Moist air is a mixture of dry air and water vapor. In atmospheric air water vapor content varies from 0 - 3% by mass. The enthalpy of moist and humid air includes the
- enthalpy of the dry air - the sensible heat
- enthalpy of the evaporated water in the air - the latent heat
The total enthalpy - sensible and latent - is used when calculating cooling and heating processes.
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 dry air.
Specific Enthalpy of Moist Air
Specific enthalpy of moist air can be expressed as:
h = ha + x hw (1)
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 - the Sensible Heat
Assuming constant pressure conditions the specific enthalpy of dry air can be expressed as:
ha = cpa t (2)
cpa= specific heat 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 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 - the Latent Heat
Assuming constant pressure conditions the specific enthalpy of water vapor can be expressed as:
hw = cpw t + hwe (3)
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 can be set to
cpw= 1.86 (kJ/kgoC)
= 0.444 (Btu/lboF)
The evaporation heat (water at 0oC, 32oF) can be set to
hwe= 2501 (kJ/kg)
= 1061 (Btu/lb)
Using (2) and (3), (1) can be modified to
h = cpa t + x [cpw t + hwe] (4)
(1b) in metric units
h = (1.006 kJ/kgoC) t + x [(1.86 kJ/kgoC) t + (2501 kJ/kg)] (5)
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 + (1061 Btu/lb)] (6)
h = enthalpy (Btu/lb)
x = mass of water vapor (lb/lb)
t = temperature (oF)
Note! - the "reference" points for the metric and imperial enthalpies are different.
- for eq. (5) metric units - the "reference" point for enthalpy h = 0 (kJ/kg) is t = 0 oC(32oF) and x = 0 kg/kg
- for eq. (6) imperial units - the "reference" point for enthalpy h = 0 (Btu/lb) is t = 0 oF(-17.8oC) and x = 0 lb/lb. The evaporation heat for water at 0 oF is 1061 Btu/lb as used in eq. (6).
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) [(1.86 kJ/kgoC) (25oC) + (2501 kJ/kg)]
= (25.15 kJ/kg) + [(0.94 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 as 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) cwt (7)
xs= humidity ratio at saturation (kg/kg)
cw= 4.19 - specific heat 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) cit- (x - xs) him (8)
ci= 2.05 - specific heat ice (kJ/kgoC)
him= 335 - melting heat of ice (kJ/kg)
Moist and humid air - psychrometric charts, Mollier diagrams, air-condition temperatures and absolute and relative humidity and moisture content.
The drying force of air depends on the air moisture holding capacity and the water surface to air evaporation capacity.
Air can be humidified by adding water or steam.
Using steam to humidify air.
Relative humidity in moist air can estimated by measuring the dry and wet bulb temperature.
The mass of water vapor present in moist air - to the mass of dry air.
Maximum water content in humid air vs. temperature.
Online calculator with figures and tables showing specific heat (Cp and Cv) of dry air vs. temperature and pressure. SI and imperial units.
Thermal properties of air at different temperatures - density, viscosity, critical temperature and pressure, triple point, enthalpi and entropi, thermal conductivity and diffusivity and more.
Heat removed from storage rooms with cooled air.
Air heating buildings - heat supply vs. air flow and temperature.
Maximum cooling tower efficiency is limited by the cooling air wet-bulb temperature.
Dry Bulb, Wet Bulb and Dew Point temperatures can be used to determine the state of humid air.
Evaporation of water from a water surface - like a swimming pool or an open tank - depends on water temperature, air temperature, air humidity and air velocity above the water surface - online calculator.
Evaporative cooling tutorial.
The Great Sensible Heat Factor is the ratio sensible to total heat in a cooling coil.
Ventilation and heat-recovery calculations, sensible and latent heat - online calculators - imperial units.
Classification of heat recovery efficiencies - temperature efficiency, moisture efficiency and enthalpy efficiency - online heat exchanger efficiency calculator.
Enthalpy change and temperature rise when heating humid air without adding moisture.
Latent heat is the heat when supplied to or removed from air results in a change in moisture content - the temperature of the air is not changed.
The change in state wwhen mixing moist air - enthalpy, heat, temperature and specific humidity.
The pressure in a mixture of dry air and water vapor - humid or moist air - can be estimated by using Daltons Law of partial pressures.
Humidity ratio of moist air to humidity ratio of saturated moist air.
Psychrometric table with humid air properties like saturation pressure, specific volume, enthalpy and entropy.
Dry and wet bulb temperatures, saturation pressure, water vapor weight, specific volume, heat and more.
Dry and wet bulb temperature, specific volume, relative humidity, enthalpy and more.
Specific humidity of moist air vs. relative humidity, water vapor and air density.
Calculating heat removed with air by measuring the wet bulb temperature.
Thermal properties of water at different temperatures like density, freezing temperature, boiling temperature, latent heat of melting, latent heat of evaporation, critical temperature and more.
Enthalpy-entropy diagram for water and steam.