Density

Density is the amount of mass per unit volume of a substance or the inverse of specific volume. Density is, therefore, a scalar quantity. The symbol used to represent density in equations is ρ with SI units of kilograms per cubic meter. This term is the reciprocal of the specific volume.

$\rho=\dfrac{m}{V}\;\left[\dfrac{\textrm{kg}}{\textrm{m}^3}\right]$

For gases, the density can vary over a wide range because the particles are free to move closer together when constrained by pressure or volume. This variation of density is referred to as compressibility. Like pressure and temperature, density is a state variable of gas, and the change in density during any process is governed by the laws of thermodynamics. For a static gas, the density is the same throughout the entire container.

Like pressure and temperature, density is a variable state of gas, and the change in density during any process is governed by the laws of thermodynamics. For a static gas, the density is the same throughout the entire container. It can be shown by the kinetic theory that the density is inversely proportional to the size of the container in which a fixed mass of gas is confined. In this case of a fixed mass, the density decreases as the volume increases.

The density of a substance is dependent on temperature and pressure; in gases, the density is directly proportional to the pressure and inversely proportional to the temperature, while in solids and liquids, being incompressible substances, the variation of their density when the pressure varies is negligible. The density of a liquid is usually close to that of a solid, and much higher than in a gas.

The term “density” can also be applied to other quantities that have a spatial distribution. For example, the ratio of the number of electrons in a given volume to the volume itself is called electron density. More generally, considering any set of objects, we talk about number density. The ratio of the total charge distributed in a volume to the volume itself is commonly referred to as charge density; light energy per unit volume is referred to as light energy density. Thus in general the volume mass of a quantity is expressed by the ratio between the quantity of the quantity contained in an assigned volume and the value of the latter. In an even broader sense the concept has been extended to other areas such as geography: “population density” measures the population of a territory per unit area.

Real density and apparent density

The definition of density given above refers to a massive amount of solid matter, i.e., without internal voids. It is also called real density since it takes into account only the volume of the solid fraction.

The apparent density of a body is calculated in a manner formally analogous to the absolute density, but takes into account the total volume occupied by the solid, i.e. its external dimensions, including empty spaces (solids with closed cavities, with open cavities or with spongy structure). The definition of bulk density is also valid for granular matter contained in vessels such as sand and grains or soil.

Density of a mixture

To calculate the density of a mixture consisting of several substances (components), the following relation can be used:

$\rho=\dfrac{1}{V}\sum_i m_i=\sum_i\rho_i$

where: $$m_i$$ is the mass of component $$i$$ in the mixture; $$V$$ is the volume of the mixture; $$\rho_i$$ is the mass concentration of component “$$i$$” in the mixture.

Density in electromagnetism

Density refers to both stationary and moving electrical charges. For electric charges distributed on elements of lines, surfaces, or volumes, the quantities are defined: electric charge density, or volumic electric charge, measured in the International System (SI) in coulombs per cubic meter (C/m3); electric charge surface density, or areic electric charge, measured in coulombs per square meter (C/m2); linear charge density, or lineal electric charge, measured in coulombs per meter (C/m). For moving electric charges, the quantities surface density and linear current density are defined.

The surface density of electric current, or areic electric current, is the ratio of the intensity of current flowing perpendicularly through the cross-section of a conductor to the area of that cross-section; it is measured in the International System (SI) in amperes per meter (A/m). The surface density of the current is constant over the entire crossed surface, if the current is continuous; it grows from the center to the periphery, if the current is alternating. Introducing this quantity, Ohm’s law is written in vector form E=ρJ, where E is the electric field strength, ρ the resistivity of the conductor, and J the vector of electric current density; J is related to the number N of charge carriers q per unit volume and their average velocity v by the relation J=Nqv.

The linear density of electric current, or lineal electric current, is a vector analogous to the areic electric current, but definable in the case that we must consider currents that cross surfaces of infinite area, which is necessary when the current density is not constant throughout the section of the conductor. It is measured in amperes per meter (A/m).

Density in astronomy

The term density appears in astronomy in many different contexts.

• In its most generic use the density is the mass per unit volume of an object or region and might have units like kg/m3 or Mo/pc3.
• The Number density is the number of a particular object or species per unit volume and might be used when describing the number of electrons per cubic centimetre in a plasma or the number of stars in the core of a globular cluster.
• Density profile is the density as a function of some variable like distance from the centre of a star.
• The mean or average density is the total mass of a region divided by the total volume of that region.

Since the behaviour of matter is often a function of density it is a very important quantity to determine when trying to explain the underlying physics of an object.

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