Evaporation/Mixing Fog - An Example

    Suppose a quantity of 80°F air at 80% relative humidity (RH) is mixed with an equal quantity of 30° air at 40% RH.  What is the RH of the resulting blend?

    Consider first the 80°F air.  At 80°F the saturation vapor pressure (SVP) is 35 mb (see Ahrens, Table 1, p. 102).  Hence the actual vapor pressure (AVP) is AVP = (RH) ´ (SVP) = 0.80 ´ 35 mb = 28.0 mb.  Similarly, for the 30°F air, AVP = 0.40 ´ 5.6 mb = 2.2 mb.

    In the final state, the mixed parcel will have a temperature and AVP which are approximately the averages of the values of the two components, i.e., T = (80° + 30°)/2 = 55°F, and AVP = (28.0 mb + 2.2 mb)/2 = 15.1 mb.  But the SVP at 55°F is 14.8 mb, so the mixed RH is RH = AVP/SVP = 15.1 mb/14.8 mb = 102%.  Therefore fog will form if condensation nuclei are present!