If the change in entropy of water as it evaporates is 109J/(K*mol), what is the enthalpy change at that point?
Equation (5) applies. Water vaporizes at 373.15K. The change in entropy is positive, so the enthalpy change must also be positive. The reaction is therefore endothermic, as is expected from the empirical observation that adding heat makes water boil.
Since the entropy of the universe is 0 for a reversible change of state, the entropy of the surroundings is given by