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The density of a material is its mass per unit volume. The symbol most often used for density is ρ (the lower case Greek letter rho). Mathematically, density is defined as mass divided by volume:

${\displaystyle \rho ={\frac {m}{V}},}$

where ρ is the density, m is the mass, and V is the volume. In some cases (for instance, in the United States oil and gas industry), density is loosely per unit volume, although this is scientifically inaccurate - this quantity is more properly called specific weight.

Different materials usually have different densities, and density may be relevant to buoyancy, purity and packaging. Osmium and iee below for a list of some of the most common units of density.

Measurement of density

The density at all points of a homogeneous object equals its total mass divided by its total volume. The mass is normally measured with a scale or balance; the volume may be measured directly (from the geometry of the object) or by the displacement of a fluid. To determine the density of a liquid or a gas, a hydrometer or dasymeter may be used, respectively. Similarly, hydrostatic weighing uses the displacement of water due to a submerged object to determine the density of the object.

If the body is not homogeneous, then its density varies between different regions of the object. In that case the density around any given location is determined by calculating the density of a small volume around that location. In the limit of an infinitesimal volume the density of an inhomogeneous object at a point becomes: ρ(r) = dm/dV, where dV is an elementary volume at position r. The mass of the body then can be expressed as

${\displaystyle m=\int _{V}\rho (\mathbf {r} )\,dV.}$

The density of granular material can be ambiguous, depending on exactly how its volume is defined, and this may cause confusion in measurement. A common example is sand: if it is gently poured into a container, the density will be low; if the same sand is then compacted, it will occupy less volume and consequently exhibit a greater density. This is because sand, like all powders and granular solids, contains a lot of air space in between individual grains. The density of the material including the air spaces is the bulk density, which differs significantly from the density of an individual grain of sand with no air included.

Changes of density

In general, density can be changed by changing either the pressure or the temperature. Increasing the pressure always increases the density of a material. Increasing the temperature generally decreases the density, but there are notable exceptions to this generalization. For example, the density of water increases between its melting point at 0 °C and 4 °C; similar behavior is observed in silicon at low temperatures.

The effect of pressure and temperature on the densities of liquids and solids is small. The compressibility for a typical liquid or solid is 10 bar (1 bar = 0.1 MPa) and a typical thermal expansivity is 10 K. This roughly translates into needing around ten thousand times atmospheric pressure to reduce the volume of a substance by one percent. (Although the pressures needed may be around a thousand times smaller for sandy soil and some clays.) A one percent expansion of volume typically requires a temperature increase on the order of thousands of degrees Celsius.

In contrast, the density of gases is strongly affected by pressure. The density of an ideal gas is

${\displaystyle \rho ={\frac {MP}{RT}},\,}$

where M is the molar mass, P is the pressure, R is the universal gas constant, and T is the absolute temperature. This means that the density of an ideal gas can be doubled by doubling the pressure, or by halving the absolute temperature.

In the case of volumic thermal expansion at constant pressure and small intervals of temperature the temperature dependence of density is :

${\displaystyle \rho ={\frac {\rho _{T_{0}}}{(1+\alpha \cdot \Delta T)}}}$

where ${\displaystyle \rho _{T_{0}}}$ is the density at a reference temperature, ${\displaystyle \alpha }$ is the thermal expansion coefficient of the material at temperatures close to ${\displaystyle T_{0}}$.

Density of solutions

The density of a solution is the sum of mass (massic) concentrations of the components of that solution.

Mass (massic) concentration of each given component ρ_i in a solution sums to density of the solution.

${\displaystyle \rho =\sum _{i}\varrho _{i}\,}$

Expressed as a function of the densities of pure components of the mixture and their volume participation, it reads:

${\displaystyle \rho =\sum _{i}\rho _{i}{\frac {V_{i}}{V}}.\,}$

provided that there is no interaction between the components.

Densities

Water

Density of water at 1 atm pressure:

Air

Density of air at 1 atm pressure:

Various materials

Unless otherwise noted, all densities given are at standard conditions for temperature and pressure, that is, 273.15 K (0.00 °C) and 100 kPa (0.987 atm).

*Air excluded when calculating density

Others

Other common units

The SI unit for density is:

• kilograms per cubic meter (kg/m)

Litres and metric tons are not part of the SI, but are acceptable for use with it, leading to the following units:

• kilograms per liter (kg/L)
• grams per milliliter (g/mL)
• metric tons per cubic meter (t/m)

Densities using the following metric units all have exactly the same numerical value, one thousandth of the value in (kg/m). Liquid water has a density of about 1 kg/dm, making any of these SI units numerically convenient to use as most solids and liquids have densities between 0.1 and 20 kg/dm.

• kilograms per cubic decimetre (kg/dm)
• grams per cubic centimetre (g/cc, gm/cc or g/cm)
  • 1 gram/cm = 1000 kg/m
• megagrams (metric tons) per cubic metre (Mg/m)

In US customary units density can be stated in:

• Avoirdupois ounces per cubic inch (oz/cu in)
• Avoirdupois pounds per cubic inch (lb/cu in)
• pounds per cubic foot (lb/cu ft)
• pounds per cubic yard (lb/cu yd)
• pounds per US liquid gallon (lb/gal)
• pounds per US bushel (lb/bu)
• slugs per cubic foot

Imperial units differing from the above (as the Imperial gallon and bushel differ from the US units) in practice are rarely used, though found in older documents. The density of precious metals could conceivably be based on Troy ounces and pounds, a possible cause of confusion.

See also

• List of elements by density
• Charge density
• Buoyancy
• Bulk density
• Dord
• Energy density
• Lighter than air
• Number density
• Orthobaric density
• Specific weight
• Spice (oceanography)
• Standard temperature and pressure
• Orders of magnitude (density)
• Density prediction by the Girolami method

References

1. The National Aeronautic and Atmospheric Administration's Glenn Research Center. "Gas Density Glenn research Center". grc.nasa.gov.
2. "Density definition in Oil Gas Glossary". Oilgasglossary.com. Retrieved 2010-09-14.
3. New carbon nanotube struructure aerographite is lightest material champ. Phys.org (2012-07-13). Retrieved on 2012-07-14.
4. Aerographit: Leichtestes Material der Welt entwickelt – SPIEGEL ONLINE. Spiegel.de (2012-07-11). Retrieved on 2012-07-14.
5. ^ "Re: which is more bouyant [sic] styrofoam or cork". Madsci.org. Retrieved 2010-09-14.
6. "Wood Densities". www.engineeringtoolbox.com. Retrieved October 15, 2012.
7. "Density of Wood". www.simetric.co.uk. Retrieved October 15, 2012.
8. CRC Press Handbook of tables for Applied Engineering Science, 2nd Edition, 1976, Table 1-59
9. glycerol composition at. Physics.nist.gov. Retrieved on 2012-07-14.
10. Density of the Earth, wolframalpha.com
11. Density of Earth's core, wolframalpha.com
12. Density of the Sun's core, wolframalpha.com
13. Extreme Stars: White Dwarfs & Neutron Stars, Jennifer Johnson, lecture notes, Astronomy 162, Ohio State University. Accessed: May 3, 2007.
14. Nuclear Size and Density, HyperPhysics, Georgia State University. Accessed: June 26, 2009.

External links

• Video: Density Experiment with Oil and Alcohol
• Video: Density Experiment with Whiskey and Water
• Glass Density Calculation – Calculation of the density of glass at room temperature and of glass melts at 1000 – 1400°C
• List of Elements of the Periodic Table – Sorted by Density
• Calculation of saturated liquid densities for some components
• Field density test
• On-line calculator for densities and partial molar volumes of aqueous solutions of some common electrolytes and their mixtures, at temperatures up to 323.15 K.
• Water – Density and specific weight
• Temperature dependence of the density of water – Conversions of density units
• A delicious density experiment
• Water density calculator Water density for a given salinity and temperature.
• Liquid density calculator Select a liquid from the list and calculate density as a function of temperature.
• Gas density calculator Calculate density of a gas for as a function of temperature and pressure.
• Densities of various materials.
• Determination of Density of Solid, instructions for performing classroom experiment.

• Density
• Physical quantities