Density  

A graduated cylinder containing various coloured liquids with different densities  
Common symbols  ρ , D 
SI unit  kg/m^{3} 
Extensive?  No 
Intensive?  Yes 
Conserved?  No 
Derivations from other quantities  
Dimension 
The density (more precisely, the volumetric mass density; also known as specific mass), of a substance is its mass per unit 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] }
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 and iridium are the densest known elements 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 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. This causes it to rise relative to more dense 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.
In a wellknown 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.^{ [3] } 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!" (Εύρηκα! Greek "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.^{ [4] } 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.^{ [5] }^{ [6] }
From the equation for density (ρ = m/V), mass density has units of 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/m^{3}) and the cgs unit of gram per cubic centimetre (g/cm^{3}) are probably the most commonly used units for density. One g/cm^{3} is equal to 1000 kg/m^{3}. 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.
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).^{ [7] } 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.
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.
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.
The bulk volume of a material—inclusive of the void 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 volumetric mass density.
To determine volumetric mass density, one must first discount the volume of the void fraction. Sometimes this can be determined by geometrical reasoning. For the closepacking of equal spheres the nonvoid 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 noncompact 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 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
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 :
where is the density at a reference temperature, is the thermal expansion coefficient of the material at temperatures close to .
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 ρ_{i} in a solution sums to density of the solution.
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:
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.
Material  ρ (kg/m^{3})^{ [note 1] }  Notes 

Hydrogen  0.0898  
Helium  0.179  
Aerographite  0.2  ^{ [note 2] }^{ [8] }^{ [9] } 
Metallic microlattice  0.9  ^{ [note 2] } 
Aerogel  1.0  ^{ [note 2] } 
Air  1.2  At sea level 
Tungsten hexafluoride  12.4  One of the heaviest known gases at standard conditions 
Liquid hydrogen  70  At approx. −255 °C 
Styrofoam  75  Approx.^{ [10] } 
Cork  240  Approx.^{ [10] } 
Pine  373  ^{ [11] } 
Lithium  535  Least dense metal 
Wood  700  Seasoned, typical^{ [12] }^{ [13] } 
Oak  710  ^{ [11] } 
Potassium  860  ^{ [14] } 
Ice  916.7  At temperature < 0 °C 
Cooking oil  910–930  
Sodium  970  
Water (fresh)  1,000  At 4 °C, the temperature of its maximum density 
Water (salt)  1,030  3% 
Liquid oxygen  1,141  At approx. −219 °C 
Nylon  1,150  
Plastics  1,175  Approx.; for polypropylene and PETE/PVC 
Tetrachloroethene  1,622  
Magnesium  1,740  
Beryllium  1,850  
Glycerol  1,261  ^{ [15] } 
Concrete  2,400  ^{ [16] }^{ [17] } 
Silicon  2,330  
Aluminium  2,700  
Diiodomethane  3,325  Liquid at room temperature 
Diamond  3,500  
Titanium  4,540  
Selenium  4,800  
Vanadium  6,100  
Antimony  6,690  
Zinc  7,000  
Chromium  7,200  
Tin  7,310  
Manganese  7,325  Approx. 
Iron  7,870  
Niobium  8,570  
Brass  8,600  ^{ [17] } 
Cadmium  8,650  
Cobalt  8,900  
Nickel  8,900  
Copper  8,940  
Bismuth  9,750  
Molybdenum  10,220  
Silver  10,500  
Lead  11,340  
Thorium  11,700  
Rhodium  12,410  
Mercury  13,546  
Tantalum  16,600  
Uranium  18,800  
Tungsten  19,300  
Gold  19,320  
Plutonium  19,840  
Rhenium  21,020  
Platinum  21,450  
Iridium  22,420  
Osmium  22,570  Densest element 
Notes: 
Entity  ρ (kg/m^{3})  Notes 

Interstellar medium  1×10^{−19}  Assuming 90% H, 10% He; variable T 
The Earth  5,515  Mean density.^{ [18] } 
Earth's inner core  13,000  Approx., as listed in Earth.^{ [19] } 
The core of the Sun  33,000–160,000  Approx.^{ [20] } 
Supermassive black hole  9×10^{5}  Density of a 4.5millionsolarmass black hole Event horizon radius is 13.5 million km. 
White dwarf star  2.1×10^{9}  Approx.^{ [21] } 
Atomic nuclei  2.3×10^{17}  Does not depend strongly on size of nucleus^{ [22] } 
Neutron star  1×10^{18}  
Stellarmass black hole  1×10^{18}  Density of a 4solarmass black hole Event horizon radius is 12 km. 
Temp. (°C)^{ [note 1] }  Density (kg/m^{3}) 

−30  983.854 
−20  993.547 
−10  998.117 
0  999.8395 
4  999.9720 
10  999.7026 
15  999.1026 
20  998.2071 
22  997.7735 
25  997.0479 
30  995.6502 
40  992.2 
60  983.2 
80  971.8 
100  958.4 
Notes:

T (°C)  ρ (kg/m^{3}) 

−25  1.423 
−20  1.395 
−15  1.368 
−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  1.164 
35  1.146 
The SI unit for density is:
The litre and metric tons 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/m^{3}). Liquid water has a density of about 1 kg/dm^{3}, making any of these SI units numerically convenient to use as most solids and liquids have densities between 0.1 and 20 kg/dm^{3}.
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/cm^{3} ≈ 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.
In physics and thermodynamics, 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 (PVT), or internal energy. Equations of state are useful in describing the properties of fluids, mixtures of fluids, solids, and 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.
Volume is the quantity of threedimensional space enclosed by a closed surface, for example, the space that a substance or shape occupies or contains. Volume is 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 that the container could hold, rather than the amount of space the container itself displaces. Three dimensional mathematical shapes are also assigned volumes. Volumes of some simple shapes, such as regular, straightedged, and circular shapes can be easily calculated using arithmetic formulas. Volumes of complicated shapes can be calculated with integral calculus if a formula exists for the shape's boundary. Onedimensional figures and twodimensional shapes are assigned zero volume in the threedimensional space.
Relative density, or specific gravity, is 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, air at room temperature is the reference. The term "relative density" is often preferred in scientific usage. It is defined as a ratio of density of particular substance to that of water.
The volumetric heat capacity of a material is the heat capacity of a sample of the substance divided by the volume of the sample. Informally, 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/m^{3} or J/(K·m^{3}).
The molar volume, symbol V_{m}, is the volume occupied by one mole of a substance at a given temperature and pressure. It is equal to the molar mass (M) divided by the mass density (ρ). It has the SI unit cubic metres per mole (m^{3}/mol), although it is more practical to use the units cubic decimetres per mole (dm^{3}/mol) for gases and cubic centimetres per mole (cm^{3}/mol) for liquids and solids.
Surface tension is the tendency of liquid surfaces to shrink into the minimum surface area possible. Surface tension allows insects, usually denser than water, to float and slide on a water surface.
The speed of sound is the distance travelled per unit 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 metres per second, or a kilometre in 2.9 s or a mile in 4.7 s. It depends strongly on temperature as well as the medium through which a sound wave is propagating.
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.
Foam is an object 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 submerged, 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 density of air or atmospheric density, denoted ρ, is the mass per unit volume of Earth's atmosphere. Air density, like air pressure, decreases with increasing altitude. It also changes with variation in atmospheric pressure, temperature and humidity. At 1013.25 hPa (abs) and 15°C, air has a density of approximately 1.225 kg/m³, about 1/1000th that of water) according to ISA.
The area density of a twodimensional object is calculated as the mass per unit area. The SI derived unit is: kilogram per square metre (kg·m^{−2}). In the paper and fabric industries, it is called grammage and is expressed in grams per square meter (gsm); for paper in particular, it may be expressed as pounds per ream of standard sizes.
In thermodynamics, the specific volume of a substance is the ratio of the substance's volume to its mass. It is the reciprocal of density and an intrinsic property of matter as well. Specific volume is defined as the number of cubic meters occupied by one kilogram of a particular substance. The standard unit is the cubic meter per kilogram .
The number density is an intensive quantity used to describe the degree of concentration of countable objects in physical space: threedimensional volumetric number density, twodimensional areal number density, or onedimensional linear number density. Population density is an example of areal number density. The term number concentration is sometimes used in chemistry for the same quantity, particularly when comparing with other concentrations.
A fluidized bed is a physical phenomenon occurring when a quantity of a solid particulate substance is placed under appropriate conditions to cause a solid/fluid mixture to behave as a fluid. This is usually achieved by the introduction of pressurized fluid through the particulate medium. This results in the medium then having many properties and characteristics of normal fluids, such as the ability to freeflow under gravity, or to be pumped using fluid type technologies.
A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of the four fundamental states of matter, and is the only state with a definite volume but no fixed shape. A liquid is made up of tiny vibrating particles of matter, such as atoms, held together by intermolecular bonds. Like a gas, a liquid is able to flow and take the shape of a container. Most liquids resist compression, although others can be compressed. 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, leading to wetting phenomena. Water is, by far, the most common liquid on Earth.
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 of 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.
In chemistry, the mass concentrationρ_{i} is defined as the mass of a constituent m_{i} divided by the volume of the mixture V.