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{{otheruses4|volumetric mass density}}
The '''density''' of a material is defined as its [[mass]] per unit [[volume]]. The symbol of density is ρ (the Greek letter [[Rho (letter)|rho]]).


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

where:
:<math>\rho</math> (rho) is the density,
:<math>m</math> is the mass,
:<math>V</math> is the volume.

Different materials usually have different densities, so density is an important concept regarding [[buoyancy]], metal purity and [[packaging]].
In some cases density is expressed as the [[dimensionless]] quantities [[specific gravity]] (SG) or [[relative density]] (RD), in which case it is expressed in multiples of the density of some other standard material, usually water or air/gas.

== History ==
In a well-known story, [[Archimedes]] was given the task of determining whether [[Hiero II of Syracuse|King Hiero]]'s [[goldsmith]] was embezzling [[gold]] during the manufacture of a [[wreath]] dedicated to the gods and replacing it with another, cheaper [[alloy]].<ref>[http://www-personal.umich.edu/~lpt/archimedes.htm Archimedes, A Gold Thief and Buoyancy] - 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 weight; but the king did not approve of this.

Baffled, Archimedes took a relaxing immersion bath and observed from the rise of the warm water upon entering that he could calculate the volume of the gold crown through the [[Displacement (fluid)|displacement]] of the water. Allegedly, upon this discovery, he went running naked through the streets shouting, "Eureka! Eureka!" (Εύρηκα! Greek "I found it"). As a result, the term "[[Eureka (word)|eureka]]" entered common parlance and is used today to indicate a moment of enlightenment.

This story first appeared in written form in [[Vitruvius]]' [[De architectura|books of architecture]], two centuries after it supposedly took place.<ref>[http://penelope.uchicago.edu/Thayer/E/Roman/Texts/Vitruvius/9*.html Vitruvius on Architecture, Book IX], paragraphs 9-12, translated into English and [http://penelope.uchicago.edu/Thayer/L/Roman/Texts/Vitruvius/9*.html in the original Latin].</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>[http://www.sciencemag.org/cgi/content/summary/305/5688/1219e The first Eureka moment], ''Science'' '''305''': 1219, August 2004.</ref><ref>[http://www.sciam.com/article.cfm?articleID=5F1935E9-E7F2-99DF-3F1D1235AF1D2CD1 Fact or Fiction?: Archimedes Coined the Term "Eureka!" in the Bath], ''Scientific American'', December 2006.</ref>

== Measurement of density ==
For a [[Homogeneous (chemistry)|homogeneous]] object, the mass divided by the volume gives the density. The mass is normally measured with an appropriate [[weighing scale|scale or balance]]; the volume may be measured directly (from the geometry of the object) or by the displacement of a fluid. [[Hydrostatic weighing]] is a method that combines these two.

If the body is not homogeneous or heterogeneous, the density is a function of the coordinates <math>\rho(\vec{r})=dm/dv</math>, where <math>dv</math> is elementary volume with coordinates <math>\vec{r}</math>. The mass of the body then can be expressed as
:<math>
m = \int_V \rho(\vec{r})dv</math>,

where the integration is over the volume of the body ''V''.

A very common instrument for the direct measurement of the density of a liquid is the [[hydrometer]], which measures the volume displaced by an object of known mass. A common laboratory device for measuring fluid density is a [[pycnometer]]; a related device for measuring the absolute density of a solid is a [[gas pycnometer]]. Another instrument used to determine the density of a [[liquid]] or a [[gas]] is the digital density meter - based on the [[oscillating U-tube]] principle.

The density of a solid 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 gently filled into a container, the density will be low; when the same sand is compacted into the same container, 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; this overall density is called the [[bulk density]], which differs significantly from the density of an individual grain of sand.
<!-- contains errors, to be fixed.

Density is often measured by units examples:volume,mass,area
== Formal definition ==
Density is defined as '''mass per unit volume'''. A concise statement of what this means may be obtained by considering a small box in a [[Cartesian coordinate system]] of dimensions <math>\Delta x</math>, <math>\Delta y</math>, <math>\Delta z</math>. If the mass is represented by a net mass function, then the density at some point will be:
:<math>\begin{align}
\rho & = \lim_{Volume \to 0}\frac{\mbox{mass of box}}{\mbox{volume of box}} \\
& = \lim_{\Delta x, \Delta y, \Delta z \to 0}\left(\frac{
m(x + \Delta x, y + \Delta y, z + \Delta z) - m(x, y, z)}{\Delta x \Delta y \Delta z}\right) \\
& = \frac{d m}{d V}\\
\end{align}\,</math>

For a homogeneous substance, this [[derivative]] is equal to net mass over net volume. For the generic case of nonhomogeneous substance (<math>m = m(x, y, z)</math>), the [[chain rule]] may be used to expand the derivative into a sensible expression:
:<math>\rho = \frac{1}{L_x^2} \frac{\partial m}{\partial x} + \frac{1}{L_y^2} \frac{\partial m}{\partial y} + \frac{1}{L_z^2} \frac{\partial m}{\partial z}\,</math>.

Where <math>L_x</math>, <math>L_y</math>, <math>L_z</math> are the scales of the axes ([[meter]]s, for example).
-->

== Common units ==
The [[SI]] unit for density is:
*[[kilogram]]s per [[cubic metre]] (kg/m³)

The following non-SI metric units all have exactly the same numerical value, one thousandth of the SI value in (kg/m³). Liquid [[water]] has a density of about 1kg/L (exactly 1.000&nbsp;kg/L by definition at 4 °C), making any of these units numerically convenient to use as most [[solid]]s and [[liquid]]s have densities between 0.1 and 20&nbsp;kg/L.; density is usually given in these units rather than the SI unit.
*[[kilogram]]s per [[litre]] (kg/L).
*kilograms per cubic decimeter (kg/dm³),
*[[gram]]s per [[millilitre]] (g/mL),
*grams per cubic centimeter (g/cc, gm/cc or g/cm³).

In [[US customary units|U.S. customary units]] density can be stated in:
*[[Avoirdupois ounce]]s per [[cubic inch]] (oz/cu&nbsp;in)
*[[Pound (mass)|Avoirdupois pound]]s per cubic inch (lb/cu&nbsp;in)
*pounds per [[cubic foot]] (lb/cu&nbsp;ft)
*pounds per [[cubic yard]] (lb/cu&nbsp;yd)
*pounds per [[U.S. liquid gallon]] or per [[U.S. dry gallon]] (lb/gal)
*pounds per U.S. [[bushel]] (lb/bu)
*[[slug (mass)|slugs]] per cubic foot.
In principle there are [[Imperial units]] 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 [[precious metal]]s could conceivably be based on [[Troy weight|Troy]] ounces and pounds, a possible cause of confusion.

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

The effect of pressure and temperature on the densities of liquids and solids is small so that a typical [[compressibility]] for a liquid or solid is 10<sup>–6</sup>&nbsp;[[bar (unit)|bar]]<sup>–1</sup> (1&nbsp;bar=0.1&nbsp;MPa) and a typical [[thermal expansivity]] is 10<sup>–5</sup>&nbsp;[[Kelvin|K]]<sup>–1</sup>.

In contrast, the density of gases is strongly affected by pressure. [[Boyle's law]] says that the density of an [[ideal gas]] is given by
:<math>
\rho = \frac {MP}{RT} \,
</math>

where <math>R</math> is the [[Gas constant|universal gas constant]], <math>P</math> is the pressure, <math>M</math> the [[molar mass]], and <math>T</math> the [[absolute temperature]].

This means that a gas at 300&nbsp;[[Kelvin|K]] and 1&nbsp;[[bar (unit)|bar]] will have its density doubled by increasing the pressure to 2&nbsp;[[bar (unit)|bar]] or by reducing the temperature to 150&nbsp;[[Kelvin|K]].

[[Osmium]] is the densest known substance at [[standard conditions for temperature and pressure]].

== Density of water ==
:''See also: [[Water (molecule)#Density of water and ice|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 meter (SI unit)<br> at various temperatures in degrees Celsius.<br>The values below 0 °C refer to [[supercooling|supercooled]] water.
|}

== Density of air ==
{|class="wikitable" style="text-align:center" align="left"
|-
!''T'' in [[Celsius|°C]] !! ''ρ'' in kg/m<sup>3</sup> (at 1&nbsp;[[Atmosphere (unit)|atm]])
|-
| –25 || 1.423
|-
| –20 || 1.395
|-
| –15 || 1.368
|-
| –10 || 1.342
|-
| –5 || 1.316
|-
| &#160;&#160;0 || 1.293
|-
| &#160;&#160;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 the mass (massic) concentrations 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.

== Density of composite material ==
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 measure the density of a composite material.
<math>
\rho = \frac{W_a}{W_a + W_w - W_b} \left (0.9975 \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>0.9975</math> is the density in g/cm<sup>3</sup> of the distilled water at 23°C

== Densities of various materials ==

{|class="wikitable sortable" style="text-align:center" align="left"
|-
! Material !! ''ρ'' in kg/m<sup>3</sup> !! Notes
|-
| [[Interstellar medium]] || 10<sup>-25</sup> &minus; 10<sup>-15</sup> || Assuming 90% H, 10% He; variable T
|-
| [[Earth's atmosphere]] || 1.2 || At sea level
|-
| [[Aerogel]] || 1 &minus; 2 ||
|-
| [[Styrofoam]] || 30 &minus; 120 || [http://www.madsci.org/posts/archives/mar2000/954534602.Ph.r.html From]
|-
| [[Cork (material)|Cork]] || 220 &minus; 260 || [http://www.madsci.org/posts/archives/mar2000/954534602.Ph.r.html From]
|-
| [[Water]] || 1000 || At [[Standard conditions for temperature and pressure|STP]]
|-
| [[Plastics]] || 850 &minus; 1400 || For [[polypropylene]] and [[PETE]]/[[PVC]]
|-

| [[Glycerol]]<ref>[http://physics.nist.gov/cgi-bin/Star/compos.pl?matno=174 glycerol composition at physics.nist.gov]</ref><ref>[http://wiki.answers.com/Q/Density_of_glycerin Glycerol density at answers.com]</ref> || 1261 ||

|-
| The [[Earth]] || 5515.3 || Mean density
|-
| [[Copper]] || 8920 &minus; 8960 || Near [[room temperature]]
|-
| [[Lead]] || 11340 || Near [[room temperature]]
|-
| [[Tungsten]] || 19250 || Near [[room temperature]]
|-
| [[Gold]] || 19300 || Near [[room temperature]]
|-
| The [[Inner Core]] of the Earth || ~13000 || As listed in [[Earth]]
|-
| [[Uranium]] || 19100 || Near [[room temperature]]
|-
| [[Iridium]] || 22500 || Near [[room temperature]]
|-
| [[Osmium]] || 22610 || Near [[room temperature]]
|-
| The core of the [[Sun]] || ~150000 ||
|-
| [[White dwarf]] star || 1 &times; 10<sup>9</sup><ref name="osln">[http://www.astronomy.ohio-state.edu/~jaj/Ast162/lectures/notesWL22.pdf Extreme Stars: White Dwarfs & Neutron Stars], Jennifer Johnson, lecture notes, Astronomy 162, [[Ohio State University]]. Accessed on line May 3, 2007.</ref> ||
|-
| [[Atomic nuclei]] || 2.3 &times; 10<sup>17</sup>&nbsp;<ref>[http://hyperphysics.phy-astr.gsu.edu/HBASE/Nuclear/nucuni.html Nuclear Size and Density], HyperPhysics, Georgia State University. Accessed on line June 26, 2009.</ref> || Does not depend strongly on size of nucleus
|-
| [[Neutron star]] || 8.4 &times; 10<sup>16</sup> — 1 &times; 10<sup>18</sup> ||
|-
| [[Black hole]] || 4 &times; 10<sup>17</sup> || Mean density inside the [[Schwarzschild radius]] of an earth-mass black hole (theoretical)
|}
{{-}}

== References ==
{{Reflist}}

== See also ==
<div style="-moz-column-count:3; column-count:3;">
*[[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)]]
*[[Girolami method|Density prediction by the Girolami method]]
</div>

==External links==
*[http://glassproperties.com/density/room-temperature/ Glass Density Calculation - Calculation of the density of glass at room temperature and of glass melts at 1000 - 1400°C]
*[http://www.science.co.il/PTelements.asp?s=Density List of Elements of the Periodic Table - Sorted by Density]
*[http://ddbonline.ddbst.de/DIPPR105DensityCalculation/DIPPR105CalculationCGI.exe Calculation of saturated liquid densities for some components]
*[http://www.engineeringtoolbox.com/water-density-specific-weight-d_595.html Water - Density and Specific Weight]
*[http://www.sengpielaudio.com/ConvDensi.htm Temperature dependence of the density of water - Conversions of density units]

[[Category:Density| ]]
[[Category:Continuum mechanics]]
[[Category:Fundamental physics concepts]]
[[Category:Introductory physics]]
[[Category:Physical quantities]]
[[Category:Physical chemistry]]
[[Category:Basic meteorological concepts and phenomena]]

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[[ja:密度]]
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[[ur:کثافت]]
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[[zh:密度]]

Revision as of 18:35, 19 November 2009

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