Density
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In [[physics]] the [[density]] (''ρ'') of a [[physical body|body]] is the [[ratio]] of its [[mass]] (''m'') to its [[volume]] (''V''), a measure of how tightly the [[matter]] within it is packed together<ref>[http://physics.about.com/od/fluidmechanics/f/density.htm About.com: What is Density?]</ref>. Its [[SI|SI units]] are [[kilogram]]s per [[cubic metre]] (kg/m³). It is also sometimes given in the [[Centimetre gram second system of units|cgs units]] of [[gram]]s per [[cubic centimetre]] (g/cm³).
Density is defined by:
: <math> \rho = \frac{m}{V}</math>
If the body is inhomogeneous, 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''.
Various substances have different densities, and it is this quantity that determines how they interact when mixed together. For example, in SI units the density of [[lead]] is 11.35 x 10<sup>3</sup>, that of [[water]] is 1 x 10<sup>3</sup>, and that of [[cork (material)|cork]] is 0.24 x 10<sup>3</sup>. The lead has a greater density than water so it sinks; the cork has a smaller density so it floats<ref>Oxford Illustrated Encyclopedia: The Physical World p. 87</ref>.
In some cases the density is expressed as a [[specific gravity]] or [[relative density]], in which case it is expressed in multiples of the density of some other standard material, usually water or air.
== History ==
In a well known problem, [[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 irregular shaped wreath could be smashed into a cube or sphere, where the volume could be calculated more easily when compared with the weight; the king did not approve of this.
Baffled, Archimedes went to take a bath and observed from the rise of the water upon entering that he could calculate the volume of the crown through the [[Displacement (fluid)|displacement]] of the water. Allegedly, upon this discovery, Archimedes went running though the streets in the nude shouting, "Eureka! Eureka!" (Greek "I have 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.
[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]] object, the mass divided by the volume gives the density. If the object has a varying mass, this prescription gives the average 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 liquid.
A very common instrument for the direct measurement of the density of a liquid is the [[hydrometer]]. A less common device for measuring fluid density is a [[pycnometer]], a similar 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 it is defined, and this may cause confusion in measurement. A common example is sand: if gently filled into a container, the density will be small; when the same sand is compacted into the same container, it will occupy less volume and consequently carry a greater density. This is because "sand" 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.
== 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 ==
[[SI]] units for density are:
* [[kilogram]]s per [[cubic metre]] (kg/m³)
* [[gram]]s per [[cubic centimetre]] (g/cm³)
Units outside the SI
* [[kilogram]]s per [[litre]] (kg/L). [[Water]] generally has a density around 1 kg/L, making this a convenient unit.
* [[gram]]s per [[millilitre]] (g/mL), which is equivalent to (g/cm³).
They also happen to be numerically equivalent to kg/L (1 kg/L = 1 g/cm³ = 1 g/mL).
In [[US customary units|U.S. customary units]] or [[Imperial units]], the units of density include:
*[[ounce]]s per [[cubic inch]] (oz/in<sup>3</sup>)
*[[Pound (mass)|pound]]s per cubic inch (lb/in<sup>3</sup>)
* pounds per [[cubic foot]] (lb/ft<sup>3</sup>)
* pounds per [[cubic yard]] (lb/yd<sup>3</sup>)
* pounds per [[gallon]] (for U.S. or [[imperial gallon]]s) (lb/gal)
* pounds per U.S. [[bushel]] (lb/bu)
* [[slug (mass)|slugs]] per cubic foot.
== 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 °C and 4 °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> [[bar (unit)|bar]]<sup>–1</sup> (1 bar=0.1 MPa) and a typical [[thermal expansivity]] is 10<sup>–5</sup> [[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 [[Kelvin|K]] and 1 [[bar (unit)|bar]] will have its density doubled by increasing the pressure to 2 [[bar (unit)|bar]] or by reducing the temperature to 150 [[Kelvin|K]].
[[Iridium]] is the densest known substance at [[standard conditions for temperature and pressure]].
== Density of water ==
{| class="wikitable"
!Temp (°C)!!Density (g/cm<sup>3</sup>)
|-
|100||0.9584
|-
|80||0.9718
|-
|60||0.9832
|-
|40||0.9922
|-
|30||0.9956502
|-
|25||0.9970479
|-
|22||0.9977735
|-
|20||0.9982071
|-
|15||0.9991026
|-
|10||0.9997026
|-
|4||0.9999720
|-
|0||0.9998395
|-
|−10||0.998117
|-
|−20||0.993547
|-
|−30||0.983854
|-
|colspan=2| <small>The density of water in grams per cubic centimeter <br> at various temperatures in degrees Celsius <ref>Lide, D. R. (Ed.) (1990). CRC Handbook of Chemistry and Physics (70th Edn.). Boca Raton (FL):CRC Press.</ref> <br>The values below 0 °C refer to [[supercooling|supercooled]] water.</small><br>
[http://www.engineeringtoolbox.com/water-density-specific-weight-d_595.html Water - Density and Specific Weight]
|}
See [[Water_(molecule)#Density_of_water_and_ice|Water Density]]
== Density of air ==
{|class="wikitable" style="text-align:center" align="left"
|-
!''T'' in [[Celsius|°C]] !! ''ρ'' in kg/m³ (at 1 [[Atmosphere (unit)|atm]])
|-
| –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 || 1.165
|}
{{-}}
== Density of solutions ==
The density of a solution is the sum of the mass (massic) concentrations of the components of that solution.
Mass (massic) concentration of a given component ρ<sub>i</sub> in a solution can be called partial density of that component.
== Densities of various materials ==
{|class="wikitable" style="text-align:center" align="left"
|-
! Material !! ''ρ'' in kg/m³ !! Notes
|-
| [[Interstellar medium]] || 10<sup>-25</sup> − 10<sup>-15</sup> || Assuming 90% H, 10% He; variable T
|-
| [[Earth's atmosphere]] || 1.2 || At sealevel
|-
| [[Aerogel]] || 1 − 2 ||
|-
| [[Styrofoam]] || 30 − 120 || [http://www.madsci.org/posts/archives/mar2000/954534602.Ph.r.html From]
|-
| [[Cork (material)|Cork]] || 220 − 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 − 1400 || For [[polypropylene]] and [[PETE]]/[[PVC]]
|-
| The [[Earth]] || 5515.3 || Mean density
|-
| [[Copper]] || 8960 || Near [[room temperature]]
|-
| [[Lead]] || 11340 || Near [[room temperature]]
|-
| The [[Inner Core]] || ~13000 || As listed in [[Earth]]
|-
| [[Uranium]] || 19100 || Near [[room temperature]]
|-
| [[Iridium]] || 22500 || Near [[room temperature]]
|-
| The core of the [[Sun]] || ~150000 ||
|-
| [[Atomic nuclei]] || ~3 × 10<sup>17</sup> || As listed in [[neutron star]]
|-
| [[Neutron star]] || 8.4 × 10<sup>16</sup> − 1 × 10<sup>18</sup> ||
|-
| [[Black hole]] || 2 × 10<sup>30</sup> || Mean density inside the [[Schwarzschild radius]] of an earth-mass black hole (theoretical)
|}
{{-}}
== References ==
{{Reflist}}
== Books ==
{{Refbegin}}
*''Fundamentals of Aerodynamics'' Second Edition, McGraw-Hill, John D. Anderson, Jr.
*''Fundamentals of Fluid Mechanics'' Wiley, B.R. Munson, D.F. Young & T.H. Okishi
*''Introduction to Fluid Mechanics'' Fourth Edition, Wiley, SI Version, R.W. Fox & A.T. McDonald
*''Thermodynamics: An Engineering Approach'' Second Edition, McGraw-Hill, International Edition, Y.A. Cengel & M.A. Boles
{{Refend}}
== 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]]
*[[Population density]]
*[[Specific weight]]
*[[Standard temperature and pressure]]
*[[Orders of magnitude (density)]]
*[[Brix |Brix, Balling and Plato scale]]
</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]
[[Category:Basic meteorological concepts and phenomena]]
[[Category:Continuum mechanics]]
[[Category:Fundamental physics concepts]]
[[Category:Introductory physics]]
[[Category:Physical quantity]]
[[Category:Physical chemistry]]
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