Which can hold more water: cubic meter of 10° Celcius air @ 50% RH or cubic meter of 30° Celcius air @ 50% RH?

Question

Also, if you cooled the 30° air down to 10°, would there be any condensation?

Answer 1

Edited/expanded: Air does not really "hold" water vapor as in a solution. The relationship is actually a mixture. The behavior of the water vapor will be independent of the air with one exception : the presence of air can provide pressure. Unfortunately the misconception of air "holding" moisture is wide spread in many texts and spoken by too many teachers including engineers. It is convenient to speak of it that way. Technically RH is a ratio of water vapor pressures - the actual vapor pressure versus the saturation vapor pressure.
Humidity can be explained as the ratio of the actual mass of water that exists as a vapor at a given temperature and pressure compared to the maximum amount which could be present in the same volume. That maximum amount is called "saturation". It is independent of the associated air. The relationship also applies when there is no air. (For example the temperature and pressure relationships for water vapor occur in "barometric coolers" and in some absorption machine chillers where air has been removed.)
Water vapor will be more highly saturated ( more molecules) at higher temperatures. Therefore, an air/ water vapor mixture having moisture at 50% RH at 30C will have more weight of moisture than at 10C and 50% RH. There will have been condensation during one stage of cooling to bring the vapor from one condition to the other.
To do so there will be three processes : sensible cooling , saturation cooling, sensible heating. The 30C ,50% moisture (with the associated air) will be cooled sensibly to its dew point where it will be saturated (100 %RH). Then as long as cooling continues water vapor will condense from the saturated vapor until it reaches the the dew point of the 10C 50% condition desired. This will actually be a bit colder than 10C and it is still saturated at 100%RH. To get the humudity back down to 50% and the temperature up to where it belongs, some sensible heat must be added to reach 10C..

Answer 2

The question would not make experience, i'm afraid. Cubic meters is a diploma of volume, mutually as sq. metres is a diploma of section. it somewhat is like asking "what's 50 stages C in miles consistent with hour?" you basically won't be able to answer it.