NationMaster - Encyclopedia: Density of air

The density of air, ρ (Greek: rho) (air density), is the mass per unit volume of Earth's atmosphere, and is a useful value in aeronautics. In the SI system it is measured as the number of kilograms of air in a cubic meter (kg/m³). At sea level and at 20 °C dry air has a density of approximately 1.2 kg/m³. varying with pressure and temperature. Air density and air pressure decrease with increasing altitude. â€œAirâ€ redirects here. ... Six F-16 Fighting Falcons with the U.S. Air Force Thunderbirds aerial demonstration team fly in delta formation in front of the Empire State Building. ... For considerations of sea level change, in particular rise associated with possible global warming, see sea level rise. ... Air pressure can refer to: Atmospheric pressure, the pressure of air environmentally Pressure of air in a system Category: ...

The density of air is about 800 times less than the density of water, which is about 1000 kg/m³ (1 g/cc). Impact from a water drop causes an upward rebound jet surrounded by circular capillary waves. ...

1 Effects of temperature and pressure
2 Effect of water vapor
3 Effects of altitude
4 Importance of temperature
5 See also
6 References
7 External links

Effects of temperature and pressure

The formula for the density of dry air is given by:

$rho = frac{p}{R cdot T}$

where ρ is the air density, p is pressure, R is the specific gas constant, and T is temperature in Kelvin. The gas constant (also known as the universal or ideal gas constant, usually denoted by symbol R) is a physical constant used in equations of state to relate various groups of state functions to one another. ...

The specific gas constant R for dry air is: To meet Wikipedias quality standards, this article or section may require cleanup. ...

$R_mathrm{dry,air} = 287.05 frac{mbox{J}}{mbox{kg} cdot mbox{K}}$

Therefore:

At standard temperature and pressure (0 °C and 101.325 kPa), dry air has a density of ρ_STP = 1.292 kg/m³.
At standard ambient temperature and pressure (25 °C and 100 kPa), dry air has a density of ρ_SATP = 1.168 kg/m³.
At standard ambient temperature and pressure (70 °F and 14.696 psia), dry air has a density of ρ_SATP = 0.075 lb_m/ft³ ~ 1.2 kg/m³.

Temperature and air pressure can vary from one place to another on the Earth, and can also vary in the same place with time. ... The pascal (symbol: Pa) is the SI derived unit of pressure or stress (also: Youngs modulus and tensile strength). ...

Effect of water vapor

The addition of water vapor to air (making the air humid) reduces the density of the air, which may at first appear contrary to logic. It has been suggested that multiple sections of steam be merged into this article or section. ...

This occurs because the molecular mass of water (18) is less than the molecular mass of air (around 29). For any gas, at a given temperature and pressure, the number of molecules present is constant for a particular volume. So when water molecules (vapor) are introduced to the air, the number of air molecules must reduce by the same number in a given volume, without the pressure or temperature increasing. Hence the mass per unit volume of the gas (its density) decreases.

The density of humid air may be calculated as a mixture of ideal gases. In this case, the partial pressure of water vapor is known as the vapor pressure. Using this method, error in the density calculation is less than 0.2% in the range of -10 °C to 50 °C. The density of humid air is found by: An ideal gas or perfect gas is a hypothetical gas consisting of identical particles of zero volume, with no intermolecular forces. ... In a mixture of ideal gases, each gas has a partial pressure which is the pressure which the gas would have if it alone occupied the volume. ... It has been suggested that multiple sections of steam be merged into this article or section. ... Vapor pressure is the pressure of a vapor in equilibrium with its non-vapor phases. ...

$rho~_{_{humid~air}} = frac{p_{d}}{R_{d} cdot T} + frac{p_{v}}{R_{v} cdot T}$ ^[1]

Where:

$rho~_{_{humid~air}} =$ Density of the humid air $frac{mbox{kg}}{m^3}$

p d =

Partial pressure of dry air (Pa)

R d =

Specific gas constant for dry air, 287.05 $frac{mbox{J}}{mbox{kg} cdot mbox{K}}$

T =

Temperature (K)

p v =

Vapor pressure of water (Pa)

R v =

Specific gas constant for water vapor, 461.495 $frac{mbox{J}}{mbox{kg} cdot mbox{K}}$

The vapor pressure of water may be calculated from the saturation vapor pressure and relative humidity. It is found by: The saturation vapor pressure is the vapor pressure of water when air is saturated with water (having the maximum amount of water vapor that air can hold for a given temperature and pressure). ... This does not adequately cite its references or sources. ...

$p_{v} = phi~ cdot p_{sat}$

Where:

p v =

Vapor pressure of water

$phi~ =$ Relative humidity

p s a t =

Saturation vapor pressure

The saturation vapor pressure of water at any given temperature is the vapor pressure when relative humidity is 100%. A simplification of the regression ^[1] used to find this, can be formulated as:

$p(mb)_{sat} = 6.1078 cdot 10^{frac{7.5 cdot T-2048.625}{T-35.85}}$

IMPORTANT:

This will give a result in mb, 1 mb=100 Pa

$p d$ is found considering partial pressure, resulting in:

p d = p - p v

Where p simply notes the absolute pressure in the observed system. In a mixture of ideal gases, each gas has a partial pressure which is the pressure which the gas would have if it alone occupied the volume. ... Pressure (symbol: p or P) is the measure of the force that acts on a unit area. ...

Effects of altitude

To calculate the density of air as a function of altitude, one requires additional parameters. They are listed below, along with their values according to the International Standard Atmosphere, using the universal gas constant instead of the specific one: The International Standard Atmosphere (ISA) is a model of the standard variation of pressure, temperature, density, and viscosity with altitude in the Earths atmosphere. ... The gas constant (also known as the universal or ideal gas constant, usually denoted by symbol R) is a physical constant used in equations of state to relate various groups of state functions to one another. ...

sea level standard atmospheric pressure p₀ = 101325 Pa
sea level standard temperature T₀ = 288.15 K
Earth-surface gravitational acceleration g = 9.80665 m/s².
temperature lapse rate L = −0.0065 K/m
universal gas constant R = 8.31447 J/(mol·K)
molecular weight of dry air M = 0.0289644 kg/mol

Temperature at altitude h meters above sea level is given by the following formula (only valid inside the troposphere): The pascal (symbol: Pa) is the SI derived unit of pressure or stress (also: Youngs modulus and tensile strength). ... For other uses, see Kelvin (disambiguation). ... The adiabatic lapse rate is the rate of temperature change that occurs in an atmosphere as a function of elevation, assuming that air behaves adiabatically. ... This article is about the unit of length. ... The mole (symbol: mol) is the SI base unit that measures an amount of substance. ... Atmosphere diagram showing the mesosphere and other layers. ...

$T = T_0 + L cdot h$

The pressure at altitude h is given by:

$p = p_0 cdot left(1 + frac{L cdot h}{T_0} right)^frac{g cdot M}{-R cdot L}$

Density can then be calculated according to a molar form of the original formula:

$rho = frac{p cdot M}{R cdot T}$

To use the above equations plus NASA averaged atmospheric research to obtain the average air density at any altitude (extending to outer space), go to the eXtreme High Altitude Calculator.

Importance of temperature

The below table demonstrates that the properties of air change significantly with temperature.

Table — speed of sound in air c, density of air ρ, acoustic impedance Z vs. temperature °C Sound is a vibration that travels through an elastic medium as a wave. ... The acoustic impedance Z (or sound impedance) is a frequency f dependent parameter and is very useful, for example, for describing the behaviour of musical wind instruments. ... For other uses, see Temperature (disambiguation). ...

Effect of temperature
°C	c in m/s	ρ in kg/m³	Z in Pa·s/m
−10	325.2	1.342	436.1
−5	328.3	1.317	432.0
0	331.3	1.292	428.4
+5	334.3	1.269	424.3
+10	337.3	1.247	420.6
+15	340.3	1.225	416.8
+20	343.2	1.204	413.2
+25	346.1	1.184	409.8
+30	349.0	1.165	406.3

Celsius is, or relates to, the Celsius temperature scale (previously known as the centigrade scale). ... This article is about the unit of length. ... Look up second in Wiktionary, the free dictionary. ... â€œKgâ€ redirects here. ... The pascal (symbol: Pa) is the SI derived unit of pressure or stress (also: Youngs modulus and tensile strength). ...

References

^ ^a ^b [1]

External links

Conversions of density units ρ
Air density and density altitude calculations

Categories: Atmospheric thermodynamics | Density

Results from FactBites:

Density Altitude Calculator - English (463 words)
	Density altitude is defined as the altitude in the International Standard Atmosphere that has the same air density as the air being evaluated.
	Air density is affected by the air pressure, temperature and humidity.
	The density of the air is reduced by decreased air pressure, increased temperatures and increased moisture.

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