Density

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Density

The density of a material is defined as its mass

Mass

In physical science, mass refers to the degree of acceleration a body acquires when subject to a force: bodies with greater mass are accelerated less by the same force....
per unit volume

Volume

The volume of any solid, liquid, plasma, vacuum or theoretical object is how much three-dimensional space it occupies, often quantified numerically....
. The symbol of density is (the Greek letter rho

Rho (letter)

Rho is the 17th letter of the Greek alphabet. In the system of Greek numerals it has a value of 100. It is derived from Proto-Canaanite alphabet R? "head" ....
).

ematically:

where: is the density, is the mass, is the volume.

Different materials usually have different densities, so density is an important concept regarding buoyancy

Buoyancy

In physics, buoyancy is the upward force that keeps things afloat. The net upward buoyancy force is equal to the magnitude of the weight of fluid displaced by the body....
, metal purity and packaging. In some cases density is expressed as the dimensionless quantities specific gravity

Specific gravity

Specific gravity is defined as the ratio of the density of a given solid or liquid substance to the density of water at a specific temperature and pressure, typically at 4?C and , making it a dimensionless quantity ....
(SG) or relative density

Relative density

Relative density, sometimes called specific density, is the ratio of the density of a substance to the density of a given reference material....
(RD), in which case it is expressed in multiples of the density of some other standard material, usually water or air/gas.

well-known story, Archimedes

Archimedes

Archimedes of Syracuse was a Greek mathematics, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity....
was given the task of determining whether King Hiero

Hiero II of Syracuse

Hieron II, king of Syracuse, Italy from 270 to 215 BC, was the illegitimate son of a Syracusan noble, Hierocles of Syracuse, who claimed descent from Gelon....
's goldsmith

Goldsmith

A goldsmith is a metalworker who specializes in working with gold and other precious metals. Since ancient times the techniques of a Goldsmith have evolved very little in order to produce items of jewelry of quality standards....
was embezzling gold

Gold

Gold is a chemical element with the symbol Au and atomic number 79. It is a highly sought-after precious metal, having been used as money, as a store of value, in jewelry, in sculpture, and for ornamentation since the beginning of recorded history....
during the manufacture of a wreath

Wreath

A wreath is a circle made of flowers, leaf and sometimes fruits that can be used as an ornament, hanging on a wall or door, or resting on a table....
dedicated to the gods and replacing it with another, cheaper alloy

Alloy

An alloy is a partial or complete solid solution of one or more chemical element in a metallic matrix. Complete solid solution alloys give single solid phase microstructure, while partial solutions give two or more phases that may be homogeneous in distribution depending on thermal history....
.

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 bath and observed from the rise of the water upon entering that he could calculate the volume of the crown through the displacement

Displacement (fluid)

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Encyclopedia

The density of a material is defined as its mass

Mass

In physical science, mass refers to the degree of acceleration a body acquires when subject to a force: bodies with greater mass are accelerated less by the same force....
per unit volume

Volume

Rho (letter)

Rho is the 17th letter of the Greek alphabet. In the system of Greek numerals it has a value of 100. It is derived from Proto-Canaanite alphabet R? "head" ....
).

Formula

Mathematically:

where: is the density, is the mass, is the volume.

Different materials usually have different densities, so density is an important concept regarding buoyancy

Buoyancy

Specific gravity

Relative density

History

In a well-known story, Archimedes

Archimedes

Hiero II of Syracuse

Hieron II, king of Syracuse, Italy from 270 to 215 BC, was the illegitimate son of a Syracusan noble, Hierocles of Syracuse, who claimed descent from Gelon....
's goldsmith

Goldsmith

Gold

Wreath

Alloy

Displacement (fluid)

In fluid mechanics, displacement occurs when an object is immersed in a fluid, pushing it out of the way and taking its place. The volume of the fluid displaced can then be measured, as in the illustration, and from this the volume of the immersed object can be deduced ....
of the water. Allegedly, upon this discovery, he went running naked though the streets shouting, "Eureka! Eureka!" (Greek "I found it"). As a result, the term "eureka

Eureka (word)

Eureka is an exclamation used as an interjection to celebrate a Discovery ....
" entered common parlance and is used today to indicate a moment of enlightenment.

This story first appeared in written form in Vitruvius

Vitruvius

File:Vitruvius.jpgMarcus Vitruvius Pollio was a Ancient Rome writer, architect and engineer , active in the 1st century BC. By his own description Vitruvius served as a Ballista , the third class of arms in the military offices....
' books of architecture

De architectura

File:De Architectura027.jpg is a treatise on architecture written by the Ancient Rome architect Vitruvius and dedicated to his patron, the emperor Caesar Augustus as a guide for Caesar Augustus#Building projects....
, 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

For a homogeneous object, the mass divided by the volume gives the density. The mass is normally measured with an appropriate scale or balance

Weighing scale

A weighing scale is a measuring instrument for measuring the weight or mass of an object. They use one of two techniques. A spring scale measures weight by the distance a spring deflects under its load....
; the volume may be measured directly (from the geometry of the object) or by the displacement of a fluid.

If the body is not homogeneous or heterogeneous, the density is a function of the coordinates , where is elementary volume with coordinates . The mass of the body then can be expressed as ,

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

Hydrometer

A hydrometer is an instrument used to measure the specific gravity of liquids; that is, the ratio of the density of the liquid to the density of water....
, which measures the volume displaced by an object of known mass. A common laboratory device for measuring fluid density is a pycnometer

Pycnometer

The pycnometer , also called pyknometer or specific gravity bottle, is a flask, usually made of glass, with a close-fitting ground glass stopper with a capillary tube through it, so that air bubbles may escape from the apparatus....
; a related device for measuring the absolute density of a solid is a gas pycnometer

Gas pycnometer

A gas pycnometer is a laboratory device used for measuring the density or more accurately the volume of solids, be they regularly shaped, Porous medium or non-porous, Single crystal, Powder , Granular material or in some way Comminution, employing some method of gas displacement and the volume:pressure relationship known as Boyle's Law....
. Another instrument used to determine the density of a liquid

Liquid

Liquid is one of the principal states of matter. A liquid is a fluid that has the particles loose and can freely form a distinct surface at the boundaries of its bulk material....
or a gas

Gas

In physics, a gas is a state of matter, consisting of a collection of particles without a definite shape or volume that are in more or less random motion....
is the digital density meter - based on the oscillating U-tube

Oscillating U-tube

The oscillating U-tube is a technique to determine the density of liquids and gases based on an electronic measurement of the frequency of oscillation, from which the density value is calculated....
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

Bulk density

Bulk density is a property of powders, granules and other "divided" solids, especially used in reference to soil. It is defined as the mass of many particles of the material divided by the total volume they occupy....
, which differs significantly from the density of an individual grain of sand.

Common units

The SI

Si, si, or SI may refer to :...
unit for density is:

kilogram
Kilogram

The kilogram or kilogrammeThe spelling kilogram is used by the International Committee for Weights and Measures and the U.S....
s per cubic metre
Cubic metre

The cubic metre is the SI derived unit of volume. It is the volume of a cube with edges one metre in length. An alternative name, which allowed a different usage with SI prefix, was the st?re....
(kg/m³)

Metric units outside the SI

kilogram
Kilogram

The kilogram or kilogrammeThe spelling kilogram is used by the International Committee for Weights and Measures and the U.S....
s per litre
Litre

The litre or liter is a unit of volume. There are two official symbols: the Latin letter L in lower and upper case . The lower case L is often written as a cursive l to avoid confusion with the number 1 in antiqua fonts....
(kg/L). At 4 °C, water
Water

Water is a common chemical substance that is essential for the survival of all known forms of life. In typical usage, water refers only to its liquid form or States of matter, but the substance also has a solid state, ice, and a gaseous state, water vapor or steam....
has a density of 1.000 kg/L, making this a convenient unit at about the room temperature,
kilograms per cubic decimeter (kg/dm³),
gram
Gram

The gram , ; symbol g, is a Physical unit of mass.Originally defined as "the absolute weight of a volume of pure water equal to the cube of the hundredth part of a metre, and at the temperature of melting ice" , a gram is now defined as one one-thousandth of the SI base unit, the kilogram, or Scientific notation kg, which itself is...
s per millilitre (g/mL),
grams per cubic centimeter (g/cc or g/cm³).

These are all numerically equivalent to kg/L (1 kg/L = 1 kg/dm³ = 1 g/cm³ = 1 g/mL).

In U.S. customary units or Imperial units, the units of density include:

ounce
Ounce

This article is about the unit of mass. For the unit of force, see Pound-force. For the unit of volume, see Fluid ounce. For all other uses, see Ounce ....
s per cubic inch
Cubic inch

A cubic inch is a non-International System of Units Units of measurement of volume, equal to the volume of a cube with sides of one inch.Cubic inches are still sometimes used as a unit of measurement in the United States and Canada, although SI is continuing to gradually displace non-SI usage....
(oz/cu in)
pound
Pound (mass)

The pound or pound-mass is a Units of measurement of massused in the Imperial unit, United States customary units and other systems of measurement....
s per cubic inch (lb/cu in)
pounds per cubic foot
Cubic foot

The cubic foot is an Imperial unit and United States customary units unit of volume, used in the United States, Canada and the United Kingdom. It is defined as the volume of a cube with sides of one foot in length.|-...
(lb/cu ft)
pounds per cubic yard
Cubic yard

A cubic yard is an Imperial unit / U.S. customary unit unit of volume, used in the United States, Canada, and the UK. It is defined as the volume of a cube with sides of 1 yard in length....
(lb/cu yd)
pounds per gallon
Gallon

A gallon is a measure of volume of approximately four litres. Historically it has had many different definitions, but there are three definitions in current use....
(for U.S. or imperial gallons) (lb/gal)
pounds per U.S. bushel
Bushel

A bushel is a unit of dry measure, usually subdivided into eight local gallons in the systems of Imperial units and U.S. customary units. It is used for volumes of dry measure commodity, not liquids, most often in agriculture....
(lb/bu)
slugs
Slug (mass)

The slug is an English unit of mass. It is a mass that accelerates by 1 ft/s? when a force of one pound-force is exerted on it. Therefore a slug has a mass of 32.17405 pounds or 14.5939 kg....
per cubic foot.

Changes of density

In general density can be changed by changing either the pressure

Pressure

Pressure is the force per unit area applied to an object in a direction surface normal to the surface. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure....
or the temperature

Temperature

In physics, temperature is a physical property of a Physical system that underlies the common notions of hot and cold; something that feels hotter generally has the greater 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

Water

Water is a common chemical substance that is essential for the survival of all known forms of life. In typical usage, water refers only to its liquid form or States of matter, but the substance also has a solid state, ice, and a gaseous state, water vapor or steam....
increases between its melting point at 0 °C and 4 °C and similar behaviour is observed in silicon

Silicon

Silicon is the most common metalloid. It is a chemical element, which has the symbol Si and atomic number 14. The atomic mass is 28.0855....
at low temperatures.

The effect of pressure and temperature on the densities of liquids and solids is small so that a typical compressibility

Compressibility

In thermodynamics and fluid mechanics, compressibility is a Measure of the relative volume change of a fluid or solid as a response to a pressure change....
for a liquid or solid is 10^–6 bar

Bar (unit)

The bar , decibar and the millibar are units of pressure. They are not SI units, nor are they cgs units, but they are accepted for use with the SI....
^–1 (1 bar=0.1 MPa) and a typical thermal expansivity is 10^–5 K

Kelvin

The kelvin is a Units of measurement of temperature and is one of the seven SI base units. The Kelvin scale is a Thermodynamic temperature scale where absolute zero, the theoretical absence of all thermal energy, is zero ....
^–1.

In contrast, the density of gases is strongly affected by pressure. Boyle's law

Boyle's law

Boyle's law is one of several gas laws and a special case of the ideal gas law. Boyle's law describes the inversely proportional relationship between the absolute pressure and volume of a gas, if the temperature is kept constant within a closed system....
says that the density of an ideal gas

Ideal gas

The ideal gas model is a model of matter in which the molecules are treated as non-interacting point particles which are engaged in a random motion that obeys conservation of energy....
is given by

where is the universal gas constant

Gas constant

The gas constant is a physical constant which is featured in a large number of fundamental equations in the physical sciences, such as the ideal gas law and the Nernst equation....
, is the pressure, the molar mass

Molar mass

Molar mass, symbol M, is the mass of one mole of a substance . It is a physical property which is characteristic of each pure substance. The base SI unit for mass is the kilogram but, for both practical and historical reasons, molar masses are almost always quoted in grams per mole , especially in chemistry....
, and the absolute temperature.

This means that a gas at 300 K

Kelvin

Bar (unit)

The bar , decibar and the millibar are units of pressure. They are not SI units, nor are they cgs units, but they are accepted for use with the SI....
will have its density doubled by increasing the pressure to 2 bar

Bar (unit)

The bar , decibar and the millibar are units of pressure. They are not SI units, nor are they cgs units, but they are accepted for use with the SI....
or by reducing the temperature to 150 K

Kelvin

Iridium

Iridium is the chemical element with atomic number 77, and is represented by the symbol Ir. A very hard, brittle, silvery-white transition metal of the platinum group, iridium is the second densest element and is the most corrosion-resistant metal, even at temperatures as high as 2000 ?C....
is the densest known substance at standard conditions for temperature and pressure

Standard conditions for temperature and pressure

In physical sciences, standard conditions for temperature and pressure are standard sets of conditions for experimental measurements, to allow comparisons to be made between different sets of data....
.

Density of water

See also: Water density
Water (molecule)

File:Blue-water-pool.jpgWater is the most abundant molecule on Earth's surface, constituting about 70% of the Earth's surface in liquid, solid, and gaseous states....

Temp (°C)	Density (kg/m³)
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
The density of water in kilograms per cubic meter (SI unit) at various temperatures in degrees Celsius. The values below 0 °C refer to supercooled Supercooling Supercooling is the process of lowering the temperature of a liquid or a gas below its melting point, without it becoming a solid.A liquid below its standard freezing point will crystallization process in the presence of a nucleation around which a crystal structure can form.... water.

Density of air

T in °C Celsius Celsius is a temperature scale that is named after the Swedish astronomer Anders Celsius , who developed a similar temperature scale two years before his death....	? in kg/m³ (at 1 atm Atmosphere (unit) The standard atmosphere is an international reference pressure defined as 101,325 Pascal and formerly used as unit of pressure . For practical purposes it has been replaced by the Bar which is 100,000 Pa.... )
–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 ?_i in a solution can be called partial density of that component.

Density of composite material

ASTM specification D792-00 describes the steps to measure the density of a composite material.

where:

is the density of the composite material, in g/cm³

and

is the weight of the specimen when hung in the air

is the weight of the partly immersed wire holding the specimen

is the weight of the specimen when immersed fully in distilled water, along with the partly immersed wire holding the specimen

is the density in g/cm³ of the distilled water at 23°C

Densities of various materials

Material	? in kg/m³	Notes
Interstellar medium Interstellar medium In astronomy, the interstellar medium is the gas and cosmic dust that pervade interstellar space: the matter that exists between the stars within a galaxy....	10^-25 − 10^-15	Assuming 90% H, 10% He; variable T
Earth's atmosphere Earth's atmosphere The Earth's atmosphere is a layer of gases surrounding the planet Earth that is retained by the Earth's gravity. Dry air contains roughly 78.08% nitrogen, 20.95% oxygen, 0.93% argon, 0.038% Carbon dioxide in the Earth's atmosphere, and trace amounts of other gases....	1.2	At sealevel
Aerogel Aerogel Aerogel is a low-density solid material derived from gel in which the liquid component of the gel has been replaced with gas. The result is an extremely low density solid with several remarkable properties, most notably its effectiveness as a thermal conductivity....	1 − 2
Styrofoam Styrofoam Styrofoam is a trademark of Dow Chemical Company for presently made for thermal insulation and craft applications .In 1940, researchers in Dow's Chemical Physics Lab found a way to make foamed polystyrene....	30 − 120
Cork Cork (material) Cork material is a prime-subset of generic Cork cambium, harvested for commercial use primarily from the Cork Oak tree, Quercus suber, with Portugal producing 50% of cork worldwide....	220 − 260
Water Water Water is a common chemical substance that is essential for the survival of all known forms of life. In typical usage, water refers only to its liquid form or States of matter, but the substance also has a solid state, ice, and a gaseous state, water vapor or steam....	1000	At STP Standard conditions for temperature and pressure In physical sciences, standard conditions for temperature and pressure are standard sets of conditions for experimental measurements, to allow comparisons to be made between different sets of data....
Plastics	850 − 1400	For polypropylene Polypropylene Polypropylene or polypropene is a thermoplastic polymer, made by the chemical industry and used in a wide variety of applications, including packaging, textiles , stationery, plastic parts and reusable containers of various types, laboratory equipment, loudspeakers, automotive components, and polymer banknotes.... and PETE Pete Pete may refer to:In athletics:* The Pete, Petersen Events Center, athletics complex and basketball arena on the campus of the University of Pittsburgh... /PVC PVC Polyvinyl chloride is a plastic.PVC may also refer to:Param Vir Chakra, India's highest military honorPeripheral venous catheter*Permanent virtual circuit, a term used in telecommunications and computer networks...
The Earth Earth Earth is the third planet from the Sun. Earth is the largest of the terrestrial planets in the Solar System in diameter, mass and density. It is also referred to as the World and Wiktionary:Terra.Note that by International Astronomical Union convention, the term "Terra" is used for naming extensive land masses, rather...	5515.3	Mean density
Copper Copper Copper is a chemical element with the symbol Cu and atomic number 29.It is a ductile metal with very high thermal and electrical conductivity....	8920 − 8960	Near room temperature Room temperature Room temperature is a common term to denote a certain temperature within enclosed space at which humans are accustomed.Room temperature is thus often indicated by general human comfort, with the common range of 10celsius to 23?C , though climate may acclimatize people to higher or lower temperatures....
Lead Lead Lead is a main-group Chemical element with symbol Pb and atomic number 82. Lead is a soft, malleable poor metal, also considered to be one of the heavy metal ....	11340	Near room temperature Room temperature Room temperature is a common term to denote a certain temperature within enclosed space at which humans are accustomed.Room temperature is thus often indicated by general human comfort, with the common range of 10celsius to 23?C , though climate may acclimatize people to higher or lower temperatures....
The Inner Core Inner core The inner core of the Earth, its innermost part as detected by seismology, is a primarily solid sphere about in radius, only about 70% that of the Moon....	~13000	As listed in Earth Earth Earth is the third planet from the Sun. Earth is the largest of the terrestrial planets in the Solar System in diameter, mass and density. It is also referred to as the World and Wiktionary:Terra.Note that by International Astronomical Union convention, the term "Terra" is used for naming extensive land masses, rather...
Uranium Uranium Uranium is a silvery-gray metallic chemical element in the actinide series of the periodic table that has the chemical symbol U and atomic number 92....	19100	Near room temperature Room temperature Room temperature is a common term to denote a certain temperature within enclosed space at which humans are accustomed.Room temperature is thus often indicated by general human comfort, with the common range of 10celsius to 23?C , though climate may acclimatize people to higher or lower temperatures....
Iridium Iridium Iridium is the chemical element with atomic number 77, and is represented by the symbol Ir. A very hard, brittle, silvery-white transition metal of the platinum group, iridium is the second densest element and is the most corrosion-resistant metal, even at temperatures as high as 2000 ?C....	22500	Near room temperature Room temperature Room temperature is a common term to denote a certain temperature within enclosed space at which humans are accustomed.Room temperature is thus often indicated by general human comfort, with the common range of 10celsius to 23?C , though climate may acclimatize people to higher or lower temperatures....
The core of the Sun Sun The Sun , a G V star, is the star at the center of the Solar System. The Earth and other matter orbit the Sun, which by itself accounts for about 98.6% of the Solar System's mass....	~150000
Atomic nuclei	~3 × 10¹⁷	As listed in neutron star Neutron star A neutron star is a type of compact star that can result from the gravitational collapse of a massive star during a Type II supernova, Type Ib and Ic supernovae supernova event....
Neutron star Neutron star A neutron star is a type of compact star that can result from the gravitational collapse of a massive star during a Type II supernova, Type Ib and Ic supernovae supernova event....	8.4 × 10¹⁶ − 1 × 10¹⁸
Black hole Black hole In general relativity, a black hole is a region of space in which the gravitational field is so powerful that nothing, including electromagnetic radiation , can escape its pull after having fallen past its event horizon....	4 × 10¹⁷	Mean density inside the Schwarzschild radius Schwarzschild radius The Schwarzschild radius is a characteristic radius associated with every mass. It is the radius for a given mass where, if that mass could be compressed to fit within that radius, no known force or Degenerate matter could stop it from continuing to collapse into a gravitational singularity.... of an earth-mass black hole (theoretical)

Density

Formula

History

Measurement of density

Common units

Changes of density

Density of water

Density of air

Density of solutions

Density of composite material

Densities of various materials

See also

External links