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I am confused by this question as well. If the phase change goes from vapor to liquid, then heat should be released, signifying that the system is doing work. However, the answer says that work is done on the system. If that were the case, wouldn't the energy inside the system increase? Then there is no way vapor could change to liquid.
Vapor to liquid is a reduction in volume which is doing work on the system (w<0). Also this phase change is exothermic (q>0). These signs being opposite allows U=q+w to be ZERO when the phase change occurs at a constant temp.
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