Density
From The Book of THoTH (Leaves of Wisdom)
Density (symbol: ρ - Greek: rho) is a measure of mass per unit of volume. 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). The SI unit of density is the kilogram per cubic metre (kg·m-3)
- rho = frac{m}{V}
where
- 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, the 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:
- {density} = frac{M N} {L a b c}
where
- M is molar mass
- N is the number of atoms in a unit cell
- L is Loschmidt or Avogadro's number
- a, b, c are the lattice parameters
The density with respect to temperature, T, has the following relation:
- frac{density(T1)} {density(T2)} = frac{1 + C * T1} {1 + C * T2}
where
- C is the coefficient of cubic expansion.
Experimentally density can be found by measuring the dry weight ( Wd ), the wet weight ( Ww) and submersed weight ( Ws), usually in water.
- density = frac{Wd * density of water} {Ww - Ws}
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.
See also
- ISO 31: volumic mass
- Dord
- Standard temperature and pressure
- Number density
- Relative density (specific gravity)
- Charge density
- Energy density
- Population density
--Angel 17:07, 26 May 2006 (CDT)
