# Density

##### Article

July 6, 2022

The density of a substance is the ratio of the mass to the volume of that substance. The SI unit of measurement is the kilogram per cubic meter, which indicates how much mass is present within 1 m³ of a substance. ρ m V. {\ displaystyle \ rho {\ dfrac {m} {V}}} In continuum mechanics, density, more correctly called volumetric mass or specific mass, is often indicated with symbols ρ {\ displaystyle \ rho} , d {\ displaystyle d} or also δ {\ displaystyle \ delta} , is defined in the phase space as the integral in the space of the conjugate linear moment of the phase density: ρ ( r , t ) ∫ n ( r , p , t ) d p {\ displaystyle \ rho (\ mathbf {r}, t) \ int n (\ mathbf {r}, \ mathbf {p}, t) \, \ mathrm {d} p} , The mass of a continuum is generally defined as the integral of the density in the reference region of the configuration space; this region in classical mechanics corresponds to the volume. The concept of density is essential in balance equations. m ∫ V. ρ d r {\ displaystyle m \ int _ {V} \ rho \, \ mathrm {d} r} In the International System, density is measured in kg / m³; in the CGS system in g / cm³. In common use, the kg / L or equivalent in g / mL is sometimes used, which correspond exactly to g / cm³. In the case of solid bodies, the density can be determined experimentally by measuring the mass of the solid body under examination with the aid of a simple balance and by measuring the volume of the body itself. If the solid body has an irregular shape, i.e. it is not easy to measure its volume through the ordinary geometric formulas for calculating the volume, it is possible to use (in the case in which it is assumed that the solid body is not permeable and that it has a density greater than the fluid in which it is immersed) the so-called "immersion method", which consists in determining the volume of the body by immersing the solid, for example, in a graduated cylinder and obtaining the volume of the body as the difference between the volume of the liquid without the immersed body and the volume of liquid when the body was immersed. Both the measurements of the mass and the measurements of the volume of the body will be repeated in order to limit the accidental errors connected to the measurement operations. In fluids, bodies with a lower density float on those with a higher density, if subjected to a gravitational field. This property is the basis of Archimedes' principle. For example, if we immerse a body in water and this has a higher density than it will sink, while on the contrary if it has a lower density it will float. We must be careful not to confuse the concept of density, which is the measure of a mass divided by a volume, with that of relative density, which is instead a dimensionless quantity.

## Relative density

In general, relative density means the ratio between the mass of the body under examination and that of a body taken as a reference, for a given temperature and pressure. The relative density is often defined as the ratio between the density of the body under examination and that of the '' pure water at a temperature of 4 ° C and pressure of 1 bar or in an equivalent manner as the ratio between the mass of the body under examination and that of an equal volume of pure water (distilled or deio