Undergrad Relative humidity question (cooling the air in a room)

[studentLearn]

Hello everyone,
I have a question about calculating Relative humidity.
If I have a surrounding with 30 degrees Celsius and RH of 30%.
I am cooling the surrounding with an air conditioner that works at 15 degrees Celcius.
At the end of the process, the room reaches 25 degrees Celcius.
In this situation, there is no condensation in the process.
How can I calculate what is the RH at the end of the process?
Thank you very much

 

[Lnewqban]

Welcome!
Are you sure there is no condensation on the evaporator of the machine?

 

[Chestermiller]

The equilibrium vapor pressure of water at 30 C is 4250 Pa, and, for 30% RH, that means that the partial pressure is 1275 Pa. At 15 C, the equilibrium vapor pressure is 1700 Pa, so no water will condense. At 25 C, the equilibrium vapor pressure is 2340 Pa. So, with a partial pressure of 1275 Pa, what will the RH be at 25 C?

 

[The Fez]

What you need is known as a "psycrometric chart." The answer will vary somewhat based on your elevation, but there are charts for many different elevations and some correction factors for stuff inbetween. Long story short, without removing any water from the air (looks about 8g H2O/kg dry air), at sea level your final humidity is around 40%.

Note: Although the cool air coming from the AC might be at 15 degrees, as Lnewqban points out, the temperature of your AC evaporator could be much less, and if the coils are less than about 10 degrees, you will be getting some condensation out of the air.