# Density

## Definition

• 1. The quality or condition of being dense; thickness; closeness of texture or consistence.
b. Electr. The quantity of electricity per unit of volume or area.
• 3. a. Crowded state; degree of aggregation.
b. concr. A dense mass or aggregation. rare.
• 4. Photogr. Opaqueness of the developed actinized film in a negative.
• 5. fig. Stupidity, crassitude.

## Description

The density of a material is defined as its mass per unit volume. The symbol of density is ρ (the Greek letter rho).

## Formula

Mathematically:

where:

ρ (rho) is the density,
m is the mass,
V is the volume.

Different materials usually have different densities, so density is an important concept regarding buoyancy, metal purity and packaging.

In some cases density is expressed as the dimensionless quantities specific gravity (SG) or relative density (RD), in which case it is expressed in multiples of the density of some other standard material, usually water or air/gas.

### History

In a well-known story, 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.[1] Archimedes knew that the irregularly shaped wreath could be crushed into a cube whose volume could be calculated easily and compared with the weight; but the king did not approve of this. Baffled, Archimedes took a relaxing immersion bath and observed from the rise of the warm water upon entering that he could calculate the volume of the gold crown through the displacement of the water.

Allegedly, upon this discovery, he went running naked through the streets shouting, "Eureka! Eureka!" (Greek "I 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.[2] 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. [3][4]

### Measurement of density

For a homogeneous object, the mass divided by the volume gives the density. The mass is normally measured with an appropriate scale or balance; the volume may be measured directly (from the geometry of the object) or by the displacement of a fluid. Hydrostatic weighing is a method that combines these two. If the body is not homogeneous or heterogeneous, the density is a function of the coordinates , where dv is elementary volume with coordinates . The mass of the body then can be expressed as , where the integration is over the volume of the body V.

A very common instrument for the direct measurement of the density of a liquid is the hydrometer, which measures the volume displaced by an object of known mass. A common laboratory device for measuring fluid density is a pycnometer; a related 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 its volume is defined, and this may cause confusion in measurement. A common example is sand: if gently filled into a container, the density will be low; when the same sand is compacted into the same container, it will occupy less volume and consequently exhibit a greater density. This is because sand, like all powders and granular solids 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.[1]

### References

1. Archimedes, A Gold Thief and Buoyancy - by Larry "Harris" Taylor, Ph.D.
2. Vitruvius on Architecture, Book IX, paragraphs 9-12, translated into English and in the original Latin.
3. The first Eureka moment, Science 305: 1219, August 2004.
4. Fact or Fiction?: Archimedes Coined the Term "Eureka!" in the Bath, Scientific American, December 2006.
5. (2004). Test Methods for Density and Specific Gravity (Relative Density) of Plastics by Displacement. ASTM Standard D792-00. Vol 81.01. American Society for Testing and Materials. West Conshohocken. PA.
6. Extreme Stars: White Dwarfs & Neutron Stars, Jennifer Johnson, lecture notes, Astronomy 162, Ohio State University. Accessed on line May 3, 2007.
7. Nuclear Size and Density, HyperPhysics, Georgia State University. Accessed on line June 26, 2009.