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{{about|mass density}}
The '''mass density''' or '''density''' of a material is defined as its ] per unit ]. The symbol most often used for density is ρ (the Greek letter ]). In some cases (for instance, in the United States oil and gas industry), density is also defined as its ] per unit ];<ref>{{cite web|url=http://oilgasglossary.com/density.html |title=Density definition in Oil Gas Glossary |publisher=Oilgasglossary.com |date= |accessdate=2010-09-14}}</ref> although, this quantity is more properly called ]. Different materials usually have different densities, so density is an important concept regarding ], purity and ]. ] and ] are the densest known metal elements at ] but not the densest materials.

Less dense fluids float on more dense fluids if they do not mix. This concept can be extended, with some care, to less dense solids floating on more dense fluids. If the average density (including any air below the waterline) of an object is less than water (1000 kg/m<sup>3</sup>) it will float in water and if it is more than water's it will sink in water.

In some cases density is expressed as the ] quantities ] (SG) or ] (RD), in which case it is expressed in multiples of the density of some other standard material, usually water or air/gas. (For example, a specific gravity less than one means that the substance floats in water.)

The mass density of a material varies with temperature and pressure. (The variance is typically small for solids and liquids and much greater for gasses.) Increasing the pressure on an object decreases the volume of the object and therefore increase its density. Increasing the temperature of a substance (with some exceptions) decreases its density by increasing the volume of that substance. In most materials, heating the bottom of a fluid results in ] of the heat from bottom to top of the fluid due to the decrease of the density of the heated fluid. This causes it to rise relative to more dense unheated material.

The reciprocal of the density of a substance is called its ], a representation commonly used in ]. Density is an ] in that increasing the amount of a substance does not increase its density; rather it increases its mass.

==History==
In a well-known but probably apocryphal tale, ] was given the task of determining whether ]'s ] was embezzling ] during the manufacture of a golden ] dedicated to the gods and replacing it with another, cheaper ].<ref> - by Larry "Harris" Taylor, Ph.D.</ref> Archimedes knew that the irregularly shaped wreath could be crushed into a cube whose volume could be calculated easily and compared with the mass; but the king did not approve of this. Baffled, Archimedes took a relaxing immersion bath and observed from the rise of the water upon entering that he could calculate the volume of the gold wreath through the ] of the water. Upon this discovery, he leaped from his bath and went running naked through the streets shouting, "Eureka! Eureka!" (Εύρηκα! Greek "I found it"). As a result, the term "]" entered common parlance and is used today to indicate a moment of enlightenment.

The story first appeared in written form in ]' ], two centuries after it supposedly took place.<ref>, paragraphs 9-12, translated into English and .</ref> Some scholars have doubted the accuracy of this tale, saying among other things that the method would have required precise measurements that would have been difficult to make at the time.<ref>, ''Science'' '''305''': 1219, August 2004.</ref><ref>, ''Scientific American'', December 2006.</ref>

Mathematically, density is defined as mass divided by volume:

:<math> \rho = \frac{m}{V},</math>

where {{math|ρ}} is the density, {{math|m}} is the mass, and {{math|V}} is the volume. From this equation, mass density must have units of a unit of mass per unit of volume. As there are many units of mass and volume covering many different magnitudes there are a large number of units for mass density in use.

The ] unit of ] per ] ({{math|kg/m³}}) and the ] unit of ] per ] ({{math|g/cm³}}) are probably the most common used units for density. (The cubic centimeter can be alternately called a ''millilitre'' or a ''cc''.) {{math|1000kg/m³}} equals one {{math|g/cm³}}. In industry, other larger or smaller units of mass and or volume are often more practical and ] may be used. See below for a list of some of the most common units of density. Further, density may be expressed in terms of weight density (the weight of the material per unit volume) or as a ratio of the density with the density of a common material such as air or water.

==Measurement of density==
The density at any point of a ] object equals its total mass divided by its total volume. The mass is normally measured with an appropriate ]; the volume may be measured directly (from the geometry of the object) or by the displacement of a fluid. For determining the density of a liquid or a gas, a ] or ] may be used, respectively. Similarly, ] uses the displacement of water due to a submerged object to determine the density of the object.

If the body is not homogeneous, then the density is a function of the position. 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: {{math|ρ('''r''')}}={{math|dm/dV}}, where {{math|dV}} is an elementary volume at position {{math|r}}. The mass of the body then can be expressed as

:<math>
m = \int_V \rho(\mathbf{r})\,dV.
</math>

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 ], which differs significantly from the density of an individual grain of sand with no air included.

==Changes of density==
{{main|Compressibility|Thermal expansivity}}

In general, density can be changed by changing either the ] or the ]. 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 ] increases between its melting point at 0&nbsp;°C and 4&nbsp;°C; similar behavior is observed in ] at low temperatures.

The effect of pressure and temperature on the densities of liquids and solids is small. The ] for a typical liquid or solid is 10<sup>−6</sup>&nbsp;]<sup>−1</sup> (1&nbsp;bar=0.1&nbsp;MPa) and a typical ] is 10<sup>−5</sup>&nbsp;]<sup>−1</sup>. 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 ].

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

:<math>
\rho = \frac {MP}{RT}, \,
</math>

where {{math|M}} is the ], {{math|P}} is the pressure, {{math|R}} is the ], and {{math|T}} is the ]. This means that the density of an ideal gas can be doubled by doubling the pressure, or by halving the absolute temperature.

==Density of water (at 1 atm)==
{{See also|Water (molecule)#Density of water and ice|l1=Water density}}

{| class="wikitable"
|-
! Temp (°C) !! Density (kg/m<sup>3</sup>)
|-
|100||958.4
|-
|80||971.8
|-
|60||983.2
|-
|40||992.2
|-
|30||995.6502
|-
|25||997.0479
|-
|22||997.7735
|-
|20||998.2071
|-
|15||999.1026
|-
|10||999.7026
|-
|4||999.9720
|-
|0||999.8395
|-
|−10||998.117
|-
|−20||993.547
|-
|−30||983.854
|-
|colspan="2"| <small>The density of water in kilograms per cubic metre (SI unit)<br> at various temperatures in degrees Celsius.<br>The values below 0 °C refer to ] water.
|}

==Density of air (at 1 atm)==
{{Main|Density of air}}
]
{| class="wikitable" style="text-align:center; float:left;"
|-
!''T'' in ] !! ''ρ'' in kg/m<sup>3</sup>
|-
| –25 || 1.423
|-
| –20 || 1.395
|-
| –15 || 1.368
|-
| –10 || 1.342
|-
| –5 || 1.316
|-
| 0 || 1.293
|-
| 5 || 1.269
|-
| 10 || 1.247
|-
| 15 || 1.225
|-
| 20 || 1.204
|-
| 25 || 1.184
|-
| 30 || 1.164
|-
| 35 || 1.146
|}
{{-}}

==Density of solutions==
The density of a solution is the sum of ] of the components of that solution.<br>
Mass (massic) concentration of a given component ρ<sub>i</sub> in a solution can be called partial density of that component.
:<math>\rho = \sum_i \rho_i \,</math>

Expressed as a function of the densities of pure components of the mixture and their volume participation, it reads:
:<math>\rho = \sum_i \rho_{i,0} \frac{V_oi}{V}.\,</math>

==Densities of various materials==
{{See|Orders of magnitude (density)}}
{| class="wikitable sortable" style="text-align:center; float:left;"
|-
! Material !! ''ρ'' in kg/m<sup>3</sup> !! Notes
|-
| ] || 10<sup>−25</sup> − 10<sup>−15</sup> || Assuming 90% H, 10% He; variable T
|-
| ] || 1.2 || At sea level
|-
| ] || 1 − 2 ||
|-
| ] || 30 − 120<ref name="madsci1">{{cite web|url=http://www.madsci.org/posts/archives/mar2000/954534602.Ph.r.html |title=Re: which is more {{sic|bou|yant|nolink=y}} styrofoam or cork |publisher=Madsci.org |date= |accessdate=2010-09-14}}</ref> ||
|-
| ] || 70 ||
|-
| ] || 220 − 260<ref name="madsci1"/> ||
|-
| ] || 860<ref name="crc2ed">CRC Press Handbook of tables for Applied Engineering Science, 2nd Edition, 1976, Table 1-59</ref> || At ]
|-
| ] || 970 || At ]
|-
| ] || 916.7 <!-- Sourced from the "Ice" page -->
|-
| ] (fresh) || 1000 || At ]
|-
| ] (salt) || 1030 ||
|-
| ] || 850 − 1400 || For ] and ]/]
|-
| ] || 1740 || At ]
|-
| ] || 1850 || At ]
|-
| ]<ref></ref> || 1261 ||
|-
| ] || 2330 || At ]
|-
| ] || 2700 || At ]
|-
| ] || 3500 || At ]
|-
| ] || 4540 || At ]
|-
| ] || 4800 || At ]
|-
| The ] || 5515.3 || Mean density
|-
| ] || 6100 || At ]
|-
| ] || 6690 || At ]
|-
| ] || 7000 || At ]
|-
| ] || 7200 || At ]
|-
| ] || 7210 - 7440 || At ]
|-
| ] || 7310 || At ]
|-
| ] || 7870 || At ]
|-
| ] || 8570 || At ]
|-
| ] || 8650 || At ]
|-
| ] || 8900 || At ]
|-
| ] || 8900 || At ]
|-
| ] || 8920 − 8960 || Near room temperature
|-
| ] || 9750 || At ]
|-
| ] || 10220 || At ]
|-
| ] || 10500 || At ]
|-
| ] || 11340 || Near room temperature
|-
| ] || 11700 || At ]
|-
| ] || 12410 || At ]
|-
| The ] of the Earth || ~13000 || As listed in ]
|-
| ] || 13546 || At ]
|-
| ] || 16600 || At ]
|-
| ] || 18800 || At ]
|-
| ] || 19300 || At ]
|-
| ] || 19320 || At ]
|-
| ] || 19840 || At ]
|-
| ] || 21450 || At ]
|-
| ] || 22420 || At ]
|-
| ] || 22570 || At ]
|-
| The core of the ] || ~150000 ||
|-
| ] star || 1 × 10<sup>9</sup><ref name="osln">, Jennifer Johnson, lecture notes, Astronomy 162, ]. Accessed on line May 3, 2007.</ref> ||
|-
| ] || 2.3 × 10<sup>17</sup>&nbsp;<ref>, HyperPhysics, Georgia State University. Accessed on line June 26, 2009.</ref> || Does not depend strongly on size of nucleus
|-
| ] || 8.4 × 10<sup>16</sup> − 1 × 10<sup>18</sup> ||
|-
| ] || 4 × 10<sup>17</sup> || Mean density inside the ] of an Earth-mass ] (theoretical)
|}
{{-}}

==Density of composite material==
In the United States, ASTM specification D792-00<ref>(2004). ''Test Methods for Density and Specific Gravity (Relative Density) of Plastics by Displacement''. ASTM Standard D792-00. Vol 81.01. American Society for Testing and Materials. West Conshohocken. PA.</ref> describes the steps to calculate the density of a composite material.
:<math>
\rho = \frac{W_a}{W_a + W_w - W_b} \left (\rho_{water} \right ) \,
</math>

where:
:<math>\rho</math> is the density of the composite material, in g/cm<sup>3</sup>

and
:<math>W_a</math> is the weight of the specimen when hung in the air
:<math>W_w</math> is the weight of the partly immersed wire holding the specimen
:<math>W_b</math> is the weight of the specimen when immersed fully in distilled water, along with the partly immersed wire holding the specimen
:<math>\rho_{water}</math> is the density in g/cm<sup>3</sup> of the distilled water at testing temperature (for example 0.9975 g/cm<sup>3</sup> at 23 °C)

==Other common units==

The ] unit for density is:
* ]s per ] (kg/m³)

Litres and metric tons are not part of the SI, but are acceptable for use with it, leading to the following units:
* ]s per ] (kg/L)
* ]s per ] (g/mL)
* ]s per cubic metre (t/m³)

Densities using the following metric units all have exactly the same numerical value, one thousandth of the value in (kg/m³). Liquid ] has a density of about 1&nbsp;kg/dm³, making any of these SI units numerically convenient to use as most ]s and ]s have densities between 0.1 and 20&nbsp;kg/dm³.
* kilograms per cubic decimetre (kg/dm³)
* grams per cubic centimetre (g/cc, gm/cc or g/cm³)
* megagrams per cubic metre (Mg/m³)

In ] density can be stated in:
* ]s per ] (oz/cu&nbsp;in)
* ] per cubic inch (lb/cu&nbsp;in)
* pounds per ] (lb/cu&nbsp;ft)
* pounds per ] (lb/cu&nbsp;yd)
* pounds per ] (lb/gal)
* pounds per U.S. ] (lb/bu)
* ] per cubic foot.
In principle there are ] different from the above as the Imperial gallon and bushel differ from the U.S. units, but in practice they are no longer used, though found in older documents. The density of ]s could conceivably be based on ] ounces and pounds, a possible cause of confusion.

==See also==
<div style="-moz-column-count:3; column-count:3;">
* ]
* ]
* ]
* ]
* ]
* ]
* ]
* ]
* ]
* ]
* ]
* ]
* ]
* ]
</div>

==References==
{{Reflist}}

==External links==
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* Water density for a given salinity and temperature.
* Select a liquid from the list and calculate density as a function of temperature.
* Calculate density of a gas for as a function of temperature and pressure.
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Revision as of 00:37, 11 November 2011

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