Density

For other senses of "density", see density (disambiguation).

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/m³)

\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:

\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 * T1} {1 + C * 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{W_d * \mbox{density of water}} {W_w - W_s}

Other units

Density in terms of the SI base units is expressed in kilograms per cubic meter (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 999.861kg·m^-3; 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^{-1^{(now 0.999 972 kg·L^{-1^{). 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·dm^{-3^{. During that period students had to learn the esoteric fact that a cubic centimetre and a millilitre were slightly different volumes, with 1 mL = 1.000 028 cm³. (often stated as 1.000 027 cm³ in earlier literature).}}}}}}

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.

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 most dense naturally occurring substance on Earth is iridium, at about 22650 kg·m^{-3^.}

A table of densities of various substances:

Substance	Density in kg·m^-3
Iridium	22650
Osmium	22610
Platinum	21450
Gold	19300
Tungsten	19250
Uranium	19050
Mercury	13580
Palladium	12023
Lead	11340
Silver	10490
Copper	8960
Iron	7870
Steel	7850
Tin	7310
Titanium	4507
Diamond	3500
Basalt	3000
Granite	2700
Aluminium	2700
Graphite	2200
Magnesium	1740
PVC	1300
Seawater	1025
Water	1000
Ice	917
Polyethylene	910
Ethyl alcohol	790
Gasoline	730
Liquid Hydrogen	68
Aerogel	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
- 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.

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Other units

Measurement of density

Density of substances

See also