Sponsored Links

When discussing specific volume of moist air its necessary to differentiate between  

• specific volume of moist air per mass unit of dry air, or
• specific volume of moist air per mass unit of dry air and water vapor

Specific Volume of Moist Air per Mass Unit of Dry Air

Specific volume is defined as the total volume of dry air and water vapor mixture per kg of dry air (SI-units). The specific volume can be expressed as:

v_da = V / m_a   (1)

where

v_da = specific volume of moist air per mass unit of dry air (m³/kg)

V = total volume of moist air (m³)

m_a = mass of dry air (kg)

When dry air and water vapor with the same temperature occupies the same volume the equation for an ideal gas can be applied. 

p_a V = m_a R_a T     (2)

where 

p_a = partial pressure air (Pa)

R_a = 286.9 - the individual gas constant air (J/kg.K) 

T = temperature of the moist air (K)

Combining (1) and (2):

v_da =  R_a T / p_a     (3)

The partial pressure of air can be expressed as: 

p_a = p - p_w   (3b)

where 

p = pressure in the humid air (Pa)

p_w = partial pressure water vapor (Pa)

Combining (3) and (2b): 

v_da =  R_a T / (p - p_w)     (3c)

The ideal gas law can also be applied for the water vapor:

p_w V = m_w R_w T     (4)

where 

p_w = partial pressure water vapor (Pa)

R_w = 455 - the individual gas constant water vapor (J/kg.K) 

T = temperature of the moist air (K)

The mass of water vapor can be expressed with the humidity ratio and the mass of air:

m_w = x m_a     (5)

where 

x = specific humidity or humidity ratio (kg/kg)

Combining (4) and (5): 

p_w V = x m_a R_w T     (6)

Combining (6) with (1):

v_da =  x R_w T / p_w     (7)

Transforming (7): 

p_w =  x R_w T / v_da    (8)

Combining (8) with (3c):

v_da =  R_a T / (p - (x R_w T / v_da))      (9)

(9) can be transformed to express the specific volume of moist air per unit mass of dry air as: 

 v_da =  (1 + x R_w / R_a) R_a T / p       (10)

Specific Volume of Moist Air per unit Mass of Dry Air and Water Vapor

Specific volume is defined as the total volume of dry air and water vapor mixture per kg of dry air and water vapor (SI-units). The specific volume can be expressed as:

v = V / m_a + m_w  (11)

where

v = specific volume of moist air per mass unit of dry air and water vapor (m³/kg)

Combining with (5): 

v = V / m_a (1 + x)  (12)

Combining with (1):

v = v_da / (1 + x)   (13)

and the specific volume of moist air per unit mass of dry air and water vapor can be expressed as: 

v = (R_a T / p) [(1 + x R_w / R_a)/ (1 + x)]    (14)

(14) can used to express the density of moist air.

Sponsored Links

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

• Densities and Specific Volumes of Dry Air and Water Vapor - Densities and specific volumes of dry air and water vapor at temperatures ranging 225 to 900 degF (107 to 482 degC)
• Density of Dry Air, Water Vapor and Moist Humid Air - Calculate the density of dry air, water vapor or the mixture of air and water vapor - moist or humid air
• Density of Moist Air - Density of moist air - pressure ranging 75 - 1000 mm Hg
• Humid Air and the Ideal Gas Law - The Ideal Gas Law relating pressure, temperature, and volume of an ideal or perfect gas used for air with water vapor - or moist air
• 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
• Moist Air Properties - A psychrometric table with moist humid air properties
• Psychrometric Terms - Dry Bulb and Wet Bulb Temperature, Specific Volume, Relative Humidity,  Enthalpy and more ..
• Water Vapor - Weight in Air - Weight of water vapor in air