- comparative of dense
In physics the density (ρ) of a body is the ratio of its mass (m) to its volume (V), a measure of how tightly the matter within it is packed together. Its SI units are kilograms per cubic metre (kg/m³). It is also sometimes given in the cgs units of grams per cubic centimetre (g/cm³).
Density is defined by:
- \rho = \frac
Various substances have different densities, and it is this quantity that determines how they interact when mixed together. For example, in SI units the density of lead is 11.35 x 103, that of water is 1 x 103, and that of cork is 0.24 x 103. The lead has a greater density than water so it sinks; the cork has a smaller density so it floats. In some cases the density is expressed as a specific gravity or relative density, in which case it is expressed in multiples of the density of some other standard material, usually water or air.
HistoryIn a well known 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.
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 "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. 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.
Measurement of densityFor 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 instrument used to determine the density of a liquid or a gas is the 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 unitsSI units for density are:
Units outside the SI
In U.S. customary units or Imperial units, the units of density include:
Changes of densityIn 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
- \rho = \frac
where R is the universal gas constant, P is the pressure, M the molar mass, and T 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
See Water Density
Density of air
Density of solutionsThe density of a solution is the sum of the mass (massic) concentrations of the components of that solution. Mass (massic) concentration of a given component ρi in a solution can be called partial density of that component.
Densities of various materials
- 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
denser in Afrikaans: Digtheid
denser in Tosk Albanian: Dichte
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denser in Belarusian: Шчыльнасць
denser in Bulgarian: Плътност
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denser in German: Dichte
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denser in Persian: چگالی
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denser in Latin: Densitas et Spissitudo
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denser in Malay (macrolanguage): Ketumpatan
denser in Dutch: Dichtheid (natuurkunde)
denser in Japanese: 密度
denser in Norwegian: Tetthet
denser in Norwegian Nynorsk: Tettleik
denser in Low German: Dicht
denser in Polish: Gęstość
denser in Portuguese: Massa volúmica
denser in Romanian: Densitate
denser in Russian: Плотность
denser in Albanian: Dendësia
denser in Slovenian: Gostota
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denser in Vietnamese: Mật độ
denser in Turkish: Yoğunluk
denser in Ukrainian: Густина
denser in Chinese: 密度