The density of a material is defined as its mass In physics, mass commonly refers to any of three properties of matter, which have been shown experimentally to be equivalent: Inertial mass, active gravitational mass and passive gravitational mass. In everyday usage, mass is often taken to mean weight, but in scientific use, they refer to different properties per unit volume Volume is how much three-dimensional space a substance or shape occupies or contains, often quantified numerically using the SI derived unit, the cubic metre. The volume of a container is generally understood to be the capacity of the container, i. e. the amount of fluid (gas or liquid) that the container could hold, rather than the amount of. The symbol of density is ρ (the Greek letter rho Rho , pronounced /ˈroʊ/ in English, is the 17th letter of the Greek alphabet. In the system of Greek numerals it has a value of 100. It is derived from Semitic Rêš "head" (see Resh). Its uppercase form is not to be confused with the Roman letter P, however both are typeset using the same glyph). In some countries (for instance, in the United States), density is also defined as its weight In one of the more common definitions, the weight of an object, often denoted by W, is defined as being equal to the force exerted on it by gravity. This force is the product of the mass m of the object and the local gravitational acceleration g. Expressed in a formula: W = mg. In the International System of Units, the unit of measurement for per unit volume Volume is how much three-dimensional space a substance or shape occupies or contains, often quantified numerically using the SI derived unit, the cubic metre. The volume of a container is generally understood to be the capacity of the container, i. e. the amount of fluid (gas or liquid) that the container could hold, rather than the amount of ^[1]. The density of a substance is the reciprocal of its specific volume Specific volume is the volume occupied by a unit of mass of a material. The specific volume of a substance is equal to the reciprocal of its mass density. Specific volume may be expressed in , or, a representation commonly used in thermodynamics In science, thermodynamics is the study of energy conversion between heat and mechanical work, and subsequently the macroscopic variables such as temperature, volume and pressure.

Formula

Mathematically: Density = Mass Divided By Volume

where:

ρ (rho) is the density,

m is the mass,

V is the volume.

Different materials usually have different densities, so density is an important concept regarding buoyancy In physics, buoyancy is an upward acting force, caused by fluid pressure, that opposes an object's weight. If the object is either less dense than the liquid or is shaped appropriately (as in a boat), the force can keep the object afloat. This can occur only in a reference frame which either has a gravitational field or is accelerating due to a, metal purity and packaging Packaging is the science, art and technology of enclosing or protecting products for distribution, storage, sale, and use. Packaging also refers to the process of design, evaluation, and production of packages. Packaging can be described as a coordinated system of preparing goods for transport, warehousing, logistics, sale, and end use. Packaging.

In some cases density is expressed as the dimensionless In dimensional analysis, a dimensionless quantity is a quantity without a physical unit and is thus a pure number. Such a number is typically defined as a product or ratio of quantities that might have units individually, but these cancel out in the combination quantities specific gravity Relative density, or specific gravity, is the ratio of the density of a substance to the density of a given reference material. Specific gravity usually means relative density with respect to water. The term "relative density" is often preferred in modern scientific usage (SG) or relative density Relative density, or specific gravity, is the ratio of the density of a substance to the density of a given reference material. Specific gravity usually means relative density with respect to water. The term "relative density" is often preferred in modern scientific usage (RD), in which case it is expressed in multiples of the density of some other standard material, usually water or air/gas.

History

In a well-known tale, Archimedes Archimedes of Syracuse was a Greek mathematician, 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. Among his advances in physics are the foundations of hydrostatics, statics and an explanation of the principle of the lever. He is was given the task of determining whether King Hiero's 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. In modern times actual goldsmiths are rare. Historically goldsmiths have also made flatware, platters, goblets, decorative was embezzling gold Gold is a chemical element with the symbol Au (from Latin: aurum, "shining dawn", hence adjective, aureate) and an atomic number of 79. It has been a highly sought-after precious metal for coinage, jewelry, and other arts since the beginning of recorded history. The metal occurs as nuggets or grains in rocks, in veins and in alluvial during the manufacture of a golden wreath A wreath is an assortment of flowers, leaves, fruits, twigs and/or various materials that is constructed to resemble a ring. They are used typically as Christmas decorations to symbolize the coming of Christ, also known as the Advent season in Christianity. They are also used as festive headdresses as attire in ceremonial events in many cultures dedicated to the gods and replacing it with another, cheaper alloy An alloy is a partial or complete solid solution of one or more elements 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. Alloys usually have different properties from those of the.^[2]

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 took a relaxing immersion bath and observed from the rise of the warm water upon entering that he could calculate the volume of the gold wreath through the displacement 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 through the streets shouting, "Eureka! Eureka!" (Εύρηκα! Greek "I found it"). As a result, the term "eureka Eureka is an exclamation used as an interjection to celebrate a discovery. It comes from the Ancient Greek Εὕρηκα/Ηὕρηκα - Heurēka/Hēurēka meaning approximately "I have found it"" entered common parlance and is used today to indicate a moment of enlightenment.

The story first appeared in written form in Vitruvius Marcus Vitruvius Pollio was a Roman writer, architect and engineer (possibly praefectus fabrum during military service or praefect architectus armamentarius of the apparitor status group), active in the 1st century BC. By his own description Vitruvius served as a Ballista (artilleryman), the third class of arms in the military offices. He likely' books of architecture De architectura is a treatise on architecture written by the Roman architect Vitruvius and dedicated to his patron, the emperor Caesar Augustus as a guide for building projects. The work is one of the most important sources of modern knowledge of Roman building methods as well as the planning and design of structures, both large (aqueducts,, two centuries after it supposedly took place.^[3] 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.^[4][5]

Measurement of density

For a homogeneous A substance that is uniform in composition is a definition of homogeneous in Chemistry. This is in contrast to a substance that is heterogeneous object, the mass divided by the volume gives the density. The mass is normally measured with an appropriate scale or balance A weighing scale is a measuring instrument for determining the weight or mass of an object. A spring scale measures weight by the distance a spring deflects under its load. A balance compares the unknown weight to a standard weight using a horizontal lever. Weighing scales are used in many industrial and commercial applications, and products from; the volume may be measured directly (from the geometry of the object) or by the displacement of a fluid. Hydrostatic weighing This method has the advantage of needing no volume information of the body . The procedure is based on Archimedes' principle, using the following three measurable values: The weight of the body outside the water, the weight of the immersed body and the density of the water. Then the formula below can be solved for the density of the body: is a method that combines these two.

If the body is not homogeneous, then the density is a function of the position: , where dv is an elementary volume at position . The mass of the body then can be expressed as

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 it is gently poured into a container, the density will be low; if 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. The density of the material including the air spaces is the 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. The total volume includes particle volume, inter-particle void volume and internal pore volume, which differs significantly from the density of an individual grain of sand with no air included.

Common units

The SI The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. It is the world's most widely used system of measurement, both in everyday commerce and in science unit for density is:

• kilograms The kilogram is the base unit of mass in the International System of Units (SI, from the French Le Système International d’Unités),[Note 2] which is the modern standard governing the metric system. The kilogram is defined as being equal to the mass of the International Prototype Kilogram (IPK),[Note 3] which is almost exactly equal to the mass per 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 metric prefixes, was the stère. Another alternative name, not widely used any more, is the kilolitre (kg/m³)

Densities using the following metric units all have exactly the same numerical value, one thousandth of the value in (kg/m³). Liquid water Water is a chemical substance with the chemical formula H2O. Its molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state, water vapor or steam has a density of about 1 kg/dm³, making any of these SI units numerically convenient to use as most solids Solid is one of the major states of matter. It is characterized by structural rigidity and resistance to changes of shape or volume. Unlike a liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire volume available to it like a gas does. The atoms in a solid are tightly bound to each other, and liquids Liquid is one of the three classical states of matter. Like a gas, a liquid is able to flow and take the shape of a container, but, like a solid, it resists compression. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly constant density. A distinctive property of the liquid state is surface tension, have densities between 0.1 and 20 kg/dm³.

• kilograms per cubic decimeter (kg/dm³)
• grams per cubic centimeter (g/cc, gm/cc or g/cm³)
• megagrams per cubic meter (Mg/m³)

Litres and metric tons are not part of the SI, but are acceptable for use with it. Since 1 L = 1 dm³, we also have these of the same size:

• kilograms The kilogram is the base unit of mass in the International System of Units (SI, from the French Le Système International d’Unités),[Note 2] which is the modern standard governing the metric system. The kilogram is defined as being equal to the mass of the International Prototype Kilogram (IPK),[Note 3] which is almost exactly equal to the mass per litre The litre is a unit of volume. There are two official symbols: the Latin letter L in lower and upper case (l and L). The lower case L is also often written as a cursive ℓ, though this symbol has no official approval by any international bureau. Although the litre is not an SI unit, it is accepted for use with the SI, and has appeared in several (kg/L)
• grams The gram , (Greek/Latin root grámma); symbol g, is a unit of mass per millilitre The litre is a unit of volume. There are two official symbols: the Latin letter L in lower and upper case (l and L). The lower case L is also often written as a cursive ℓ, though this symbol has no official approval by any international bureau. Although the litre is not an SI unit, it is accepted for use with the SI, and has appeared in several (g/mL)
• metric tons The tonne or metric ton (U.S.), also referred to as a metric tonne, is a unit of mass equal to 1,000 kg (2,204.62262 lb) or approximately the mass of one cubic metre of water at four degrees Celsius. It is sometimes abbreviated as mt in the United States, but this conflicts with other SI symbols. The tonne is not a unit in the International System per cubic metre (t/m³)

In U.S. customary units The United States customary system is the most commonly used system of measurement in the United States. It is similar but not identical to the British Imperial units. The U.S. is the only industrialized nation that does not mainly use the metric system in its commercial and standards activities, although the International System of Units (SI, density can be stated in:

• Avoirdupois ounces per cubic inch A cubic inch is a non-SI unit of volume, equal to the volume of a cube with sides of one inch (oz/cu in)
• Avoirdupois pounds The pound or pound-mass is a unit of mass used in the imperial, United States customary and other systems of measurement. A number of different definitions have been used, the most common today being the international avoirdupois pound of exactly 0.45359237 kilograms per cubic inch (lb/cu in)
• pounds per cubic foot The cubic foot is an and US customary (non-metric) unit of volume, used in the United States and the United Kingdom. It is defined as the volume of a cube with sides of one foot (0.3048 m) in length (lb/cu ft)
• pounds per cubic yard A cubic yard is an Imperial / U.S. customary 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 (3 feet, 36 inches, 0.9144 metres) in length (lb/cu yd)
• pounds per U.S. liquid gallon The United States customary system is the most commonly used system of measurement in the United States. It is similar but not identical to the British Imperial units. The U.S. is the only industrialized nation that does not mainly use the metric system in its commercial and standards activities, although the International System of Units (SI, (lb/gal)
• pounds per U.S. bushel A bushel is an imperial and U.S. customary unit of dry volume, equivalent in each of these systems to 4 pecks or 8 gallons. It is used for volumes of dry commodities , most often in agriculture. It is abbreviated as bsh. or bu. The name derives from the 14th century buschel or busschel, a box (lb/bu)
• slugs The slug is a unit of mass associated with Imperial units. It is a mass that accelerates by 1 ft/s2 when a force of one pound-force is exerted on it. Therefore a slug has a mass of 32.17405 pound-mass or 14.5939 kg per cubic foot.

In principle there are Imperial units Imperial units or the imperial system is a system of units, first defined in the British Weights and Measures Act of 1824, later refined and reduced. The system came into official use across the British Empire. By the late 20th century most nations of the former empire had officially adopted the metric system as their main system of measurement different from the above as the Imperial gallon and bushel differ from the U.S. units, but in practice they are no longer used, though found in older documents. The density of precious metals A precious metal is a rare, naturally occurring metallic chemical element of high economic value, which is not radioactive . Chemically, the precious metals are less reactive than most elements, have high lustre, are softer or more ductile, and have higher melting points than other metals. Historically, precious metals were important as currency, could conceivably be based on Troy Troy weight is a system of units of mass customarily used for precious metals, black powder, and gemstones ounces and pounds, a possible cause of confusion.

Changes of density

In general, density can be changed by changing either the pressure Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure or the temperature Historically, two equivalent concepts of temperature have developed, the thermodynamic description and a microscopic explanation based on statistical physics. Since thermodynamics deals entirely with macroscopic measurements, the thermodynamic definition of temperature, first stated by Lord Kelvin, is stated entirely in empirical, measurable. 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 generalization. For example, the density of water Water is a chemical substance with the chemical formula H2O. Its molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state, water vapor or steam increases between its melting point at 0 °C and 4 °C; similar behaviour 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.

In contrast, the density of gases is strongly affected by pressure. The density of an ideal gas is

where R is the universal gas constant, P is the pressure, M is the molar mass, 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.

Osmium is the densest known substance at standard conditions for temperature and pressure.

Density of water (at 1 atm)

See also: Water density

Density of air (at 1 atm)

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 a given component ρ_i in a solution can be called partial density of that component.

Density of composite material

ASTM specification D792-00^[6] describes the steps to measure the density of a composite material.

where:

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

and

W_a is the weight of the specimen when hung in the air

W_w is the weight of the partly immersed wire holding the specimen

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

0.9975 is the density in g/cm³ of the distilled water at 23 °C.

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