Density

For other uses, see Density (disambiguation).

In physics the density (ρ) of a body is the ratio of its mass (m) to its volume (V), a measure of how tightly the matter within it is packed together. Its SI units are kilograms per cubic metre (kg/m³). It is also sometimes given in the cgs units of grams per cubic centimetre (g/cm³).

Density is defined by:

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

Various substances have different densities, and it is this quantity that determines how they interact when mixed together. For example, in SI units the density of lead is 11.35 x 10³, that of water is 1 x 10³, and that of cork is 0.24 x 10³. The lead has a greater density than water so it sinks; the cork has a smaller density so it floats.

In some cases the density is expressed as a specific gravity or relative density, in which case it is expressed in multiples of the density of some other standard material, usually water or air. For the stars, planets, satellites the effective density, includes the atmosphere, ionosphere and the troposphere.

History

In a well known problem, 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.

Archimedes knew that the irregular shaped wreath could be smashed into a cube or sphere, where the volume could be calculated more easily when compared with the weight; the king did not approve of this.

Baffled, Archimedes went to take a bath and observed from the rise of the water upon entering that he could calculate the volume of the crown through the displacement of the water. Allegedly, upon this discovery, Archimedes went running though the streets in the nude shouting, "Eureka! Eureka!" (Greek "I have 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. 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.

Measurement of density

For a homogeneous object, the formula mass/volume may be used. The mass is normally measured with an appropriate scale; the volume may be measured directly (from the geometry of the object) or by the displacement of a liquid. A very common instrument for the direct measurement of the density of a liquid is the hydrometer. A less common device for measuring fluid density is a pycnometer, a similar 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 it is defined, and this may cause confusion in measurement. A common example is sand: if gently filled into a container, the density will be small; when the same sand is compacted into the same container, it will occupy less volume and consequently carry a greater density. This is because "sand" 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.

Common units

SI units for density are:

• kilograms per cubic metre (kg/m³)
• grams per cubic centimetre (g/cm³)

Units outside the SI

• kilograms per litre (kg/L). Water generally has a density around 1 kg/L, making this a convenient unit.
• grams per millilitre (g/mL), which is equivalent to (g/cm³).

They also happen to be numerically equivalent to kg/L (1 kg/L = 1 g/cm³ = 1 g/mL).

In U.S. customary units or Imperial units, the units of density include:

• ounces per cubic inch (oz/in³)
• pounds per cubic inch (lb/in³)
• pounds per cubic foot (lb/ft³)
• pounds per cubic yard (lb/yd³)
• pounds per gallon (for U.S. or imperial gallons) (lb/gal)
• pounds per U.S. bushel (lb/bu)
• slugs per cubic foot.

Changes of density

In general density can be changed by changing either the pressure or the temperature. Increasing the pressure will always increase the density of a material. Increasing the temperature generally decreases the density, but there are notable exceptions to this generalisation. For example, the density of water increases between its melting point at 0 °C and 4 °C and similar behaviour is observed in silicon at low temperatures.

The effect of pressure and temperature on the densities of liquids and solids is small so that a typical compressibility for a liquid or solid is 10^–6 bar^–1 (1 bar=0.1 MPa) and a typical thermal expansivity is 10^–5 K^–1.

In contrast, the density of gases is strongly affected by pressure. Boyle's law says that the density of an ideal gas is given by

$\rho ={\frac {MP}{RT}}$

where $R$ is the universal gas constant, $P$ is the pressure, $M$ the molar mass, and $T$ the absolute temperature.

This means that a gas at 300 K and 1 bar will have its density doubled by increasing the pressure to 2 bar or by reducing the temperature to 150 K.

Iridium is the densest known substance at standard conditions for temperature and pressure.

Density of water

Temp (°C)	Density (g/cm3)
100	0.9584
80	0.9718
60	0.9832
40	0.9922
30	0.9956502
25	0.9970479
22	0.9977735
20	0.9982071
15	0.9991026
10	0.9997026
4	0.9999720
0	0.9998395
−10	0.998117
−20	0.993547
−30	0.983854
The density of water in grams per cubic centimeter at various temperatures in degrees Celsius The values below 0 °C refer to supercooled water. Water - Density and Specific Weight

See Water Density

Density of air

T in °C	ρ in kg/m³ (at 1 atm)
–10	1.342
–5	1.316
0	1.293
5	1.269
10	1.247
15	1.225
20	1.204
25	1.184
30	1.165

Density of solutions

The density of a solution is the sum of the mass (massic) concentrations of the components of that solution. Mass (massic) concentration of a given component ρ_i in a solution can be called partial density of that component.

Densities of various materials

Material	ρ in kg/m³	Notes
Interstellar medium	10-25 − 10-15	Assuming 90% H, 10% He; variable T
Earth's atmosphere	1.2	At sealevel
Aerogel	1 − 2
Styrofoam	30 − 120	From
Cork	220 − 260	From
Water	1000	At STP
Plastics	850 − 1400	For polypropylene and PETE/PVC
The Earth	5515.3	Mean density
Copper	8960	Near room temperature
Lead	11340	Near room temperature
The Inner Core	~13000	As listed in Earth
Uranium	19100	Near room temperature
The core of the Sun	~150000
Atomic nuclei	~3 × 1017	As listed in neutron star
Neutron star	8.4 × 1016 − 1 × 1018
Black hole	2 × 1030	Mean density inside the Schwarzschild radius of an earth-mass black hole (theoretical)

Books

• Fundamentals of Aerodynamics Second Edition, McGraw-Hill, John D. Anderson, Jr.
• Fundamentals of Fluid Mechanics Wiley, B.R. Munson, D.F. Young & T.H. Okishi
• Introduction to Fluid Mechanics Fourth Edition, Wiley, SI Version, R.W. Fox & A.T. McDonald
• Thermodynamics: An Engineering Approach Second Edition, McGraw-Hill, International Edition, Y.A. Cengel & M.A. Boles

See also

• List of elements by density
• Charge density
• Buoyancy
• Bulk density
• Dord
• Energy density
• Lighter than air
• Number density
• Population density
• Specific weight
• Standard temperature and pressure
• Orders of magnitude (density)
• Brix, Balling and Plato scale

External links

• Glass Density Calculation - Calculation of the density of glass at room temperature and of glass melts at 1000 - 1400°C
• List of Elements of the Periodic Table - Sorted by Density