How to Calculate Air Density

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Though it may seem like nothing, the air around you has a density. The density of air can be measured and studied for features of physics and chemistry such as its weight, mass or volume. Scientists and engineers use this knowledge in creating equipment and products that take advantage of air pressure when inflating tires, sending materials through suction pumps and creating vacuum-tight seals.

Air Density Formula

The most basic and straightforward air density formula is simply dividing the mass of air by its volume. This is the standard definition of density as ρ = m/V for density ρ ("rho") generally in kg/m3, mass m in kg and volume V in m3. For example, if you had 100 kg of air that took up a volume of 1 m3, the density would be 100 kg/m3.

To get a better idea of the density of air specifically, you need to account for how air is made of different gases when formulating its density. At a constant temperature, pressure and volume, dry air is typically made of 78% nitrogen (N2), 21% oxygen (O2) and one percent argon (Ar).

To take into account the effect that these molecules have on air pressure, you can calculate the mass of air as the sum of nitrogen's two atoms of 14 atomic units each, oxygen's two atoms of 16 atomic units each and argon's single atom of 18 atomic units.

If the air isn't completely dry, you can also add some water molecules (H2O) which are two atomic units for the two hydrogen atoms and 16 atomic units for the singular oxygen atom. If you calculate how much mass of air you have, you can assume that these chemical constituents are distributed throughout it uniformly and then calculate the percent of these chemical components in dry air.

You can also use the specific weight, the ratio of the weight to volume in calculating density. The specific weight γ ("gamma") is given by the equation γ = (m * g)/V = ρ * g that adds an additional variable g as the constant of gravitational acceleration 9.8 m/s2. In this case, the product of mass and gravitational acceleration is the weight of the gas, and dividing this value by the volume V can tell you the gas's specific weight.

Air Density Calculator

An online air density calculator such as the one by Engineering Toolbox let you calculate theoretical values for air density at given temperatures and pressures. The website also provides an air density table of values at different temperatures and pressures. These graphs show how density and specific weight decrease at higher values of temperature and pressure.

You can do this because of Avogadro's law, which states, "equal volumes of all gases, at the same temperature and pressure, have the same number of molecules." For this reason, scientists and engineers use this relationship in determining temperature, pressure or density when they know other information about a volume of gas they are studying.

The curvature of these graphs means there is a logarithmic relationship between these quantities. You can show that this matches theory by re-arranging the ideal gas law: PV = mRT for pressure P, volume V, mass of the gas m, gas constant R (0.167226 J/kg K) and temperature T to get ρ = P/RT in which ρ is density in units of m/V mass/volume (kg/m3). Keep in mind this version of the ideal gas law uses the R gas constant in units of mass, not moles.

The variation of the ideal gas law shows that, as temperature increases, density increases logarithmically because 1/T is proportional to ρ. This inverse relationship describes the curvature of the air density graphs and air density tables.

Air Density vs. Altitude

Dry air can fall under one of two definitions. It can be air without any trace of water in it or it can be air with low relativity humidity, which can be changed at higher altitudes. Air density tables such as the one on Omnicalculator show how air density changes with respect to altitude. Omnicalculator also has a calculator to determine air pressure at a given altitude.

As altitude increases, air pressure decreases primarily due to the gravitational attraction between air and the earth. This is because the gravitational attraction between earth and the molecules of air decreases, lessening the pressure of the forces between the molecules when you go to higher altitudes.

It also happens because the molecules have less weight themselves because lesser weight due to gravity at higher altitudes. This explains why some foods take longer to cook when at higher altitudes as they'll need more heat or a higher temperature to excite the gas molecules within them.

Aircraft altimeters, instruments that measure altitude, take advantage of this by measuring pressure and using that to estimate altitude, usually in terms of mean-sea-level (MSL). Global positions systems (GPS) gives you a more precise answer by measuring the actual distance above sea level.

Units of Density

Scientists and engineers mostly use the SI units for density of kg/m3. Other uses may be more applicable based on the case and purpose. Smaller densities such as those of trace elements in solid objects like steel can generally be expressed more easily using units of g/cm3. Other possible units of density include kg/L and g/mL.

Keep in mind, when converting between different units for density, you need to account for the three dimensions of volume as an exponential factor if you need to change the units for volume.

For example, if you wanted to convert 5 kg/cm3 to kg/m3, you would multiply 5 by 1003, not just 100, to get the result of 5 x 106 kg/m3.

Other handy conversions include 1 g/cm3 = .001 kg/m3, 1 kg/L = 1000 kg/m3 and 1 g/mL = 1000 kg/m3. These relationships show the versatility of density units for the desired situation.

In the United States customary standards of units, you may be more accustomed to using units like feet or pounds instead of meters or kilograms, respectively. In these scenarios, you can remember some useful conversions like 1 oz/in3 = 108 lb / ft3, 1 lb / gal ≈ 7.48 lb / ft3 and 1 lb/yd3 ≈ 0.037 lb / ft3. In these cases, ≈ refers to an approximation because these numbers for conversion are not exact.

These units of density can give you a better idea of how to measure density of more abstract or nuanced concepts such as the energy density of materials used in chemical reactions. This could be the energy density of fuels cars use in ignition or how much nuclear energy can be stored in elements like uranium.

Comparing air density to density of electric field lines around an electrically charged object, for example, can give you a better idea of how to integrate quantities over different volumes.

References

About the Author

S. Hussain Ather is a Master's student in Science Communications the University of California, Santa Cruz. After studying physics and philosophy as an undergraduate at Indiana University-Bloomington, he worked as a scientist at the National Institutes of Health for two years. He primarily performs research in and write about neuroscience and philosophy, however, his interests span ethics, policy, and other areas relevant to science.

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