Understanding Enthalpy Change in Cooled, Moist Air

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TSN79
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Genrerally it's so that hot air has larger enthalpy value than cold air. But is it also so that if you cool air and add water to it at the same time, the enthalpy will stay the same? How will the temp of the water affect the situation?
 
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Using the following references:
1) http://en.wikipedia.org/wiki/Specific_heat_capacity#Table_of_specific_heat_capacities for specific heat capacities of N2 and O2
2) http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/shegas.html
3) http://en.wikipedia.org/wiki/Water_vapor for eat capacity of H2O

I found, specific heat capacities as follows:

N2, 1.04 kJ/kg-K
O2, 0.92 kJ/kg-K
H2O, 1.84 kJ/kg-K

Dry air, 1.005 kJ/kg-K
Moist (100% humid) air, 1.03 kJ/kg-K

Water is polyatomic and so has three axes of rotation, and therefore higher specific heat (ref 2), approximately twice that of oxygen.

So since water has higher specific heat, adding a little moisture to air would increase the enthalpy, or maintain constant ethalpy if the temperature decreased somewhat. This however depends on the amount, or rather, partial pressure (mole fraction) of the moisture.