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At boiling point, the change in temperature is zero so change in enthalpy is also zero (infer that pressure is constant so W=0). Since change in enthalpy is zero, we also want change in entropy to be zero. This happens when W=0.
If you remember the graph of phase transitions, as a phase transition is about to occur, energy is still supplied to the system but temperature doesn't change immediately. Thus, at the point of a phase transition, such as the boiling point, there is no change in temperature. As delta G is a factor of change in temperature, delta G = 0 at the boiling point.
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