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Density (volumetric mass density or specific mass) is the substance's
mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different eleme ...
per unit of 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: :$\rho = \frac$ 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 The specific weight, also known as the unit weight, is the weight per unit volume of a material. A commonly used value is the specific weight of water on Earth at , which is .National Council of Examiners for Engineering and Surveying (2005). ...
. 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 Buoyancy (), or upthrust, is an upward force exerted by a fluid that opposes the weight of a partially or fully immersed object. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus the ...
, purity and packaging. Osmium and iridium are the densest known elements at
standard conditions for temperature and pressure Standard temperature and pressure (STP) are standard sets of conditions for experimental measurements to be established to allow comparisons to be made between different sets of data. The most used standards are those of the International Union ...
. To simplify comparisons of density across different systems of units, it is sometimes replaced by the dimensionless quantity "
relative density Relative density, or specific gravity, is the ratio of the density (mass of a unit volume) of a substance to the density of a given reference material. Specific gravity for liquids is nearly always measured with respect to water at its dens ...
" 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 relative to water 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, which causes it to rise relative to denser unheated material. The reciprocal of the density of a substance is occasionally called its
specific volume In thermodynamics, the specific volume of a substance (symbol: , nu) is an intrinsic property of the substance, defined as the ratio of the substance's volume () to its mass (). It is the reciprocal of density ( rho) and it is related to ...
, a term sometimes used in
thermodynamics Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws o ...
. Density is an intensive property in that increasing the amount of a substance does not increase its density; rather it increases its mass. Other conceptually comparable quantities or ratios include
specific density Specific density is the ratio of the mass versus the volume of a material. Density vs. gravity Specific density is based upon units of mass and volume, while specific gravity is dimensionless. References Physical quantities Density ...
, relative density (specific gravity), and
specific weight The specific weight, also known as the unit weight, is the weight per unit volume of a material. A commonly used value is the specific weight of water on Earth at , which is .National Council of Examiners for Engineering and Surveying (2005). ...
.

# History

In a well-known but probably apocryphal tale, Archimedes was given the task of determining whether King Hiero's goldsmith was embezzling
gold Gold is a chemical element with the Symbol (chemistry), symbol Au (from la, aurum) and atomic number 79. This makes it one of the higher atomic number elements that occur naturally. It is a Brightness, bright, slightly orange-yellow, dense, s ...
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.

# Measurement of density

A number of techniques as well as standards exist for the measurement of density of materials. Such techniques include the use of a hydrometer (a buoyancy method for liquids), Hydrostatic balance (a buoyancy method for liquids and solids), immersed body method (a buoyancy method for liquids), pycnometer (liquids and solids), air comparison pycnometer (solids), oscillating densitometer (liquids), as well as pour and tap (solids). However, each individual method or technique measures different types of density (e.g. bulk density, skeletal density, etc.), and therefore it is necessary to have an understanding of the type of density being measured as well as the type of material in question.

## Unit

From the equation for density (''ρ'' = ''m''/''V''), mass density has any unit that is ''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 The cubic metre (in Commonwealth English and international spelling as used by the International Bureau of Weights and Measures) or cubic meter (in American English) is the unit of volume in the International System of Units (SI). Its symbol is ...
(kg/m3) and the cgs unit of
gram The gram (originally gramme; SI unit symbol g) is a unit of mass in the International System of Units (SI) equal to one one thousandth of a kilogram. Originally defined as of 1795 as "the absolute weight of a volume of pure water equal ...
per cubic centimetre (g/cm3) are probably the most commonly used units for density. One g/cm3 is equal to 1000 kg/m3. 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.

## Homogeneous materials

The density at all points of a homogeneous object equals its total
mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different eleme ...
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 hydrometer or lactometer is an instrument used for measuring density or relative density of liquids based on the concept of buoyancy. They are typically calibrated and graduated with one or more scales such as specific gravity. A hydrometer ...
, a
dasymeter A dasymeter was meant initially as a device to demonstrate the buoyant effect of gases like air (as shown in the adjacent pictures). A dasymeter which allows weighing acts as a densimeter used to measure the density of gases. Principle The ...
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: $\rho\left(\vec\right) = dm/dV$, where $dV$ is an elementary volume at position $r$. The mass of the body then can be expressed as :$m = \int_V \rho\left(\vec\right)\,dV.$

## 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 Bulk density, also called apparent density or volumetric density, is a property of powders, granules, and other "divided" solids, especially used in reference to mineral components ( soil, gravel), chemical substances, ( pharmaceutical) ingred ...
. 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

In general, density can be changed by changing either the pressure or the
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied o ...
. 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 10−6  bar−1 (1 bar = 0.1 MPa) and a typical thermal expansivity is 10−5  K−1. 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 :$\rho = \frac ,$ where is the
molar mass In chemistry, the molar mass of a chemical compound is defined as the mass of a sample of that compound divided by the amount of substance which is the number of moles in that sample, measured in moles. The molar mass is a bulk, not molecul ...
, is the pressure, is the
universal gas constant The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment pe ...
, and 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 :$\rho = \frac,$ where $\rho_$ is the density at a reference temperature, $\alpha$ is the thermal expansion coefficient of the material at temperatures close to $T_0$.

# 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 ρi in a solution sums to density of the solution, :$\rho = \sum_i \varrho_i .$ 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: :$\rho = \sum_i \rho_i \frac\, = \sum_i \rho_i \varphi_i = \sum_i \rho_i \frac,$ 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: :$\overline_i = RT \frac.$

# Densities

## Various materials

:''Selected chemical elements are listed here. For the densities of all chemical elements, see List of chemical elements''

## Air ## Molar volumes of liquid and solid phase of elements # Common units

The SI unit for density is: * kilogram per
cubic metre The cubic metre (in Commonwealth English and international spelling as used by the International Bureau of Weights and Measures) or cubic meter (in American English) is the unit of volume in the International System of Units (SI). Its symbol is ...
(kg/m3) The litre and tonne are not part of the SI, but are acceptable for use with it, leading to the following units: * kilogram per
litre The litre (international spelling) or liter (American English spelling) (SI symbols L and l, other symbol used: ℓ) is a metric unit of volume. It is equal to 1 cubic decimetre (dm3), 1000 cubic centimetres (cm3) or 0.001 cubic metre ( ...
(kg/L) *
gram The gram (originally gramme; SI unit symbol g) is a unit of mass in the International System of Units (SI) equal to one one thousandth of a kilogram. Originally defined as of 1795 as "the absolute weight of a volume of pure water equal ...
per millilitre (g/mL) *
tonne The tonne ( or ; symbol: t) is a unit of mass equal to 1000  kilograms. It is a non-SI unit accepted for use with SI. It is also referred to as a metric ton to distinguish it from the non-metric units of the short ton (United States ...
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 water has a density of about 1 kg/dm3, making any of these SI units numerically convenient to use as most solids and liquids have densities between 0.1 and 20 kg/dm3. * kilogram per cubic decimetre (kg/dm3) * gram per cubic centimetre (g/cm3) ** 1 g/cm3 = 1000 kg/m3 * megagram (metric ton) per cubic metre (Mg/m3) In US customary units density can be stated in: * Avoirdupois ounce per cubic inch (1 g/cm3 ≈ 0.578036672 oz/cu in) * Avoirdupois ounce per
fluid ounce A fluid ounce (abbreviated fl oz, fl. oz. or oz. fl., old forms ℥, fl ℥, f℥, ƒ ℥) is a unit of volume (also called ''capacity'') typically used for measuring liquids. The British Imperial, the United States customary, and the United S ...
(1 g/cm3 ≈ 1.04317556 oz/US fl oz = 1.04317556 lb/US fl pint) * Avoirdupois pound per cubic inch (1 g/cm3 ≈ 0.036127292 lb/cu in) * pound per
cubic foot Cubic may refer to: Science and mathematics * Cube (algebra), "cubic" measurement * Cube, a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex ** Cubic crystal system, a crystal system ...
(1 g/cm3 ≈ 62.427961 lb/cu ft) * pound per cubic yard (1 g/cm3 ≈ 1685.5549 lb/cu yd) * pound per
US liquid gallon The gallon is a unit of volume in imperial units and United States customary units. Three different versions are in current use: *the imperial gallon (imp gal), defined as , which is or was used in the United Kingdom, Ireland, Canada, Aust ...
(1 g/cm3 ≈ 8.34540445 lb/US gal) * pound per US bushel (1 g/cm3 ≈ 77.6888513 lb/bu) *
slug Slug, or land slug, is a common name for any apparently shell-less terrestrial gastropod mollusc. The word ''slug'' is also often used as part of the common name of any gastropod mollusc that has no shell, a very reduced shell, or only a sm ...
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/cm3 ≈ 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. Knowing the volume of the
unit cell In geometry, biology, mineralogy and solid state physics, a unit cell is a repeating unit formed by the vectors spanning the points of a lattice. Despite its suggestive name, the unit cell (unlike a unit vector, for example) does not necessari ...
of a crystalline material and its formula weight (in daltons), the density can be calculated. One dalton per cubic
ångström The angstromEntry "angstrom" in the Oxford online dictionary. Retrieved on 2019-03-02 from https://en.oxforddictionaries.com/definition/angstrom.Entry "angstrom" in the Merriam-Webster online dictionary. Retrieved on 2019-03-02 from https://www.m ...
is equal to a density of 1.660 539 066 60 g/cm3.

* Densities of the elements (data page) * List of elements by density * Air density * Area density *
Bulk density Bulk density, also called apparent density or volumetric density, is a property of powders, granules, and other "divided" solids, especially used in reference to mineral components ( soil, gravel), chemical substances, ( pharmaceutical) ingred ...
*
Buoyancy Buoyancy (), or upthrust, is an upward force exerted by a fluid that opposes the weight of a partially or fully immersed object. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus the ...
*
Charge density In electromagnetism, charge density is the amount of electric charge per unit length, surface area, or volume. Volume charge density (symbolized by the Greek letter ρ) is the quantity of charge per unit volume, measured in the Systeme Internat ...
* Density prediction by the Girolami method *
Dord The word ''dord'' is a dictionary error in lexicography. It was accidentally created, as a ghost word, by the staff of G. and C. Merriam Company (now part of Merriam-Webster) in the '' New International Dictionary'', second edition (1934). That ...
*
Energy density In physics, energy density is the amount of energy stored in a given system or region of space per unit volume. It is sometimes confused with energy per unit mass which is properly called specific energy or . Often only the ''useful'' or ex ...
*
Lighter than air A lifting gas or lighter-than-air gas is a gas that has a density lower than normal atmospheric gases and rises above them as a result. It is required for aerostats to create buoyancy, particularly in lighter-than-air aircraft, which include free ...
*
Linear density Linear density is the measure of a quantity of any characteristic value per unit of length. Linear mass density (titer in textile engineering, the amount of mass per unit length) and linear charge density (the amount of electric charge per unit ...
*
Number density The number density (symbol: ''n'' or ''ρ''N) is an intensive quantity used to describe the degree of concentration of countable objects ( particles, molecules, phonons, cells, galaxies, etc.) in physical space: three-dimensional volumetric num ...
* Orthobaric density * Paper density *
Specific weight The specific weight, also known as the unit weight, is the weight per unit volume of a material. A commonly used value is the specific weight of water on Earth at , which is .National Council of Examiners for Engineering and Surveying (2005). ...
* Spice (oceanography) * Standard temperature and pressure

# References

* *
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

* ttp://www.adamequipment.com/education/Documents/EdExp1.pdf 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.

Determination of Density of Solid
instructions for performing classroom experiment. * * {{Authority control Physical quantities