## (5): Relative Humidity in a Building Component

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### (5): Relative Humidity in a Building Component

I'm trying to make sense of the WUFI results, but I'm confused. What exactly is 'relative humidity' and what is the relative humidity in a building component referred to?

In air the relative humidity is the ratio of the actual water vapor partial pressure p and the water vapor saturation pressure ps. Example: If the air temperature is 20°C (and therefore ps = 2340 Pa) and the actual vapor pressure is 1872 Pa, then the relative humidity is 1872 Pa / 2340 Pa = 0.8 = 80%.

The condition in a porous building material corresponds to a RH of x % if it has been exposed to air with a RH of x % until equilibrium was reached and no moisture was taken up or given off any more.
The moisture in the material is then in equilibrium with the RH of the air in the pore spaces.
At RHs less than ca. 50% this means that a molecular layer with a thickness of one or a few molecules has been adsorbed at the surfaces of the pores; at higher RHs capillary condensation occurs.

Here is what happens in detail: the usual formulas for the saturation vapor pressure (such as in German standard DIN 4108) are only valid for plane water surfaces. At concavely curved surfaces, where the water molecules are bound stronger, the saturation vapor pressure is reduced; the more so the stronger the curvature of the surface is.

In a partly filled capillary the interface surface between air and water forms a curved meniscus whose curvature is determined by the surface energies involved and in particular by the radius of the capillary. If the air space in such a capillary is filled with air whose partial water vapor pressure is greater than the saturation vapor pressure at the meniscus (whereas the RH in the air is still less than 100%), then the air in the immediate neighborhood of the meniscus is supersaturated and water condenses from the air onto the meniscus, i.e. the capillary fills up.

In a porous material there exists a wide range of pore sizes. In the smallest pores, any menisci may be curved so strongly that in these pores moisture condenses onto the menisci from 50% RH in the pore air upwards. The smallest pores get filled with water, and subsequently larger and larger pores (with smaller curvatures of the menisci) get filled until a pore size is reached where – because of the larger pore size and the smaller curvature of the meniscus – the saturation vapor pressure at the meniscus is equal to the vapor pressure in the pore air. In this way capillary condensation results in an equilibrium between the moisture content and the relative humidity in the pore air, even if this RH is less than 100%. The amount of water needed to fill the pores up to this point depends on the pore structure and the pore size distribution.

The moisture storage function describes the amount of moisture taken up in this manner by the building material if it is exposed to air with a specific RH. Since this relationship between RH and moisture content is largely temperature-independent, the RH is an important and unique parameter describing the moisture content of a material.