# Density

In physics, density is mass m per unit volume V—how heavy something is compared to its size. A small, heavy object, such as a rock or a lump of lead, is denser than a lighter object of the same size or a larger object of the same weight, such as pieces of cork or foam.

For the common case of a homogeneous substance, density is expressed as:
where, in SI Units:
ρ (rho) is the density of the substance, measured in kg·m–3
m is the mass of the substance, measured in kg
V is the volume of the substance, measured in m3

## History

In a famous problem, Archimedes was given the task of determining whether King Hiero's goldsmith was embezzling gold during the manufacture of a wreath dedicated to the Gods and replacing it with another, cheaper alloy.[1]

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 of the water. Allegedly, upon this discovery Archimedes went running though the streets in the nude shouting, "Eureka! Eureka!" (Greek for "I have found it!"). As a result, the term "eureka" entered common parlance and is used today to indicate a moment of enlightenment.

This story first appeared in written form in Vitruvius' books of architecture, two centuries after it supposedly took place.[2] 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.[3]

## Measurement of density

For a homogeneous object, the formula mass/volume may be used. The mass is normally measured with an appropriate scale; 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 possibility for determining the density of a liquid or a gas is the measurement with a 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.

## Common units

In U.S. customary units or Imperial units, the units of density include:
ounces per cubic inch (oz/in3)
pounds per cubic inch (lb/in3)
pounds per cubic foot (lb/ft3)
pounds per cubic yard (lb/yd3)
pounds per gallon (for U.S. or imperial gallons) (lb/gal)
pounds per U.S. bushel (lb/bu)
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 10–6 bar–1 (1 bar=0.1 MPa) and a typical thermal expansivity is 10–5 K–1.

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

where is the universal gas constant, is the pressure, the molar mass, and the absolute temperature.

This means that a gas at 300 K and 1 bar will have its density doubled by increasing the pressure to 2 bar or by reducing the temperature to 150 K.

## Density of water

Temperature °C °F Density[4] (at 1 atm) 0.0 32.0 999.8425 4.0 39.2 999.9750 15.0 59.0 999.1026 20.0 68.0 998.2071 25.0 77.0 997.0479 37.0 98.6 993.3316 50.0 122.0 988.04 100.0 212.0 958.3665

## Density of air

T in °C ρ in kg/m³ (at 1 atm)
–101.342
–51.316
01.293
51.269
101.247
151.225
201.204
251.184
301.164

## References

1. ^ Archimedes, A Gold Thief and Buoyancy - by Larry "Harris" Taylor, Ph.D.
2. ^ Vitruvius on Architecture, Book IX, paragraphs 9-12, translated into English and in the original Latin.
3. ^ The first Eureka moment, Science 305: 1219, August 2004. Fact or Fiction?: Archimedes Coined the Term "Eureka!" in the Bath, Scientific American, December 2006.
4. ^ Density of water, as reported by Daniel Harris in Quantitative Chemical Analysis, 4th ed., p. 36, W. H. Freeman and Company, New York, 1995.

## Books

• 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

Physics is the science of matter[1] and its motion[2][3], as well as space and time[4][5] —the science that deals with concepts such as force, energy, mass, and charge.
Mass is a fundamental concept in physics, roughly corresponding to the intuitive idea of "how much matter there is in an object". Mass is a central concept of classical mechanics and related subjects, and there are several definitions of mass within the framework of relativistic
The volume of a solid object is the three-dimensional concept of how much space it occupies, often quantified numerically. One-dimensional figures (such as lines) and two-dimensional shapes (such as squares) are assigned zero volume in the three-dimensional space.
International System of Units (abbreviated SI from the French Le Système international d'unités) is the modern form of the metric system.
kilogram or kilogramme (symbol: kg) is the SI base unit of mass. The kilogram is defined as being equal to the mass of the International Prototype Kilogram (IPK), which is almost exactly equal to the mass of one liter of water.
cubic metre (symbol ) is the SI derived unit of volume. It is the volume of a cube with edges one metre in length. In the United States it is spelled cubic meter. An alternate name, which allowed a different usage with SI prefixes, was the stère.
Archimedes of Syracuse (Greek: Άρχιμήδης c. 287 BC – c. 212 BC) was an ancient Greek mathematician, physicist and engineer.
Hiero I was the brother of Gelo and tyrant of Syracuse from 478 to 467 BC. In succeeding Gelo, he conspired against a third brother Polyzelos. During his reign, he greatly increased the power of Syracuse.
A goldsmith is a metalworker who specializes in working with precious metals, usually, to make jewelry, valuable flatware, platters, goblets, decorative and serviceable utensils, as well as ceremonial or religious items.
GOLD refers to one of the following:
• GOLD (IEEE) is an IEEE program designed to garner more student members at the university level (Graduates of the Last Decade).
• GOLD (parser) is an open source BNF parser.

An alloy is a homogeneous hybrid of two or more elements, at least one of which is a metal, and where the resulting material has metallic properties. The resulting metallic substance usually has different properties (sometimes substantially different) from those of its components.
In fluid mechanics, displacement occurs when an object is immersed in a fluid, pushing it out of the way and taking its place, so that it can be weighed.

An object that sinks also displaces an amount of fluid equal to the object's volume.
Eureka (Greek "I have found it") is an exclamation used as an interjection to celebrate a discovery. It is most famously attributed to Archimedes; he reportedly uttered the word when, while bathing, he suddenly understood that the volume of an irregular object could be calculated
Marcus Vitruvius Pollio (born ca. 80/70 BC?; died ca. 25 BC) was a Roman writer, architect and engineer (possibly praefectus fabrum or architectus armamentarius of the apparitor status group), active in the 1st century BC.
De architectura (Latin: "On architecture") is a treatise on architecture written by the Roman architect Vitruvius and dedicated to his patron, the emperor Caesar Augustus.
Generally, homogeneity means being the same throughout. For various specialized meanings, see:
• Homogeneous (mathematics), a variety of meanings
• In statistics homogeneity can refer to

A hydrometer is an instrument used for determining the specific gravity of liquids. It is usually made of glass and consists of a cylindrical stem and a bulb weighted with mercury or shot to make it float upright.
pycnometer (from the Greek puknos, meaning "density", also called pyknometer or specific gravity bottle), is a flask with a close-fitting ground glass stopper with a fine hole through it, so that a given volume can be accurately obtained.
Liquid is one of the four principal states of matter. A liquid is a fluid that can freely form a distinct surface at the boundaries of its bulk material.

## Characteristics

A liquid's shape is determined by, not confined to, the container it fills.
Gas is one of the four major states of matter, consisting of freely moving atoms or molecules without a definite shape. Compared to the solid and liquid states of matter a gas has lower density and a lower viscosity.
oscillating U-tube principle, the density of liquids and gases is determined based on an electronic measurement of the frequency of oscillation, from which the density value is calculated. This measuring principle is based on the Mass-Spring Model.
Bulk density a property of particulate materials. It is the mass of many particles of the material divided by the volume they occupy. The volume includes the space between particles as well as the space inside the pores of individual particles.
U.S. customary units, also known in the United States as English units[1] (but see English unit) or standard units, are units of measurement that are currently used in the USA, in some cases alongside units from SI (the International System of Units
Imperial units or the Imperial system is a collection of units, first defined in the British Weights and Measures Act of 1824, later refined (until 1959) and reduced.
ounce (abbreviation: oz) is the name of a unit of mass in a number of different systems, including various systems of mass that form part of English units, Imperial units, and United States customary units. Its size can vary from system to system.
A cubic inch (plural: cubic inches) is a non-SI unit 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 engineering contexts, not household contexts) in the United States and United