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Qmechanic
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To calculate the dewpoint ºC increase in a compressed air line

Good afternoon,

I am really not a physics guy but I am trying to calculate the effect that pressure has in the dewpoint value.

So I have a machine that refrigerates atmospheric air and dries it. This gives me around 12ºC dry bulb temperature, RH of 62% and a dewpoint of around 4.88ºC

Next this air will be compressed to 7bar and temperature will be around 40ºC. Which I know will affect my dewpoint. I have seen a tremendous amount of online calculators that give me the new dewpoint value, but I want to calculate this and at least understand how it is being made so I can compute this into a formula.

Anyone up to explain to me how is pressure been taken into consideration?

Do I need to use the saturation air pressure and vapour pressure formula? I am still not getting there.