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# Moist Air - Specific Volume

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 (m 3 /kg)

V = total volume of moist air (m 3 )

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 of dry air (Pa)

R a = 286.9 - the individual gas constant dry 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 the air can be expressed as

p a = p - p w (3b)

where

p = pressure in the moist air (Pa)

p w = partial pressure water vapor (Pa)

Combining (3) and (2):

v da =  R a T / (p - p w ) (3c)

The ideal gas law can also be applied to the water vapor as

p w V = m w R w T (4)

where

p w = partial pressure of water vapor (Pa)

R w = individual gas constant water vapor ( 461.4 J/kg.K)

T = temperature of the moist air (K)

The mass of the water vapor can be calculated by using the humidity ratio and the mass of air as

m w = x m a (5)

where

x = m w / m a = specific humidity or humidity ratio (kg h2o /kg dry_air )

m w = mass of water vapor (kg)

m a = mass of dry air (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 (m 3 /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 (moist air) can be expressed as

v = (R a T / p) [(1 + x R w / R a )/ (1 + x)] (14)

(14) can used to express the inverse of the specific volume - the density - of moist air as

ρ = 1 / v

= (p / R a T) (1 + x) / (1 + x R w / R a ) (15)

## Related Topics

### • Air Psychrometrics

Moist and humid air - psychrometric charts, Mollier diagrams, air-condition temperatures and absolute and relative humidity and moisture content.

## Related Documents

### Air - Composition and Molecular Weight

Dry air is a mechanical mixture of nitrogen, oxygen, argon and several other gases in minor amounts.

### Air - Density vs. Pressure and Temperatures

Air density at pressure ranging 1 to 10 000 bara (14.5 - 145000 psi) and constant selected temperatures.

### Air - Density, Specific Weight and Thermal Expansion Coefficient vs. Temperature and Pressure

Online calculator, figures and tables showing density, specific weight and thermal expansion coefficients of air at temperatures ranging -100 to 1600 °C (-140 to 2900 °F) at atmospheric and higher pressure - Imperial and SI Units.

### Air - Diffusion Coefficients of Gases in Excess of Air

Diffusion coefficients (D12) for gases in large excess of air at temperatures ranging 0 - 400 °C.

### Air - Dynamic and Kinematic Viscosity

Online calculator, figures and tables with dynamic (absolute) and kinematic viscosity for air at temperatures ranging -100 to 1600°C (-150 to 2900°F) and at pressures ranging 1 to 10 000 bara (14.5 - 145000 psia) - SI and Imperial Units.

### Air - Humidity Measurement from Dry and Wet Bulb Temperature

Relative humidity in moist air can estimated by measuring the dry and wet bulb temperature.

### Air - Humidity Ratio

The mass of water vapor present in moist air - to the mass of dry air.

### Air - Maximum Moisture Carrying Capacity

Maximum water content in humid air vs. temperature.

### Air - Moisture Holding Capacity vs. Temperature

The moisture holding capacity of air increases with temperature.

### Air - Prandtl Number

Prandtl number for air vs. temperature and pressure.

### Air - Properties at Gas-Liquid Equilibrium Conditions

Properties of air change along the boiling and condensation curves (temperature and pressure between triple point and critical point conditions). An air phase diagram included.

### Air - Thermal Conductivity vs. Temperature and Pressure

Online calculator with figures and tables showing air thermal conductivity vs. temperature and pressure. SI and imperial units.

### Air - Thermal Diffusivity vs. Temperature and Pressure

Figures and tables withdry air thermal diffusivity vs. temperarure and pressure. SI and Imperial units.

### Dry Air and Water Vapor - Density and Specific Volume vs. Temperature - Imperial Units

Density and specific volume of dry air and water vapor at temperatures ranging 225 to 900 degF (107 to 482 degC).

### Humid Air vs. the Ideal Gas Law

Pressure, temperature and volume in a perfect ideal gas like moist air (air with water vapor).

### Moist Air - Daltons Law of Partial Pressure

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.

### Moist Air - Density vs. Pressure

Density of moist air vs. pressure ranging 75 - 1000 mmHg.

### Moist Air - Density vs. Water Content and Temperature

Density of the mix of dry air and water vapor - moist humid air.

### Moist Air - Properties

Psychrometric table with humid air properties like saturation pressure, specific volume, enthalpy and entropy.

### Moist Air - Psychrometric Table for Pressure 29.92 inHg

Dry and wet bulb temperatures, saturation pressure, water vapor weight, specific volume, heat and more.

### Moist Air - Psychrometric Terms

Dry and wet bulb temperature, specific volume, relative humidity,  enthalpy and more.

### Moist Air - Specific vs. Relative Humidity

Specific humidity of moist air vs. relative humidity, water vapor and air density.

### Moist Air - Weight of Water Vapor

Weight of water vapor in air

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