The higher an object's density, the higher its mass per volume. The average density of an object equals its total mass divided by its total volume. A denser object (such as iron) will have less volume than an equal mass of some less dense substance (such as water).
- ρ is the object's density (measured in kilograms per cubic metre)
- m is the object's total mass (measured in kilograms)
- V is the object's total volume (measured in cubic metres)
Under specified conditions of temperature and pressure, density of a fluid is defined as described above.
However, the density of a solid material can be different, depending on exactly how it is defined. Take sand for example. If you gently fill a container with sand, and divide the mass of sand by the container volume you get a value termed loose bulk density. If you took this same container and tapped on it repeatedly, allowing the sand to settle and pack together, and then calculate the results, you get a value termed tapped or packed bulk density. Tapped bulk density is always greater than or equal to loose bulk density. In both types of bulk density, some of the volume is taken up by the spaces between the grains of sand.
Also, in terms of candy making, density is affected by the melting and cooling processes. Loose granular sugar, like sand, contains a lot of air and is not tightly packed, but when it has melted and starts to boil, the sugar loses its granularity and entrained air and becomes a fluid. When you mold it to make a smaller, compacted shape, the syrup tightens up and loses more air. As it cools, it contracts and gains moisture, making the already heavy candy even more dense.
A more theoretical definition is also available. Density can be calculated based on crystallographic information and molar mass:
- M is molar mass
- N is the number of atoms in a unit cell
- a, b, c are the lattice parameters
The density with respect to temperature, T, has the following relation:
- C is the coefficient of cubic expansion.
Experimentally density can be found by measuring the dry weight ( ), the wet weight ( ) and submersed weight ( ), usually in water.
Density in terms of the SI base units is expressed in terms of kilograms per cubic metre (kg·m−3). Other units fully within the SI include grams per cubic centimetre (g·cm−3) and megagrams per cubic metre (Mg·m−3). Since both the litre and the tonne or metric ton are also acceptable for use with the SI, a wide variety of units such as kilograms per litre (kg·L−1) are also used. Imperial units or U.S. customary units, the units of density include pounds per cubic foot (lb/ft³), pounds per cubic yard (lb/yd³), pounds per cubic inch (lb/in³), ounces per cubic inch (oz/in³), pounds per gallon (for U.S. or imperial gallons) (lb/gal), pounds per U.S. bushel (lb/bu), in some engineering calculations slugs per cubic foot, and other less common units.
The maximum density of pure water at a pressure of one standard atmosphere is 999.972 kg·m−3; this occurs at a temperature of about 3.98 °C (277.13 K).
Measurement of density
A table of densities of various substances:
|Substance||Density in kg·m-3|
|any gas||0.0446 times the average molecular mass, hence between 0.09 and ca. 13.1 (at room temperature and pressure)|
|For example air||1.2|
|Density of air ρ vs. temperature °C|
|T in °C||ρ in kg·m-3|
Note the low density of aluminium compared to most other metals. For this reason, aircraft are made of aluminium. Also note that air has a nonzero, albeit small, density. Aerogel is the world's lightest solid.
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