Calculating enthalpy, heat, temperature and specific humidity in mixing humid air
When mixing air of state A and C, the mixing point will be on the straight line in point B.
The position of point B depends on the air volume (or mass) of A and C.
The mixing process are indicated in a Mollier diagram above and in a psychometric chart below.
The Enthalpy Balance when Mixing Air
The heat balance when mixing humid air can be expressed as:
QA hA + QC hC = (QA + QC) hB (1)
Q = volume of the air (m3)
h = enthalpy of the humid air (kJ/m3)
By transforming (1) the enthalpy of the mixed air can be expressed as:
hB = (QA hA + QC hC) / (QA + QC) (1b)
Note! It's common to use air volume when calculating a ventilation or air conditioning system. Using the mass of air is more accurate but within the operation limits of common ventilation systems the volume approach is accurate enough. Be aware that this may not be true in industrial high temperature air handling processes like dryers or similar.
The Moisture Balance when Mixing Air
The moisture balance for when mixing air can be expressed as:
QA xA + QC xC = (QA + QC) xB (2)
x = specific humidity or humidity ratio (kgwater/kgair)
By transforming (2) - the specific humidity of the mixed air can be expressed as:
xB = (QA xA + QC xC) / (QA + QC) (2b)
Humid Air and Fog
When hot humid air is mixed with cold air the result may be fog.
The mixing point is below the saturation line, and the moisture in the air condensates as small droplets floating in the air. The fog process can be expressed in the Mollier diagram as:
For temperatures below 0oC the water droplets freezes to ice.
Resulting Temperature when mixing Humid Air
Mixing Point is above Saturation Line
As long as the mixed air is above the saturation line (no fog in the mix), the temperature balance can be expressed by modifying the enthalpy balance like
QA cpa tA + QC cpa tC = (QA + QC) cpa tB (3)
cpa = 1.01 - specific heat capacity of air at constant pressure (kJ/kgoC, kWs/kgK)
The temperature in the mix can be expressed by transforming (3):
tB = (QA tA + QC tC) / (QA + QC) (3b)
Mixing Point is below Saturation Line
If the mixing point is below the saturation line - water is condensated as droplets and fog is created.
The amount of condensate water can be found by following the constant enthalpy line from B to the saturation line. The condensate water is the difference between the specific humidity in point B and in the point where the enthalpy line crosses the saturation line.
The mixed temperature is where the enthalpy line crosses the saturation line.
Example - Mixing Humid Air
Mixing Point is above the Saturation Line
1 m3 of air at 25oC and 50% relative humidity (C) is mixed with 1 m3 air at -5oC and 80% relative humidity (A).
The humidity ratio of the mixture can be calculated like
xB = (QA xA + QC xC) / (QA + QC) (4)
= ((1 kg) (0.002 kg/kg) + (1 kg) (0.0097 kg/kg) ) / ((1 kg) + (1 kg))
= 0.0058 kg/kg
The enthalpy of the mixed air can be calculated like
hB = ((1 kg) (0 kJ/kg) + (1 kg) (50 kJ/kg)) / ((1 kg) + (1 kg))
= 25 kJ/kg
The temperature of the mixed air can be calculated as:
tB = ((1 kg) (-5oC) + (1 kg) (25oC)) / ((1 kg) + (1 kg))
Based on the information above and the Mollier diagram - the relative humidity in the mixing point can be estimated to approximately 80%.
The Mixing Point is below the Saturation Line
1 m3 of air at 25oC and 90% relative humidity (C) is mixed with 1 m3 air at -5oC and 80% relative humidity (A).
The enthalpy of the mixture can be calculated as:
hB = ((1 kg) (0 kJ/kg) + (1 kg) (70 kJ/kg)) / ((1 kg) + (1 kg))
= 35 kJ/kg
The humidity ratio of the mixture can be calculated as:
xB = ((1 kg) (0.002 kg/kg) + (1 kg) (0.018 kg/kg)) / ((1 kg) + (1 kg))
= 0.01 kg/kg
Note! This is the humidity ratio including the water droplets - the fog.
The "virtual" mixing point in the Mollier diagram is where the enthalpy line - 35 kJ/kg and the humidity ratio line - 0.01 kg/kg - intersect.
The temperature in the mixed air can be found in the diagram where the enthalpy line - 35 kJ/kg - crosses the saturation line. From the Mollier diagram the mixed temperature is approximately 12.7 oC.
According the Mollier diagram the moisture ratio at this point is aprox. 0.0089 kg/kg. The moisture created as fog or droplets is
(0.01 kg/kg) - (0.0089 kg/kg)
= 0.0011 kg/kg
- en: humid air mixing