Density of air

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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.

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

[edit] 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 kelvins.

The specific gas constant R for dry air is:

$R_\mathrm{dry\,air} = 287.05 \frac{\mbox{J}}{\mbox{kg} \cdot \mbox{K}}$

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.

[edit] 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.

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:

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

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

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.

[edit] 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:

sea level 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):

$T = T_0 + L \cdot h$

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.

[edit] 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

Impact 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