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

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 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)

    = 1075 (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 + (1075 Btu/lb)]         (1d)

where

h = enthalpy (Btu/lb)

x = mass of water vapor (lb/lb)

t = temperature (oF)

Note! - that the reference points for metric and imperial enthalpies are different.

  • the "reference" enthalpy h = 0 (kJ/kg) is at t = 0 oC and x = 0 kg/kg for metric units 
  • the "reference" enthalpy h = 0 (Btu/lb) is at t = 0 oF and x = 0 lb/lb for imperial units 

You can not convert from metric to imperial enthalpy or vice versa directly.

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) + (50.77 kJ/kg)]

= 76.9 (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)

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

Related Documents

  • Humidity Ratio of Air - Humidity ratio (GPP) is the ratio between actual mass of water vapor present in moist air - to the mass of dry air
  • Air Properties - Temperature, density, specific heat, thermal conductivity, expansion coefficient, kinematic viscosity and Prandtl's number for temperatures ranging -150 - 400 oC
  • Heat-Recovery - Ventilation and heat-recovery calculations, sensible and latent heat - online calculators - imperial units
  • Great Sensible Heat Factor - GSHF - The Great Sensible Heat Factor is the ratio between the sensible and total heat for a cooling coil
  • Psychrometric Terms - Dry Bulb and Wet Bulb Temperature, Specific Volume, Relative Humidity,  Enthalpy and more ..
  • Ice - Thermal Properties - Thermal and thermodynamic properties of ice - density, thermal conductivity and specific heat at temperatures from 0 to -100 oC
  • Water - Thermal Properties - Thermal properties of water - density, freezing temperature, boiling temperature, latent heat of melting, latent heat of evaporation, critical temperature and more
  • Air Heating Systems - Using air to heat buildings - temperature rise diagram
  • Mixing Humid Air - Calculating enthalpy, heat, temperature and specific humidity in mixing humid air
  • Heat Removed in Cooling Air - Heat removed in cooling air to storage room conditions
  • Specific Heat of Dry Air - Specific heat of dry air varies with temperature
  • Moist Air Properties - A psychrometric table with moist humid air properties

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