# Density

Density (symbol: ρ - Greek: rho) is a measure of mass per volume. The average density of an object equals its total mass divided by its total volume. An object made from a comparatively dense material (such as iron) will have less volume than an object of equal mass made from some less dense substance (such as water). The SI unit of density is the kilogram per cubic metre (kg/m3)

$\rho = \frac{m}{V}$

where

ρ is the object's density (measured in kilograms per cubic meter)
m is the object's total mass (measured in kilograms)
V is the object's total volume (measured in cubic meters)

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:

$\mbox{density} = \frac{M \cdot N} {L \cdot a \cdot b \cdot c}$

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:

$\frac{\mbox{density}(T1)} {\mbox{density}(T2)} = \frac{1 + C \cdot T1} {1 + C \cdot T2}$

where

C is the coefficient of cubic expansion.

Experimentally density can be found by measuring the dry weight ( $W_d$ ), the wet weight ( $W_w$) and submersed weight ( $W_s$), usually in water.

$\mbox{density} = \frac{\mbox{density of water} \cdot W_d} {W_w - W_s}$

## Other units

Density in terms of the SI base units is expressed in kilograms per cubic meter (kg/m3). Other units fully within the SI include grams per cubic centimeter (g/cm3) and megagrams per cubic metre (Mg/m3). 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) 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 999.861kg/m3; this occurs at a temperature of about 3.98 °C (277.13 K).

From 1901 to 1964, a litre was defined as exactly the volume of 1 kg of water at maximum density, and the maximum density of pure water was 1.000 000 kg/L (now 0.999 972 kg/L). However, while that definition of the litre was in effect, just as it is now, the maximum density of pure water was 0.999 972 kg/dm3. During that period students had to learn the esoteric fact that a cubic centimeter and a milliliter were slightly different volumes, with 1 mL = 1.000 028 cm³. (often stated as 1.000 027 cm³ in earlier literature).

Density will determine the 'order' in which each substance will appear in a bottle. For example, if substance A has a density of .64g/cm3, and Substance B has a density of .84g/cm3, Substance A will be above Substance B in a container due to the simple fact that its density is lower. One example of this is oil and water, where the oil will remain above.

## Measurement of Density

A common device for measuring fluid density is a pycnometer. A device for measuring absolute density of a solid is a gas pycnometer.

For a rectagular solid, the formula Mass / (Length x Width x Height) can be used. For an irregularly shaped solid, Displacement (fluid) can be used in place of L x W x H.

## Density of substances

Perhaps the highest density known is reached in neutron star matter (see neutronium). The singularity at the centre of a black hole, according to general relativity, does not have any volume, so its density is undefined.

The densest naturally occurring substance on Earth appears to be iridium, at about 22650 kg/m3. However, because this calculation requires a strong theoretical basis, and the difference between iridium and osmium is so small, definitively stating one or the other is more dense is not possible at this time.

A table of masses of various substances:

 Substance Density in kg/m3 Particles per cubic metre Iridium 22650 1.06 ×1029 Osmium 22610 7.16 ×1028 Platinum 21450 6.62 ×1028 Gold (0°C) 19300 5.90 ×1028 Tungsten 19250 6.31 ×1028 Uranium 19050 4.82 ×1028 Mercury 13580 4.08 ×1028 Palladium 12023 6.8 ×1028 Lead 11340 3.3 ×1028 Silver 10490 5.86 ×1028 Copper 8960 8.49 ×1028 Iron 7870 8.49 ×1028 Steel 7850 Tin 7310 3.71 ×1028 Titanium 4507 5.67 ×1028 Diamond 3500 1.75 ×1029 Basalt 3000 Granite 2700 Aluminium 2700 6.03 ×1028 Graphite 2200 1.10 ×1029 Magnesium 1740 4.31 ×1028 PVC 1300 Seawater (15°C) 1025 Water (25 °C) 998 3.34 ×1028 Ice (0°C) 917 3.07 ×1028 Polyethylene 910 Ethyl alcohol 790 1.03 ×1028 Gasoline 730 Liquid Hydrogen 68 4.06 ×1028 Aerogel 3 any gas 0.0446 times the average molecular mass (in g/mol), hence between 0.09 and ca. 13.1 (at 0°C and 1 atm) For example air (0°), (25°) 1.29, 1.17
 Density of air ρ vs. temperature °C T in °C ρ in kg/m3 - 10 1.341 - 5 1.316 0 1.293 + 5 1.269 + 10 1.247 + 15 1.225 + 20 1.204 + 25 1.184 + 30 1.164

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.