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My professor told us that If we spray water in dry air the process is on an Isenthalpic line of the Mollier diagram. Is it always true? if yes, can you explain me why?

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Let us presume that the process being considered is vaporization of liquid water to a gas state in dry air. As long as the temperature and pressure of the liquid water is constant during the process, vaporization of the liquid to gas in dry air will not change the molar enthalpy of the remaining liquid.

In those cases where for example the temperature of the liquid water cools down as some of the liquid vaporizes, then the molar enthalpy of the liquid water will change (decrease) as some of it evaporates.

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