# Density

Last updated

Density
A test tube holding four non-miscible colored liquids with different densities
Common symbols
ρ , D
SI unit kg/m3
Extensive?No
Intensive?Yes
Conserved?No
Derivations from
other quantities
${\displaystyle \rho ={\frac {m}{V}}}$
Dimension ${\displaystyle {\mathsf {L}}^{-3}{\mathsf {M}}}$

Density (volumetric mass density or specific mass) is a substance's mass 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: [1]

## Contents

${\displaystyle \rho ={\frac {m}{V}},}$

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, [2] although this is scientifically inaccurate  this quantity is more specifically called specific weight.

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, purity and packaging. Osmium is the densest known element at standard conditions for temperature and pressure.

To simplify comparisons of density across different systems of units, it is sometimes replaced by the dimensionless 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 (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, a term sometimes used in thermodynamics. 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, relative density (specific gravity), and specific weight.

## History

### Density, floating, and sinking

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: [3]

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.

Aristotle, Meteorologica, Book II, Chapter III

### Volume vs. density; volume of an irregular shape

In a well-known but probably apocryphal tale, Archimedes was given the task of determining whether King Hiero's goldsmith was embezzling gold during the manufacture of a golden wreath dedicated to the gods and replacing it with another, cheaper alloy. [4] 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!" (Ancient Greek : Εύρηκα!, lit. '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. [5] 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. [6] [7]

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 [8]

## Units

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 (kg/m3) and the cgs unit of gram 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.

The litre and tonne are not part of the SI, but are acceptable for use with it, leading to the following units:

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:

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 of a crystalline material and its formula weight (in daltons), the density can be calculated. One dalton per cubic ångström is equal to a density of 1.660 539 066 60 g/cm3.

## 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). [9] 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 a homogeneous object equals its total mass 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 dasymeter 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: ${\displaystyle \rho ({\vec {r}})=dm/dV}$, where ${\displaystyle dV}$ is an elementary volume at position ${\displaystyle {\vec {r}}}$. The mass of the body then can be expressed as

${\displaystyle m=\int _{V}\rho ({\vec {r}})\,dV.}$

### 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 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 determines bulk 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 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. 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

${\displaystyle \rho ={\frac {MP}{RT}},}$

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

In the case of volumic thermal expansion at constant pressure and small intervals of temperature the temperature dependence of density is

${\displaystyle \rho ={\frac {\rho _{T_{0}}}{1+\alpha \cdot \Delta T}},}$

where ${\displaystyle \rho _{T_{0}}}$ is the density at a reference temperature, ${\displaystyle \alpha }$ is the thermal expansion coefficient of the material at temperatures close to ${\displaystyle T_{0}}$.

## 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 ${\displaystyle \rho _{i}}$ in a solution sums to density of the solution,

${\displaystyle \rho =\sum _{i}\rho _{i}.}$

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:

${\displaystyle \rho =\sum _{i}\rho _{i}{\frac {V_{i}}{V}}\,=\sum _{i}\rho _{i}\varphi _{i}=\sum _{i}\rho _{i}{\frac {V_{i}}{\sum _{i}V_{i}+\sum _{i}{V^{E}}_{i}}},}$

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:

${\displaystyle {\overline {V^{E}}}_{i}=RT{\frac {\partial \ln \gamma _{i}}{\partial P}}.}$

## List of densities

### Various materials

Densities of various materials covering a range of values
Materialρ (kg/m3) [note 1] Notes
Hydrogen 0.0898
Helium 0.179
Aerographite 0.2 [note 2] [10] [11]
Metallic microlattice 0.9 [note 2]
Aerogel 1.0 [note 2]
Air 1.2At sea level
Tungsten hexafluoride 12.4One of the heaviest known gases at standard conditions
Liquid hydrogen 70At approximately −255 °C
Styrofoam 75Approximate [12]
Cork 240Approximate [12]
Pine 373 [13]
Lithium 535Least dense metal
Wood 700Seasoned, typical [14] [15]
Oak 710 [13]
Potassium 860 [16]
Ice 916.7At temperature < 0 °C
Cooking oil 910–930
Sodium 970
Water (fresh)1,000At 4 °C, the temperature of its maximum density
Water (salt)1,0303%
Liquid oxygen 1,141At approximately −219 °C
Nylon 1,150
Plastics 1,175Approximate; for polypropylene and PETE/PVC
Glycerol 1,261 [17]
Tetrachloroethene 1,622
Sand 1,600Between 1,600 and 2000 [18]
Magnesium 1,740
Beryllium 1,850
Silicon 2,330
Concrete 2,400 [19] [20]
Glass 2,500 [21]
Quartzite 2,600 [18]
Granite 2,700 [18]
Gneiss 2,700 [18]
Aluminium 2,700
Limestone 2,750Compact [18]
Basalt 3,000 [18]
Diiodomethane 3,325Liquid at room temperature
Diamond 3,500
Titanium 4,540
Selenium 4,800
Antimony 6,690
Zinc 7,000
Chromium 7,200
Tin 7,310
Manganese 7,325Approximate
Mild steel 7,850
Iron 7,870
Niobium 8,570
Brass 8,600 [20]
Cobalt 8,900
Nickel 8,900
Copper 8,940
Bismuth 9,750
Molybdenum 10,220
Silver 10,500
Thorium 11,700
Rhodium 12,410
Mercury 13,546
Tantalum 16,600
Uranium 19,100
Tungsten 19,300
Gold 19,320
Plutonium 19,840
Rhenium 21,020
Platinum 21,450
Iridium 22,420
Osmium 22,570Densest natural element on Earth
1. Unless otherwise noted, all densities given are at standard conditions for temperature and pressure,
that is, 273.15  K (0.00 °C) and 100 kPa (0.987 atm).
2. Air contained in material excluded when calculating density

### Others

Entityρ (kg/m3)Notes
Interstellar medium 1.7×10−26Based on 10−5 hydrogen atoms per cubic centimetre [22]
Local Interstellar Cloud 5×10−22Based on 0.3 hydrogen atoms per cubic centimetre [22]
Interstellar medium 1.7×10−16Based on 105 hydrogen atoms per cubic centimetre [22]
The Earth 5,515Mean density. [23]
Earth's inner core 13,000Approx., as listed in Earth. [24]
The core of the Sun 33,000–160,000Approx. [25]
White dwarf star2.1×109Approx. [26]
Atomic nuclei 2.3×1017Does not depend strongly on size of nucleus [27]
Neutron star 1×1018

### Water

Density of liquid water at 1 atm pressure
Temp. (°C) [note 1] Density (kg/m3)
−30983.854
−20993.547
−10998.117
0999.8395
4999.9720
10999.7026
15999.1026
20998.2071
22997.7735
25997.0479
30995.6502
40992.2
60983.2
80971.8
100958.4
Notes:
1. Values below 0 °C refer to supercooled water.

### Air

Density of air at 1 atm pressure
T (°C)ρ (kg/m3)
−251.423
−201.395
−151.368
−101.342
−51.316
01.293
51.269
101.247
151.225
201.204
251.184
301.164
351.146

## Related Research Articles

In physics and chemistry, an equation of state is a thermodynamic equation relating state variables, which describe the state of matter under a given set of physical conditions, such as pressure, volume, temperature, or internal energy. Most modern equations of state are formulated in the Helmholtz free energy. Equations of state are useful in describing the properties of pure substances and mixtures in liquids, gases, and solid states as well as the state of matter in the interior of stars.

Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure is the pressure relative to the ambient pressure.

In thermodynamics, the specific heat capacity of a substance is the heat capacity of a sample of the substance divided by the mass of the sample, also sometimes referred to as massic heat capacity or as the specific heat. Informally, it is the amount of heat that must be added to one unit of mass of the substance in order to cause an increase of one unit in temperature. The SI unit of specific heat capacity is joule per kelvin per kilogram, J⋅kg−1⋅K−1. For example, the heat required to raise the temperature of 1 kg of water by 1 K is 4184 joules, so the specific heat capacity of water is 4184 J⋅kg−1⋅K−1.

Volume is a measure of regions in three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length (cubed) is interrelated with volume. The volume of a container is generally understood to be the capacity of the container; i.e., the amount of fluid that the container could hold, rather than the amount of space the container itself displaces. By metonymy, the term "volume" sometimes is used to refer to the corresponding region.

Relative density, also called specific gravity, is a dimensionless quantity defined as the ratio of the density 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 densest ; for gases, the reference is air at room temperature. The term "relative density" is often preferred in scientific usage, whereas the term "specific gravity" is deprecated.

The volumetric heat capacity of a material is the heat capacity of a sample of the substance divided by the volume of the sample. It is the amount of energy that must be added, in the form of heat, to one unit of volume of the material in order to cause an increase of one unit in its temperature. The SI unit of volumetric heat capacity is joule per kelvin per cubic meter, J⋅K−1⋅m−3.

In chemistry and related fields, the molar volume, symbol Vm, or of a substance is the ratio of the volume occupied by a substance to the amount of substance, usually given at a given temperature and pressure. It is equal to the molar mass (M) divided by the mass density (ρ):

The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elastic medium. At 20 °C (68 °F), the speed of sound in air is about 343 m/s, or one km in 2.91 s or one mile in 4.69 s. It depends strongly on temperature as well as the medium through which a sound wave is propagating. At 0 °C (32 °F), the speed of sound in air is about 331 m/s. More simply, the speed of sound is how fast vibrations travel.

In thermodynamics and fluid mechanics, the compressibility is a measure of the instantaneous relative volume change of a fluid or solid as a response to a pressure change. In its simple form, the compressibility may be expressed as

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 pressure at the bottom of a column of fluid is greater than at the top of the column. Similarly, the pressure at the bottom of an object submerged in a fluid is greater than at the top of the object. The pressure difference results in a net upward force on the object. The magnitude of the force is proportional to the pressure difference, and is equivalent to the weight of the fluid that would otherwise occupy the submerged volume of the object, i.e. the displaced fluid.

Foams are materials formed by trapping pockets of gas in a liquid or solid.

Archimedes' principle states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially, is equal to the weight of the fluid that the body displaces. Archimedes' principle is a law of physics fundamental to fluid mechanics. It was formulated by Archimedes of Syracuse.

The area density of a two-dimensional object is calculated as the mass per unit area. The SI derived unit is the kilogram per square metre (kg·m−2). A related area number density can be defined by replacing mass in by number of particles or other countable quantity.

In thermodynamics, the specific volume of a substance is a mass-specific intrinsic property of the substance, defined as the quotient of the substance's volume to its mass. It is the reciprocal of density ρ (rho) and it is also related to the molar volume and molar mass:

A fluidized bed is a physical phenomenon that occurs when a solid particulate substance is under the right conditions so that it behaves like a fluid. The usual way to achieve a fluidized bed is to pump pressurized fluid into the particles. The resulting medium then has many properties and characteristics of normal fluids, such as the ability to free-flow under gravity, or to be pumped using fluid technologies.

In atmospheric thermodynamics, the virtual temperature of a moist air parcel is the temperature at which a theoretical dry air parcel would have a total pressure and density equal to the moist parcel of air. The virtual temperature of unsaturated moist air is always greater than the absolute air temperature, however, as the existence of suspended cloud droplets reduces the virtual temperature.

A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a nearly constant volume independent of pressure. It is one of the four fundamental states of matter, and is the only state with a definite volume but no fixed shape.

Porosity or void fraction is a measure of the void spaces in a material, and is a fraction of the volume of voids over the total volume, between 0 and 1, or as a percentage between 0% and 100%. Strictly speaking, some tests measure the "accessible void", the total amount of void space accessible from the surface.

In thermodynamics, the volume of a system is an important extensive parameter for describing its thermodynamic state. The specific volume, an intensive property, is the system's volume per unit mass. Volume is a function of state and is interdependent with other thermodynamic properties such as pressure and temperature. For example, volume is related to the pressure and temperature of an ideal gas by the ideal gas law. The physical region covered by a system may or may not coincide with a control volume used to analyze the system.

In chemistry, the mass concentrationρi is defined as the mass of a constituent mi divided by the volume of the mixture V.

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