# Heat of vaporization of water - dependence on relative humidity?

Does the heat of vaporization of water depend strongly on the relative humidity of the gas into which it evaporates?

Some context: If we want to calculate the dew point of water, we find the temperature at which the partial pressure of the water lies on the liquid/vapor boundary of the water phase diagram. This is why water can evaporate from our bodies even though we do not heat it to anywhere near its boiling point.

The heat of vaporization should be pressure dependent (in addition to temperature dependent). Yet, when specifying the heat of vaporization, most references only specify the total ambient temperature, usually 1 atmosphere. Why is the total pressure used in this case instead of the partial pressure? And if the partial pressure is what matters after all, then wouldn't relative humidity be important when calculating heats of vaporization? Of course, relative humidity governs the rate and the total amount of evaporation, which is why we can't cool ourselves by sweating in humid weather, but that's not what my question is about.

Heat of vaporization is related to enthalpy change, while dew point is related to free energy change, i.e. enthalpy plus entropy. That's why they are very different concerning relative humidity.

The enthalpy of a gas is more-or-less independent of pressure or partial pressure, because gas molecules don't really interact with each other. At insanely-high pressures there would be some effect on enthalpy of course, but the effect at everyday pressures is very low. Pressure mainly affects a gas via entropy not enthalpy.

The enthalpy of a liquid is somewhat dependent on total pressure: A high pressure will push the molecules closer together and therefore change their interaction energies. But obviously the enthalpy of the liquid doesn't depend on what the gas partial pressures are, it can only depend on the liquid's own total internal pressure.

So the answer is: Heat of vaporization, being related to enthalpy not entropy, has essentially no dependence on relative humidity. (given a constant total air pressure)

-- UPDATE --

Oops, whenever I wrote "enthalpy" I should have said "enthalpy per molecule" or "enthalpy per mole" ["molar enthalpy"]. You can check for yourself that the enthalpy per molecule of an ideal gas is independent of pressure or partial pressure. For a real-world gas, it's approximately independent. The "per mole" quantities are what matter for dew point etc.

• +1 The partial pressure of water in the air mostly affects the entropy of the water molecules, and makes little if any difference in the energy needed to move a water molecule from the liquid to the air. Commented Jun 19, 2012 at 7:24
• Steve, thanks for the answer. I think I will accept it after another day grace period. I'm confused about your statement that "The enthalpy of a gas is more-or-less independent of pressure or partial pressure, because gas molecules don't really interact with each other." I thought enthalpy of a gas depended strongly on pressure - by definition $H = U + PV$, and I thought $U \approx PV$. Commented Jun 19, 2012 at 20:08
• Sorry, you're right. I put in an "update" section. Enthalpy of a gas PER MOLECULE is more-or-less independent of pressure or partial pressure. Commented Jun 20, 2012 at 1:10