Density - wikipedia Density This article is about mass density. For other uses, see Density ( disambiguation ). Density Common symbols ρ SI unit kg / m A graduated cylinder containing various coloured liquids with different densities. The density, or more precisely, the volumetric mass density, of a substance is its mass per unit volume. The symbol most often used for density is ρ ( the lower case Greek letter rho ), although the Latin letter D can also be used. Mathematically, density is defined as mass divided by volume : ρ = m V ( 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 defined as its weight per unit volume, although this is scientifically inaccurate -- this quantity is more specifically called specific weight. For a pure substance the density has the same numerical value as its mass concentration. Different materials usually have different densities, and density may be relevant to buoyancy, purity and packaging. Osmium and iridium are the densest known elements at standard conditions for temperature and pressure but certain chemical compounds may be denser. To simplify comparisons of density across different systems of units, it is sometimes replaced by the dimensionless quantity `` relative density '' or `` specific gravity '', i.e. the ratio of the density of the material to that of a standard material, usually water. Thus a relative density less than one means that the substance floats in water. The density of a material varies with temperature and pressure. This variation is typically small for solids and liquids but much greater for gases. Increasing the pressure on an object decreases the volume of the object and thus increases its density. Increasing the temperature of a substance ( with a few exceptions ) decreases its density by increasing its volume. In most materials, heating the bottom of a fluid results in convection of the heat from the bottom to the top, due to the decrease in 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 occasionally called its specific volume, a term sometimes used in thermodynamics. Density is an intensive property in that increasing the amount of a substance does not increase its density ; rather it increases its mass. Contents 1 History 2 Measurement of density 2.1 Homogeneous materials 2.2 Heterogeneous materials 2.3 Non-compact materials 3 Changes of density 4 Density of solutions 5 Densities 5.1 Various materials 5.2 Others 5.3 Water 5.4 Air 5.5 Molar volumes of liquid and solid phase of elements 6 Common units 7 See also 8 References 9 External links History In a well - known but probably apocryphal tale, Archimedes was given the task of determining whether King Hiero 's goldsmith was embezzling gold during the manufacture of a golden wreath dedicated to the gods and replacing it with another, cheaper alloy. 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 is said to have taken an immersion bath and observed from the rise of the water upon entering that he could calculate the volume of the gold wreath through the displacement of the water. Upon this discovery, he leapt from his bath and ran naked through the streets shouting, `` Eureka ! Eureka ! '' ( Εύρηκα ! Greek `` I have found it '' ). As a result, the term `` eureka '' entered common parlance and is used today to indicate a moment of enlightenment. The story first appeared in written form in Vitruvius ' books of architecture, two centuries after it supposedly took place. 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. From the equation for density ( ρ = m / V ), mass density has units of mass divided by 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 SI unit of kilogram per cubic metre ( kg / m ) and the cgs unit of gram per cubic centimetre ( g / cm ) are probably the most commonly used units for density. One g / cm is equal to one thousand kg / m. One cubic centimetre ( abbreviation cc ) is equal to one millilitre. In industry, other larger or smaller units of mass and or volume are often more practical and US customary units may be used. See below for a list of some of the most common units of density. Measurement of density Homogeneous materials 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, a dasymeter or a Coriolis flow meter may be used, respectively. Similarly, hydrostatic weighing uses the displacement of water due to a submerged object to determine the density of the object. Heterogeneous materials 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 → ) = d m / d V ( displaystyle \rho ( ( \vec ( r ) ) ) = dm / dV ), where d V ( displaystyle dV ) is an elementary volume at position r ( displaystyle r ). The mass of the body then can be expressed as m = ∫ V ρ ( r → ) d V. ( displaystyle m = int _ ( V ) \rho ( ( \vec ( r ) ) ) , dV. ) Non-compact materials In practice, bulk materials such as sugar, sand, or snow contain voids. Many materials exist in nature as flakes, pellets, or granules. Voids are regions which contain something other than the considered material. Commonly the void is air, but it could also be vacuum, liquid, solid, or a different gas or gaseous mixture. The bulk volume of a material -- inclusive of the void fraction -- is often obtained by a simple measurement ( e.g. with a calibrated measuring cup ) or geometrically from known dimensions. Mass divided by bulk volume determines bulk density. This is not the same thing as volumetric mass density. To determine volumetric mass density, one must first discount the volume of the void fraction. Sometimes this can be determined by geometrical reasoning. For the close - packing of equal spheres the non-void fraction can be at most about 74 %. It can also be determined empirically. Some bulk materials, however, such as sand, have a variable void fraction which depends on how the material is agitated or poured. It might be loose or compact, with more or less air space depending on handling. In practice, the void fraction is not necessarily air, or even gaseous. In the case of sand, it could be water, which can be advantageous for measurement as the void fraction for sand saturated in water -- once any air bubbles are thoroughly driven out -- is potentially more consistent than dry sand measured with an air void. In the case of non-compact materials, one must also take care in determining the mass of the material sample. If the material is under pressure ( commonly ambient air pressure at the earth 's surface ) the determination of mass from a measured sample weight might need to account for buoyancy effects due to the density of the void constituent, depending on how the measurement was conducted. In the case of dry sand, sand is so much denser than air that the buoyancy effect is commonly neglected ( less than one part in one thousand ). Mass change upon displacing one void material with another while maintaining constant volume can be used to estimate the void fraction, if the difference in density of the two voids materials is reliably known. Changes of density Main articles : Compressibility and Thermal expansivity 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 ρ = M P R T, ( 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 : ρ = ρ T 0 1 + α ⋅ Δ T ( displaystyle \rho = ( \frac ( \rho _ ( T_ ( 0 ) ) ) ( 1 + alpha cdot Delta T ) ) ) where ρ T 0 ( displaystyle \rho _ ( T_ ( 0 ) ) ) is the density at a reference temperature, α ( displaystyle alpha ) is the thermal expansion coefficient of the material at temperatures close to T 0 ( 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 in a solution sums to density of the solution. ρ = ∑ i ρ i ( displaystyle \rho = sum _ ( i ) \varrho _ ( i ) , ) Expressed as a function of the densities of pure components of the mixture and their volume participation, it allows the determination of excess molar volumes : ρ = ∑ i ρ i V i V = ∑ i ρ i φ i = ∑ i ρ i V i ∑ i V i + ∑ i V E i ( displaystyle \rho = sum _ ( i ) \rho _ ( i ) ( \frac ( V_ ( i ) ) ( V ) ) , = sum _ ( i ) \rho _ ( i ) \varphi _ ( i ) = sum _ ( i ) \rho _ ( i ) ( \frac ( V_ ( i ) ) ( sum _ ( i ) V_ ( i ) + sum _ ( i ) ( V ^ ( E ) ) _ ( i ) ) ) ) provided that there is no interaction between the components. Knowing the relation between excess volumes and activity coefficients of the components, one can determine the activity coefficients. V E  ̄ i = R T ∂ ln ⁡ γ i ∂ P ( displaystyle ( overline ( V ^ ( E ) ) ) _ ( i ) = RT ( \frac ( partial ln gamma _ ( i ) ) ( partial P ) ) ) Densities Various materials Further information : Orders of magnitude ( density ) Densities of various materials covering a range of values Material ρ ( kg / m ) Notes Hydrogen 0.0898 Helium 0.179 Aerographite 0.2 Metallic microlattice 0.9 Aerogel 1.0 Air At sea level Tungsten hexafluoride 12.4 One of the heaviest known gases at standard conditions Liquid hydrogen 70 At approx. − 255 ° C Styrofoam 75 Approx. Cork 240 Approx. Pine 373 Lithium 535 Wood 700 Seasoned, typical Oak 710 Potassium 860 Ice 916.7 At temperature < 0 ° C Cooking oil 910... 930 Sodium 970 Water ( fresh ) 1,000 At 4 ° C, the temperature of its maximum density Water ( salt ) 1,030 0.9 % Liquid oxygen 1,141 At approx. − 219 ° C Nylon 1,150 Plastics 1,175 Approx. ; for polypropylene and PETE / PVC Tetrachloroethene 1,622 Magnesium 1,740 Beryllium 1,850 Glycerol 1,261 Concrete 2,400 Silicon 2,330 Aluminium 2,700 Diiodomethane 3,325 Liquid at room temperature Diamond 3,500 Titanium 4,540 Selenium 4,800 Vanadium 6,100 Antimony 6,690 Zinc 7,000 Chromium 7,200 Tin 7,310 Manganese 7,325 Approx. Iron 7,870 Niobium 8,570 Brass 8,600 Cadmium 8,650 Cobalt 8,900 Nickel 8,900 Copper 8,940 Bismuth 9,750 Molybdenum 10,220 Silver 10,500 Lead 11,340 Thorium 11,700 Rhodium 12,410 Mercury 13,546 Tantalum 16,600 Uranium 18,800 Tungsten 19,300 Gold 19,320 Plutonium 19,840 Rhenium 21,020 Platinum 21,450 Iridium 22,420 Osmium 22,570 Notes : Jump up ^ 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 ). ^ Jump up to : Air contained in material excluded when calculating density Others Entity ρ ( kg / m ) Notes Interstellar medium 6981099999999999999 ♠ 1 × 10 Assuming 90 % H, 10 % He ; variable T The Earth 5,515 Mean density. The inner core of the Earth 13,000 Approx., as listed in Earth. The core of the Sun 33,000 -- 160,000 Approx. Super-massive black hole 7005900000000000000 ♠ 9 × 10 Density of a 4.5 - million - solar - mass black hole Event horizon radius is 13.5 million km. White dwarf star 7009210000000000000 ♠ 2.1 × 10 Approx. Atomic nuclei 7017229999999999999 ♠ 2.3 × 10 Does not depend strongly on size of nucleus Neutron star 7018100000000000000 ♠ 1 × 10 Stellar - mass black hole 7018100000000000000 ♠ 1 × 10 Density of a 4 - solar - mass black hole Event horizon radius is 12 km. Water See also : Water density Density of liquid water at 1 atm pressure Temp. ( ° C ) Density ( kg / m ) − 30 983.854 − 20 993.547 − 10 998.117 0 999.8395 999.9720 10 999.7026 15 999.1026 20 998.2071 22 997.7735 25 997.0479 30 995.6502 40 992.2 60 983.2 80 971.8 100 958.4 Notes : Jump up ^ Values below 0 ° C refer to supercooled water. Air Main article : Density of air Air density vs. temperature Density of air at 1 atm pressure T ( ° C ) ρ ( kg / m ) − 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 Molar volumes of liquid and solid phase of elements Molar volumes of liquid and solid phase of elements Common units The SI unit for density is : kilogram per cubic metre ( kg / m ) The litre and metric tons are not part of the SI, but are acceptable for use with it, leading to the following units : kilogram per litre ( kg / L ) gram per millilitre ( g / mL ) metric ton per cubic metre ( 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. kilogram per cubic decimetre ( kg / dm ) gram per cubic centimetre ( g / cm ) 1 g / cm = 1000 kg / m megagram ( metric ton ) per cubic metre ( Mg / m ) In US customary units density can be stated in : Avoirdupois ounce per cubic inch ( 1 g / cc ≈ 0.578036672 oz / cu in ) Avoirdupois ounce per fluid ounce ( 1 g / cc ≈ 1.04317556 oz / fl. oz = 1.04317556 lbs / pint ) Avoirdupois pound per cubic inch ( 1 g / cc ≈ 0.036127292 lb / cu in ) pound per cubic foot ( 1 g / cc ≈ 62.427961 lb / cu ft ) pound per cubic yard ( 1 g / cc ≈ 1685.5549 lb / cu yd ) pound per US liquid gallon ( 1 g / cc ≈ 8.34540445 lb / gal ) pound per US bushel ( 1 g / cc ≈ 77.6888513 lb / bu ) slug 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 Imperial gallon was based on the concept that an Imperial fluid ounce of water would have a mass of one Avoirdupois ounce, and indeed 1 g / cc ≈ 1.00224129 ounces per Imperial fluid ounce = 10.0224129 pounds per Imperial gallon. 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 Air density Area density Bulk density Buoyancy Charge density Density prediction by the Girolami method Dord Energy density Lighter than air Linear density Number density Orders of magnitude ( density ) Orthobaric density Paper density Specific weight Spice ( oceanography ) Standard temperature and pressure References Jump up ^ The National Aeronautic and Atmospheric Administration 's Glenn Research Center. `` Gas Density Glenn research Center ''. grc.nasa.gov. Archived from the original on April 14, 2013. Jump up ^ `` Density definition in Oil Gas Glossary ''. Oilgasglossary.com. Archived from the original on August 5, 2010. Retrieved September 14, 2010. Jump up ^ Archimedes, A Gold Thief and Buoyancy Archived August 27, 2007, at the Wayback Machine. -- by Larry `` Harris '' Taylor, Ph. D. Jump up ^ Vitruvius on Architecture, Book IX, paragraphs 9 -- 12, translated into English and in the original Latin. Jump up ^ `` EXHIBIT : The First Eureka Moment ''. Science. 305 ( 5688 ) : 1219e. 2004. doi : 10.1126 / science. 305.5688. 1219e. Jump up ^ Fact or Fiction ? : Archimedes Coined the Term `` Eureka ! '' in the Bath, Scientific American, December 2006. Jump up ^ New carbon nanotube struructure aerographite is lightest material champ Archived October 17, 2013, at the Wayback Machine... Phys.org ( July 13, 2012 ). Retrieved on July 14, 2012. Jump up ^ Aerographit : Leichtestes Material der Welt entwickelt -- SPIEGEL ONLINE Archived October 17, 2013, at the Wayback Machine... Spiegel.de ( July 11, 2012 ). Retrieved on July 14, 2012. ^ Jump up to : `` Re : which is more bouyant ( sic ) styrofoam or cork ''. Madsci.org. Archived from the original on February 14, 2011. Retrieved September 14, 2010. ^ Jump up to : Raymond Serway ; John Jewett ( 2005 ), Principles of Physics : A Calculus - Based Text, Cengage Learning, p. 467, ISBN 0 - 534 - 49143 - X, archived from the original on May 17, 2016 Jump up ^ `` Wood Densities ''. www.engineeringtoolbox.com. Archived from the original on October 20, 2012. Retrieved October 15, 2012. Jump up ^ `` Density of Wood ''. www.simetric.co.uk. Archived from the original on October 26, 2012. Retrieved October 15, 2012. Jump up ^ CRC Press Handbook of tables for Applied Engineering Science, 2nd Edition, 1976, Table 1 - 59 Jump up ^ glycerol composition at Archived February 28, 2013, at the Wayback Machine... Physics.nist.gov. Retrieved on July 14, 2012. Jump up ^ ( 1 ) ^ Jump up to : Hugh D. Young ; Roger A. Freedman. University Physics with Modern Physics Archived April 30, 2016, at the Wayback Machine... Addison - Wesley ; 2012. ISBN 978 - 0 - 321 - 69686 - 1. p. 374. Jump up ^ Density of the Earth, wolframalpha.com, archived from the original on October 17, 2013 Jump up ^ Density of Earth 's core, wolframalpha.com, archived from the original on October 17, 2013 Jump up ^ Density of the Sun 's core, wolframalpha.com, archived from the original on October 17, 2013 Jump up ^ Extreme Stars : White Dwarfs & Neutron Stars Archived September 25, 2007, at the Wayback Machine., Jennifer Johnson, lecture notes, Astronomy 162, Ohio State University. Accessed : May 3, 2007. Jump up ^ Nuclear Size and Density Archived July 6, 2009, at the Wayback Machine., HyperPhysics, Georgia State University. Accessed : June 26, 2009. External links `` Density ''. Encyclopædia Britannica. 8 ( 11th ed. ). 1911. `` Density ''. The New Student 's Reference Work. 1914. 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 prediction density prediction NDL : 00567732 Mole concepts Physical quantities Mass concentration Molar concentration Molality Mass Volume Density Mole fraction Mass fraction Amount of substance Molar mass Atomic mass Particle number Avogadro constant Pressure Kelvin temperature Gas constant Molar volume Specific volume Laws Charles 's law Boyle 's law Gay - Lussac 's law Combined gas law Ideal gas law Retrieved from `` https://en.wikipedia.org/w/index.php?title=Density&oldid=843212644 '' Categories : Density Physical quantities Hidden categories : Webarchive template wayback links Wikipedia pages semi-protected against vandalism Wikipedia indefinitely move - protected pages Use mdy dates from October 2015 Wikipedia articles incorporating a citation from the 1911 Encyclopaedia Britannica with Wikisource reference Wikipedia articles incorporating citation to the NSRW Wikipedia articles incorporating citation to the NSRW with an wstitle parameter All articles with dead external links Articles with dead external links from March 2018 Articles with permanently dead external links Talk View source Contents About Wikipedia Afrikaans Alemannisch Aragonés অসমীয়া Asturianu Azərbaycanca تۆرکجه বাংলা Bân - lâm - gú Беларуская Беларуская ( тарашкевіца ) ‎ भोजपुरी Български Boarisch Bosanski Català Čeština ChiShona Cymraeg Dansk Deutsch Eesti Ελληνικά Español Esperanto Euskara فارسی Français Frysk Furlan Gaeilge Gàidhlig Galego 한국어 Հայերեն हिन्दी Hrvatski Ido Igbo Bahasa Indonesia Interlingua Íslenska Italiano עברית Basa Jawa ಕನ್ನಡ ქართული Қазақша Kiswahili Kreyòl ayisyen Kurdî Кыргызча Latina Latviešu Lëtzebuergesch Lietuvių La. lojban. 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Question: what is the symbol of density in physics
Answer: ρ