Enthalpy of Moist and Humid Air
The enthalpy of moist and humid air consist of sensible heat and latent heat - enthalpy is used to calculate cooling and heating processes
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Moist air is a mixture of dry air and water vapor. In atmospheric air, water vapor content varies from 0 to 3% by mass. The enthalpy of moist and humid air includes the
- enthalpy of the dry air - the sensible heat - and
- the enthalpy of the evaporated water - the latent heat
Specific enthalpy - h - (J/kg, Btu/lb) of moist air is defined as the total enthalpy (J, Btu) of the dry air and the water vapor mixture - per unit mass (kg, lb) of moist air.
Specific Enthalpy of Moist Air
Specific enthalpy of moist air can be expressed as:
h = ha + x hw (1)
where
h = specific enthalpy of moist air (kJ/kg, Btu/lb)
ha = specific enthalpy of dry air (kJ/kg, Btu/lb)
x = humidity ratio (kg/kg, lb/lb)
hw = specific enthalpy of water vapor (kJ/kg, Btu/lb)
Specific Enthalpy of Dry Air - Sensible Heat
Assuming constant pressure conditions the specific enthalpy of dry air can be expressed as:
ha = cpa t (2)
where
cpa = specific heat capacity of air at constant pressure (kJ/kgoC, kWs/kgK, Btu/lboF)
t = air temperature (oC, oF)
For air temperature between -100oC (-150oF) and 100oC (212oF) the specific heat capacity can be set to
cpa = 1.006 (kJ/kgoC)
= 0.240 (Btu/lboF)
Note! that the enthalpy is 0 kJ/kg at 0oC. This is not correct according the definition of enthalpy in the thermodynamics, but for practical purposes in air psychrometrics this assumption is good enough since our interest is the enthalpy difference.
Specific Enthalpy of Water Vapor - Latent Heat
Assuming constant pressure conditions the specific enthalpy of water vapor can be expressed as:
hw = cpw t + hwe (3)
where
cpw = specific heat capacity of water vapor at constant pressure (kJ/kgoC, kWs/kgK)
t = water vapor temperature (oC)
hwe = evaporation heat of water at 0oC (kJ/kg)
For water vapor the specific heat capacity can be set to
cpw = 1.84 (kJ/kgoC)
= 0.444 (Btu/lboF)
The evaporation heat (water at 0oC) can be set to
hwe = 2501 kJ/kg)
= 970 (Btu/lb)
Using (2) and (3), (1) can be modified to
h = cpa t + x [cpw t + hwe] (1b)
(1b) in metric units
h = (1.006 kJ/kgoC) t + x [(1.84 kJ/kgoC) t + (2501 kJ/kg)] (1c)
where
h = enthalpy (kJ/kg)
x = mass of water vapor (kg/kg)
t = temperature (oC)
(1b) in Imperial units
h = (0.240 Btu/lboF) t + x [(0.444 Btu/lboF) t + (970 Btu/lb)] (1d)
where
h = enthalpy (Btu/lb)
x = mass of water vapor (lb/lb)
t = temperature (oF)
Example - Enthalpy in Moist Air
The enthalpy of humid air at 25oC with specific moisture content x = 0.0203 kg/kg (saturation), can be calculated as:
h = (1.006 kJ/kgoC) (25oC) + (0.0203 kg/kg) [(1.84 kJ/kgoC) (25oC) + (2501 kJ/kg)]
= (25.15 kJ/kg) + (0.93 kJ/kg) + (51.70 kJ/kg)
= 77.8 (kJ/kg)
Note! The latent heat due to evaporation of water is the major part of the enthalpy. The sensible heat due to heating evaporated water vapor can be almost neglected.
Enthalpy of Moist Air containing Water - Fog
If the air contains more water than limited by saturation, some of the water exists as droplets - as fog. The enthalpy of moist air with fog can be expressed as:
h = cpa t + xs [cpw t + hwe] + (x - xs) cw t (2)
where
xs = humidity ratio at saturation (kg/kg)
cw = 4.19 - specific heat capacity of water (kJ/kgoC)
Enthalpy of Moist Air containing Ice or Snow
If the air contains water as ice or snow, the enthalpy of air can be expressed as:
h = cpa t + xs [cpw t + hwe] + (x - xs) ci t - (x - xs) him (3)
where
ci = 2.05 - specific heat capacity of ice (kJ/kg.oC)
him= 335 - melting heat of ice (kJ/kg)
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Related Topics
- Air Psychrometrics - The study of moist and humid air - air condition - psychrometric charts, Mollier diagrams, air temperature, absolute and relative humidity, moisture content and more .
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