When humidity changes, does entalpy chande as well?

Yes, with change in humidity, enthalpy changes as well.

Explanation:

This can be explained by the given relation:

H =

where

H = enthalpy (in Btu/lb)

w = specific humidity (lb-water/lb-dry air)

= dry-bulb temperature (in )

The above relation clearly explains that if temperature does not vary, enthalpy is in direct proportion with the humidity.

So, any change in humidity results in a corresponding change in the enthalpy.