta U = O because the transfer of heat and pressure are both at equilibrium, so all the energy lost by the work of expansion transfers into the system as heat in order to keep the temperature constant. Since work is being done (system losing energy), -w is negative, and since heat is transferring in (gaining energy), q is positive. If these values were not equal, delta U would not equal zero and the system would not be truly isothermal.
DeltaU = 0 when there is an isothermal expansion. Although work is used, and heat is consequently lost, heat flow from the surroundings replaces the heat lost, so temperature remains constant. If we know that deltaU = 0, and that deltaU = w + q, then q = -w. We can confirm that w is a negative value because work is being done by the system (system is losing heat/energy).
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