Density (volumetric mass density orspecific mass) is the ratio of a substance'smass to itsvolume. The symbol most often used for density isρ (the lower caseGreek letterrho), although the Latin letterD (ord) can also be used:[1]whereρ is the density,m is the mass, andV is the volume. In some cases (for instance, in the United States oil and gas industry), density is loosely defined as itsweight per unitvolume,[2] although this is scientifically inaccurate – this quantity is more specifically calledspecific weight.
To simplify comparisons of density across different systems of units, it is sometimes replaced by thedimensionless 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 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 while maintaining a constant pressure decreases its density by increasing its volume (with a few exceptions). In most fluids, heating the bottom of the fluid results inconvection 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 itsspecific volume, a term sometimes used inthermodynamics. Density is anintensive property in that increasing the amount of a substance does not increase its density; rather it increases its mass.
The understanding that different materials have different densities, and of a relationship between density, floating, and sinking must date to prehistoric times. Much later it was put in writing.Aristotle, for example, wrote:[5]
There is so great a difference in density between salt and fresh water that vessels laden with cargoes of the same weight almost sink in rivers, but ride quite easily at sea and are quite seaworthy. And an ignorance of this has sometimes cost people dear who load their ships in rivers. The following is a proof that the density of a fluid is greater when a substance is mixed with it. If you make water very salt by mixing salt in with it, eggs will float on it. ... If there were any truth in the stories they tell about the lake in Palestine it would further bear out what I say. For they say if you bind a man or beast and throw him into it he floats and does not sink beneath the surface.
In a well-known but probablyapocryphal tale,Archimedes was given the task of determining whetherKing Hiero'sgoldsmith was embezzlinggold during the manufacture of a goldenwreath dedicated to the gods and replacing it with another, cheaperalloy.[6] 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 thedisplacement of the water. Upon this discovery, he leapt from his bath and ran naked through the streets shouting, "Eureka! Eureka!" (Ancient Greek:Εύρηκα!,lit. 'I have found it'). As a result, the termeureka entered common parlance and is used today to indicate a moment of enlightenment.
The story first appeared in written form inVitruvius'books of architecture, two centuries after it supposedly took place.[7] 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.[8][9]
Nevertheless, in 1586,Galileo Galilei, in one of his first experiments, made a possible reconstruction of how the experiment could have been performed with ancient Greek resources.[10]
Units
From the equation for density (ρ =m/V), mass density has any unit that ismass divided by volume. As there are many units ofmass andvolume covering many different magnitudes there are a large number of units for mass density in use. TheSI unit ofkilogram per cubic metre (kg/m3) and thecgs unit ofgram per cubic centimetre (g/cm3) are probably the most commonly used units for density. In industry, other larger or smaller units of mass and or volume are often more practical andUS customary units may be used. See below for a list of some of the most common units of density.
Densities using the following metric units all have exactly the same numerical value, one-thousandth of the value in kg/m3. Liquidwater has a density of about 1 g/cm3 or 1000 kg/m3, making any of these SI units numerically convenient to use as mostsolids andliquids have densities between 0.1 and 20 g/cm3.
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 anImperial 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 ofprecious metals could conceivably be based onTroy ounces and pounds, a possible cause of confusion.
The density of a crystalline material and be calculated from its formula mass (indaltons) and the volume of itsunit cell, the density can be calculated. One dalton per cubicångström is equal to a density of1.66053906892(52) g/cm3, based on the 2022CODATA recommended value of the dalton.[11]
Measurement
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).[12] 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.
Homogeneous materials
The density at all points of ahomogeneous object equals its totalmass divided by its total volume. The mass is normally measured with ascale 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, ahydrometer, adasymeter or aCoriolis 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:, where is an elementary volume at position. The mass of the body then can be expressed as
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.
Thebulk volume of a material—inclusive of thevoid space 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 determinesbulk density. This is not the same thing as the material volumetric mass density. To determine the material volumetric mass density, one must first discount the volume of the void fraction. Sometimes this can be determined by geometrical reasoning. For theclose-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 avariable 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.
In general, density can be changed by changing either thepressure or thetemperature. 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 ofwater increases between its melting point at 0 °C and 4 °C; similar behavior is observed insilicon at low temperatures.
The effect of pressure and temperature on the densities of liquids and solids is small. Thecompressibility for a typical liquid or solid is 10−6bar−1 (1 bar = 0.1 MPa) and a typicalthermal expansivity is 10−5K−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 degreesCelsius.
In contrast, the density of gases is strongly affected by pressure. The density of anideal gas iswhereM is themolar mass,P is the pressure,R is theuniversal gas constant, andT is theabsolute 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 iswhere is the density at a reference temperature, is the thermal expansion coefficient of the material at temperatures close to.
Mass (massic) concentration of each given component in a solution sums to density of the solution,
Expressed as a function of the densities of pure components of the mixture and theirvolume participation, it allows the determination ofexcess molar volumes: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:
List of densities
Various materials
This section is about the listing of only certain chemical elements. For the densities of all chemical elements, seeList of chemical elements.
Densities of various materials covering a range of values
Molar volumes of liquid and solid phase of elements
Molar volumes of liquid and solid phase of elements
Generalization: volumic quantities
The qualifiervolumic is recommended in theInternational System of Quantities (ISO 80000-1) to denote the quotient of anyphysical quantity by volume.[3] The expressions "per unit volume" or "volume ... density" (or simply "density") are also often used, with resulting units involvingreciprocal cubic metre (m−3), for example:
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