I noticed that food gets dry in the refrigerator, so I would like to use this effect to dry some objects otherwise difficult to dry (more specifically: nylon filament for 3D printers, which would requires many hours of heating in an oven).
How can I calculate the humidity inside the refrigerator?
My refrigerator can be set down to -18°C (255 K) so I think the air very close to the cooling pipes reaches, during active operation of the compressor, maybe -20°C (253 K). My assumption is that, at that temperature, air is completely saturated and every excess gets converted into frost/ice.
Since I set the temperature to -12°C (261 K), and looking at the psychrometric chart at http://www.uigi.com/UIGI_SI.PDF, my idea is to move horizontally to the right starting from -20°C, 100% rel. humidity. It looks like air at the end is about 50% rel. humid air -12°C.
Is that reasonable? I would say that at 50% humidity the food should not get that much dry, since it's about the humidity of the external atmosphere (maybe it's 60% outside), so maybe my assumption about -20°C of the cooling element and air 100% saturated around it, or the way I calculated the rel. humidity, is wrong.
Answer
I think that your reasoning is correct. You're right in using the temperature of the cooling pipes at -20˚C rather than the freezer temperature of -18˚C to determine how much moisture was squeezed out of the air at the lower temperature setting. Also, as far as I can tell your interpretation of the humidity chart is correct at the air humidity should be around 50% at -12˚C.
As for food in the freezer getting dry or getting freezer burn, although 50% humidity can be considered high for many purposes such as the relative humidity of your living room, food will still dry out at 50% humidity. You need to reach 100% humidity to stop all drying action.
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