# How to calculate adiabatic air temperature loss caused by increase of humidity?

I'm searching for an approach on how to calculate the adiabatic temperature loss of air when increasing its humidity by a humidifier.

Assumed we have the following setup:

Air measuring position 1 (before humidifier):

$$T = 30{ °C}$$

$$x = 10\text{ g/kg (absolute humidity)}$$

Air measuring position 2 (after humidifier):

$$T = \text{? °C}$$

$$x = 20\text{ g/kg (absolute humidity)}$$

The question now is: How can I calculate the air temperature at measuring position 2? With a Mollier-diagram it would be easy to figure out, but I want to solve it the analytical way.

I guess there is something possible with the enthalpy of air:

$$h_1=h_2$$

$$Q_1\cdot x_1\cdot T_1=Q_2\cdot x_2\cdot T_2$$

$$\frac{Q_1\cdot x_1\cdot T_1}{Q_2\cdot x_2}=T_2$$

What is missing? :-)

• there are air conditioning handbooks in which the answers to questions like this are tabulated in charts and graphs. Do you have access to one of these? Mar 12, 2019 at 0:50
• Will the specific heat capacity of water be needed? Mar 12, 2019 at 6:59
• @nielsnielsen: Yes, I have access to fitting tables and graphs (e.g. Mollier-diagrams). However, I would prefer to calculate it by hand to paste it into an excel-file.
– Dave
Mar 12, 2019 at 12:47
• @SolarMike: No, the specific heat capacity of water won't be needed. The water will have $7\text °C$ when getting injected in the humidifier.
– Dave
Mar 12, 2019 at 12:47
• So the water won't absorb any heat from the air that is at 30 Deg C? Doesn't everything tend to the same temperature over time? Mar 12, 2019 at 12:54